Showing papers on "Statistical hypothesis testing published in 1988"

A Test of Missing Completely at Random for Multivariate Data with Missing Values

Abstract: A common concern when faced with multivariate data with missing values is whether the missing data are missing completely at random (MCAR); that is, whether missingness depends on the variables in the data set. One way of assessing this is to compare the means of recorded values of each variable between groups defined by whether other variables in the data set are missing or not. Although informative, this procedure yields potentially many correlated statistics for testing MCAR, resulting in multiple-comparison problems. This article proposes a single global test statistic for MCAR that uses all of the available data. The asymptotic null distribution is given, and the small-sample null distribution is derived for multivariate normal data with a monotone pattern of missing data. The test reduces to a standard t test when the data are bivariate with missing data confined to a single variable. A limited simulation study of empirical sizes for the test applied to normal and nonnormal data suggests th...

Parameter Estimation and Hypothesis Testing in Linear Models

Abstract: This textbook on theoretical geodesy deals with the estimation of unknown parameters, the testing of hypothesis and the estimation of intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model, as well as the mixed model for estimation random parameters. To make the book self-contained most of the necessary theorems of vector and matrix-algebra and the probability distributions for the test statistics are derived. Students of geodesy, as well as of mathematics and engineering, will find the geodetical application of mathematical and statistical models extremely useful.

Statistical decision theory and related topics IV

Abstract: 1 - Selection, Ranking, and Multiple Comparisons.- Sequential Selection Procedures for Multi-Factor Experiments Involving Koopman-Darmois Populations with Additivity.- Selection Problem for a Modified Multinomial (Voting) Model.- A Decision Theory Formulation for Population Selection Followed by Estimating the Mean of the Selected Population.- On the Problem of Finding the Largest Normal Mean under Heteroscedasticity.- On Least Favorable Configurations for Some Poisson Selection Rules and Some Conditional Tests.- Selection of the Best Normal Populations better Than a Control: Dependence Case.- Inference about the Change-Point in a Sequence of Random Variables: A Selection Approach.- On Confidence Sets in Multiple Comparisons.- 2 - Asymptoticand Sequential Analysis.- The VPRT: Optimal Sequential and Nonsequential Testing.- An Edgeworth Expansion for the Distribution of the F-Ratio under a Randomization Model for the Randomized Block Design.- On Bayes Sequential Tests.- Stochastic Search in a Square and on a Torus.- Distinguished Statistics, Loss of Information and a Theorem of Robert B. Davies.- Prophet Inequalities for Threshold Rules for Independent Bounded Random Variables.- Weak Convergence of the Aalen Estimator for a Censored Renewal Process.- Sequential Stein-Rule Maximum Likelihood Estimation: General Asymptotics.- Fixed Proportional Accuracy in Three Stages.- 3 - Estimationand Testing.- Dominating Inadmissible Tests in Exponential Family Models.- On Estimating Change Point in a Failure Rate.- A Nonparametric, Intersection-Union Test for Stochastic Order.- On Estimating the Number of Unseen Species and System Reliability.- The Effects of Variance Function Estimation on Prediction and Calibration: An Example.- On Estimating a Parameter and Its Score Function, II.- A Simple Test for the Equality of Correlation Matrices.- Conditions of Rao's Covariance Method Type for Set-Valued Estimators.- Conservation of Properties of Optimality of Some Statistical Tests and Point Estimators under Extensions of Distributions.- Some Recent Results in Signal Detection.- 4 - Design, and Comparisonof Experimentsand Distributions.- Comparison of Experiments and Information in Censored Data.- A Note on Approximate D-Optimal Designs for G x 2m.- Some Statistical Design Aspects of Estimating Automotive Emission Deterioration Factors.- Peakedness in Multivariate Distributions.- Spatial Designs.

The Meaning and Strategic Use of Factor Analysis

Abstract: The general surveys of multivariate analysis methods in other chapters in this and the first edition give some idea of the relation of factor analysis to other methods in a mathematical sense. However, factor analysis differs also in a wide, experimental, strategic sense, from, for example, both multiple-correlation linear equations, and discriminant functions, in not arbitrarily choosing a criterion variable or criterion group, but in arriving at a reduced number of abstract variables and a weighting of observed variables according to structural indications in the data itself. It is thus a means of creating concepts, not merely of employing them or checking their fit to new data, though the new methods of Maxwell, Lawley, and Joreskog also fit it for hypothesis testing.

A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models

Abstract: 2. The data generation process and optimization estimators 3. Consistency of optimization estimators 4. More on near epoch dependence 5. Asymptotic mormality 6. Estimating asymptotic cavariance matrices 7. Hypothesis testing

Interval estimates for correlation coefficients corrected for within-person variation: implications for study design and hypothesis testing

Abstract: It is well known that random measurement error can attenuate the correlation coefficient between two variables. One possible solution to this problem is to estimate the correlation coefficient based on an average of a large number of replicates for each individual. As an alternative, several authors have proposed an unattenuated (or corrected) correlation coefficient which is an estimate of the true correlation between two variables after removing the effect of random measurement error. In this paper, the authors obtain an estimate of the standard error for the corrected correlation coefficient and an associated 100% x (1-alpha) confidence interval. The standard error takes into account the variability of the observed correlation coefficient as well as the estimated intraclass correlation coefficient between replicates for one or both variables. The standard error is useful in hypothesis testing for comparisons of correlation coefficients based on data with different degrees of random error. In addition, the standard error can be used to evaluate the relative efficiency of different study designs. Specifically, an investigator often has the option of obtaining either a few replicates on a large number of individuals, or many replicates on a small number of individuals. If one establishes the criterion of minimizing the standard error of the corrected coefficient while fixing the total number of measurements obtained, in almost all instances it is optimal to obtain no more than five replicates per individual. If the intraclass correlation is greater than or equal to 0.5, it is usually optimal to obtain no more than two replicates per individual.

Towards a unified theory of inequality constrained testing in multivariate analysis

Abstract: Summary In this paper a distributional theory of test statistics in various problems of multivariate analysis involving inequality constraints is examined. A unified point of view based on geometrical properties of convex cones is presented. Chi-bar-squared and E-bar-squared test statistics are introduced. Their applications to hypothesis testing problems are discussed.

On bootstrap resampling and iteration

Abstract: SUMMARY We propose a single unifying approach to bootstrap resampling, applicable to a very wide range of statistical problems. It enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem, such as coverage error or length for confidence intervals, or bias for point estimation. Our approach leads easily and directly to a very general form of bootstrap iteration, unifying and generalizing present disparate accounts of this subject. It also provides simple solutions to relatively complex problems, such as a suggestion by Lehmann (1986) for 'conditionally' short confidence intervals. We set out a single unifying principle guiding the operation of bootstrap resampling, applicable to a very wide range of statistical problems including bias reduction, shrinkage, hypothesis testing and confidence interval construction. Our principle differs from other approaches in that it focuses attention directly on a measure of quality or accuracy, expressed in the form of an equation whose solution is sought. A very general form of bootstrap iteration is an immediate consequence of iterating the empirical solution to this equation so as to improve accuracy. When employed for bias reduction, iteration of the resampling principle yields a competitor to the generalized jackknife, enabling bias to be reduced to arbitrarily low levels. When applied to confidence intervals it produces the techniques of Hall (1986) and Beran (1987). The resampling principle leads easily to solutions of new, complex problems, such as empirical versions of confidence intervals proposed by Lehmann (1986). Lehmann argued that an 'ideal' confidence interval is one which is short when it covers the true parameter value but not necessarily otherwise. The resampling principle suggests a simple empirical means of constructing such intervals. Section 2 describes the general principle, and ? 3 shows how it leads naturally to bootstrap iteration. There we show that in many problems of practical interest, such as bias reduction and coverage-error reduction in two-sided confidence intervals, each iteration reduces error by the factor n-1, where n is sample size. In the case of confidence intervals our result sharpens one of Beran (1987), who showed that coverage error is reduced by the factor n-2 in two-sided intervals. The main exception to our n-1 rule is coverage error of one-sided intervals, where error is reduced by the factor n-A at each iteration. Our approach to bootstrap iteration serves to unify not just the philosophy of iteration for different statistical problems, but also different techniques of iteration for the same

The Number of Iterations in Monte Carlo Studies of Robustness.

Abstract: A recent survey of simulation studies concluded that an overwhelming majority of papers do not report a rationale for the number of iterations carried out in Monte Carlo robustness (MCR) experiments. The survey suggested that researchers might benefit from adopting a hypothesis testing strategy in the planning and reporting of simulation studies. This paper presents a table of the number of iterations necessary to detect departures from a series of nominal Type I error rates based upon hypothesis testing logic. The table is indexed by effect size, by significance level, and by power level for the two-tailed test that a proportion equals some constant. An alternative approach based upon the construction of a confidence interval is discussed and dismissed. The MCR research design demands an adequate definition of robustness and a sufficient sample size to detect departures from that definition. (Author/TJH) monoommommommoommommommommommmommommommommommom Reproductions supplied by EDRS are the best that can be made from the original document. 30000000000800000000000000000000000000000000000000000000000000000000000(

Interpreting the medical literature

Abstract: Interpreting the Medical Literature 4th edition Preface 1. Tasting an Article Reasons to Read The Bones of an Article Approaching an Article 2. Study Design: General Considerations Descriptive Studies Explanatory Studies More Confusing Terminology Summary 3. Study Design: The Case-Control Approach Advantages of the Case-Control Design Problems of Case-Control Designs Summary 4. Study Design: The Cross-Sectional and Follow-up Approaches Cross-Sectional Designs Follow-up Studies Summary 5. Study Design: The Experimental Approach Enrollment: Who Gets In Allocation: Sorting Subjects & Controls Follow-Up Analysis Summary 6. Study Design: Variations Real-World Considerations Practical Constraints Ethical Concerns Summary 7. Making Measurements Reliability & Validity Variability of the Unsystematic Sort Systematic Error Reducing Measurement Error Summary 8. Analysis: Statistical Significance Inference Sampling Variability The Null Hypothesis & Statistical Significance Some Problems of Statistical Significance Beta Errors & Statistical Power Confidence Intervals Summary 9. Analysis: Some Statistical Tests Tests for Categorical Data Tests for Continuous Data Correlation Regression Summary 10. Interpretation: Sensitivity, Specificity, and Predictive Value Prevalence Making Choices Likelihood Ratios ROC Curves Modeling Spectrum Standards Summary 11. Interpretation: Risk Expressing Statements of Risk Risk Differences Balancing Risks Costs & Benefits Summary 12. Interpretation: Causes Confounding Dealing with Confounding Making Associations into Causes Summary 13. Case Series, Editorials, and Reviews Case Series Editorials & Letters to the Editor Reviews Summary 14. A Final Word Clarity Apologies, Tentative Conclusions, Self-Criticism, & the Like Critical Assistance The Final Word Summary Index

Self-contained GPS integrity check using maximum solution separation

Abstract: Previous approaches to the self-contained GPS integrity problem have been in a hypothesis testing setting where the two hypotheses are: (1) a single satellite has failed, or (2) there is no failure. In this setting, selective availability is the major source of noise that impedes the detection scheme’s ability to detect failures and, at the same time, have a low false alarm rate. This paper poses the problem in a different setting where the basic questions posed are: (1) is the radial position error less than some preset bound? or (2) is it greater than that bound? This is a more fundamental approach, because the pilot does not really care where the error comes from; rather, he is only concerned that the radial position error does not exceed a certain specified level. Results of simulations using a 24-satellite constellation and maximum separation of redundant solutions as the test statistic are presented. These results indicate that this scheme could provide radial error protection of about 250 m with acceptably low alarm and miss rates.

Bispectral-Based Tests for the Detection of Gaussianity and Linearity in Time Series

Abstract: Statistical techniques have been developed that use estimated bispectrum values to test whether a sample of a time series is consistent with the hypothesis that the observations are generated by a linear process. The magnitude of the test statistics indicates the amount of divergence between the observations and the linear model hypothesis. It is important to investigate such a divergence, since the usual linear model coefficients can be shown to be biased in the face of nonlinear time series structure. The tests presented here can thus be considered diagnostic as well as confirmatory. These tests are applied to a variety of real series previously modeled with linear models. The results indicate nonlinear models may yield better results, because many of the series analyzed appear to have considerable nonlinear lagged interactions.

Statistical theory of edge detection

Abstract: The conventional way of edge detection is to first filter the image and then use simple techniques to detect edges. However, filtering the noise will also blur the edges since edges correspond to the high frequencies. Our suggestion is that both filtering and edge detection should take place at the same time. The way of doing this is by statistical theory of hypothesis testing. A simple form of decision rule is derived and the generalization of this result to more complicated situations is also discussed in detail. The decision rule can make a decision whether in a given small neighborhood there is an edge, or a line, or a point, or a corner edge, or just a smooth region. During the computation of the decision rule, the by-products are the mean and variance of the neighborhood and these can be used for split and merge analysis. Calculation of the mean acts as filtering of the neighborhood pixels. In fact, representation of the neighborhood by its mean and variance can be generalized by Haralick's sloped-facet model, which has a more complete characterization of the local changes of intensities.

Optimal appropriateness measurement

Abstract: The test-taking behavior of some examinees may be so idiosyncratic that their test scores may not be comparable to the scores of more typical examinees Appropriateness measurement attempts to use answer patterns to recognize atypical examinees In this report appropriateness measurement procedures are viewed as statistical tests for choosing between a null hypothesis of normal test-taking behavior and an alternative hypothesis of atypical test-taking behavior Most powerful tests for inappropriateness are described together with methods for computing their power A recursion greatly simplifying the calculation of optimal test statistics is described and illustrated

Applied Statistics: Analysis of Variance and Regression.

Abstract: Preface.1. Data Screening.1.1 Variables and Their Classification.1.2 Describing the Data.1.2.1 Errors in the Data.1.2.2 Descriptive Statistics.1.2.3 Graphical Summarization.1.3 Departures from Assumptions.1.3.1 The Normal Distribution.1.3.2 The Normality Assumption.1.3.3 Transformations.1.3.4 Independence.1.4 Summary.Problems.References.2. One-Way Analysis of Variance Design.2.1 One-Way Analysis of Variance with Fixed Effects.2.1.1 Example.2.1.2 The One-Way Analysis of Variance Model with Fixed Effects.2.1.3 Null Hypothesis: Test for Equality of Population Means.2.1.4 Estimation of Model Terms.2.1.5 Breakdown of the Basic Sum of Squares.2.1.6 Analysis of Variance Table.2.1.7 The F Test.2.1.8 Analysis of Variance with Unequal Sample Sizes.2.2 One-Way Analysis of Variance with Random Effects.2.2.1 Data Example.2..2.2 The One-Way Analysis of Variance Model with Random Effects.2.2.3 Null Hypothesis: Test for Zero Variance of Population Means.2.2.4 Estimation of Model Terms.2.2.5 The F Test.2.3 Designing an Observational Study or Experiment.2.3.1 Randomization for Experimental Studies.2.3.2 Sample Size and Power.2.4 Checking if the Data Fit the One-Way ANOVA Model.2.4.1 Normality.2.4.2 Equality of Population Variances.2.4.3 Independence.2.4.4 Robustness.2.4.5 Missing Data.2.5 What to Do if the Data Do Not Fit the Model.2.5.1 Making Transformations.2.5.2 Using Nonparametric Methods.2.5.3 Using Alternative ANOVAs.2.6 Presentation and Interpretation of Results.2.7 Summary.Problems.References.3. Estimation and Simultaneous Inference.3.1 Estimation for Single Population Means.3.1.1 Parameter Estimation.3.1.2 Confidence Intervals.3.2 Estimation for Linear Combinations of Population Means.3.2.1 Differences of Two Population Means.3.2.2 General Contrasts for Two or More Means.3.2.3 General Contrasts for Trends.3.3 Simultaneous Statistical Inference.3.1.1 Straightforward Approach to Inference.3.3.2 Motivation for Multiple Comparison Procedures and Terminology.3.3.3 The Bonferroni Multiple Comparison Method.3.3.4 The Tukey Multiple Comparison Method.3.3.5 The Scheffe Multiple Comparison Method.3.4 Inference for Variance Components.3.5 Presentation and Interpretation of Results.3.6 Summary.Problems.References.4. Hierarchical or Nested Design.4.1 Example.4.2 The Model.4.3 Analysis of Variance Table and F Tests.4.3.1 Analysis of Variance Table.4.3.2 F Tests.4.3.3 Pooling.4.4 Estimation of Parameters.4.4.1 Comparison with the One-Way ANOVA Model of Chapter 2.4.5 Inferences with Unequal Sample Sizes.4.5.1 Hypothesis Testing.4.5.2 Estimation.4.6 Checking If the Data Fit the Model.4.7 What to Do If the Data Don't Fit the Model.4.8 Designing a Study.4.8.1 Relative Efficiency.4.9 Summary.Problems.References.5. Two Crossed Factors: Fixed Effects and Equal Sample Sizes.5.1 Example.5.2 The Model.5.3 Interpretation of Models and Interaction.5.4 Analysis of Variance and F Tests.5.5 Estimates of Parameters and Confidence Intervals.5.6 Designing a Study.5.7 Presentation and Interpretation of Results.5.8 Summary.Problems.References.6 Randomized Complete Block Design.6.1 Example.6.2 The Randomized Complete Block Design.6.3 The Model.6.4 Analysis of Variance Table and F Tests.6.5 Estimation of Parameters and Confidence Intervals.6.6 Checking If the Data Fit the Model.6.7 What to Do if the Data Don't Fit the Model.6.7.1 Friedman's Rank Sum Test.6.7.2 Missing Data.6.8 Designing a Randomized Complete Block Study.6.8.1 Experimental Studies.6.8.2 Observational Studies.6.9 Model Extensions.6.10 Summary.Problems.References.7. Two Crossed Factors: Fixed Effects and Unequal Sample Sizes.7.1 Example.7.2 The Model.7.3 Analysis of Variance and F Tests.7.4 Estimation of Parameters and Confidence Intervals.7.4.1 Means and Adjusted Means.7.4.2 Standard Errors and Confidence Intervals.7.5 Checking If the Data Fit the Two-Way Model.7.6 What To Do If the Data Don't Fit the Model.7.7 Summary.Problems.References.8. Crossed Factors: Mixed Models.8.1 Example.8.2 The Mixed Model.8.3 Estimation of Fixed Effects.8.4 Analysis of Variance.8.5 Estimation of Variance Components.8.6 Hypothesis Testing.8.7 Confidence Intervals for Means and Variance Components.8.7.1 Confidence Intervals for Population Means.8.7.2 Confidence Intervals for Variance Components.8.8 Comments on Available Software.8.9 Extensions of the Mixed Model.8.9.1 Unequal Sample Sizes.8.9.2 Fixed, Random, or Mixed Effects.8.9.3 Crossed versus Nested Factors.8.9.4 Dependence of Random Effects.8.10 Summary.Problems.References.9. Repeated Measures Designs.9.1 Repeated Measures for a Single Population.9.1.1 Example.9.1.2 The Model.9.1.3 Hypothesis Testing: No Time Effect.9.1.4 Simultaneous Inference.9.1.5 Orthogonal Contrasts.9.1.6 F Tests for Trends over Time.9.2 Repeated Measures with Several Populations.9.2.1 Example.9.2.2 Model.9.2.3 Analysis of Variance Table and F Tests.9.3 Checking if the Data Fit the Repeated Measures Model.9.4 What to Do if the Data Don't Fit the Model.9.5 General Comments on Repeated Measures Analyses.9.6 Summary.Problems.References.10. Linear Regression: Fixed X Model.10.1 Example.10.2 Fitting a Straight Line.10.3 The Fixed X Model.10.4 Estimation of Model Parameters and Standard Errors.10.4.1 Point Estimates.10.4.2 Estimates of Standard Errors.10.5 Inferences for Model Parameters: Confidence Intervals.10.6 Inference for Model Parameters: Hypothesis Testing.10.6.1 t Tests for Intercept and Slope.10.6.2 Division of the Basic Sum of Squares.10.6.3 Analysis of Variance Table and F Test.10.7 Checking if the Data Fit the Regression Model.10.7.1 Outliers.10.7.2 Checking for Linearity.10.7.3 Checking for Equality of Variances.10.7.4 Checking for Normality.10.7.5 Summary of Screening Procedures.10.8 What to Do if the Data Don't Fit the Model.10.9 Practical Issues in Designing a Regression Study.10.9.1 Is Fixed X Regression an Appropriate Technique?10.9.2 What Values of X Should Be Selected?10.9.3 Sample Size Calculations.10.10 Comparison with One-Way ANOVA.10.11 Summary.Problems.References.11. Linear Regression: Random X Model and Correlation.11.1 Example.11.1.1 Sampling and Summary Statistics.11.2 Summarizing the Relationship Between X and Y.11.3 Inferences for the Regression of Y and X.11.3.1 Comparison of Fixed X and Random X Sampling.11.4 The Bivariate Normal Model.11.4.1 The Bivariate Normal Distribution.11.4.2 The Correlation Coefficient.11.4.3 The Correlation Coefficient: Confidence Intervals and Tests.11.5 Checking if the Data Fit the Random X Regression Model.11.5.1 Checking for High-Leverage, Outlying, and Influential Observations.11.6 What to Do if the Data Don't Fit the Random X Model.11.6.1 Nonparametric Alternatives to Simple Linear Regression.11.6.2 Nonparametric Alternatives to the Pearson Correlation.11.7 Summary.Problem.References.12. Multiple Regression.12.1 Example.12.2 The Sample Regression Plane.12.3 The Multiple Regression Model.12.4 Parameters Standard Errors, and Confidence Intervals.12.4.1 Prediction of E(Y\X1,...,Xk).12.4.2 Standardized Regression Coefficients.12.5 Hypothesis Testing.12.5.1 Test That All Partial Regression Coefficients Are 0.12.5.2 Tests that One Partial Regression Coefficient is 0.12.6 Checking If the Data Fit the Multiple Regression Model.12.6.1 Checking for Outlying, High Leverage and Influential Points.12.6.2 Checking for Linearity.12.6.3 Checking for Equality of Variances.12.6.4 Checking for Normality of Errors.12.6.5 Other Potential Problems.12.7 What to Do If the Data Don't Fit the Model.12.8 Summary.Problems.References.13. Multiple and Partial Correlation.13.1 Example.13.2 The Sample Multiple Correlation Coefficient.13.3 The Sample Partial Correlation Coefficient.13.4 The Joint Distribution Model.13.4.1 The Population Multiple Correlation Coefficient.13.4.2 The Population Partial Correlation Coefficient.13.5 Inferences for the Multiple Correlation Coefficient.13.6 Inferences for Partial Correlation Coefficients.13.6.1 Confidence Intervals for Partial Correlation Coefficients.13.6.2 Hypothesis Tests for Partial Correlation Coefficients.13.7 Checking If the Data Fit the Joint Normal Model.13.8 What to Do If the Data Don't Fit the Model.13.9 Summary.Problems.References.14. Miscellaneous Topics in Regression.14.1 Models with Dummy Variables.14.2 Models with Interaction Terms.14.3 Models with Polynomial Terms.14.3.1 Polynomial Model.14.4 Variable Selection.14.4.1 Criteria for Evaluating and Comparing Models.14.4.2 Methods for Variable Selection.14.4.3 General Comments on Variable Selection.14.5 Summary.Problems.References.15. Analysis of Covariance.15.1 Example.15.2 The ANCOVA Model.15.3 Estimation of Model Parameters.15.4 Hypothesis Tests.15.5 Adjusted Means.15.5.1 Estimation of Adjusted Means and Standard Errors.15.5.2 Confidence Intervals for Adjusted Means.15.6 Checking If the Data Fit the ANCOVA Model.15.7 What to Do if the Data Don't Fit the Model.15.8 ANCOVA in Observational Studies.15.9 What Makes a Good Covariate.15.10 Measurement Error.15.11 ANCOVA versus Other Methods of Adjustment.15.12 Comments on Statistical Software.15.13 Summary.Problems.References.16. Summaries, Extensions, and Communication.16.1 Summaries and Extensions of Models.16.2 Communication of Statistics in the Context of Research Project.References.Appendix A.A.1 Expected Values and Parameters.A.2 Linear Combinations of Variables and Their Parameters.A.3 Balanced One-Way ANOVA, Expected Mean Squares.A.3.1 To Show EMS(MSa) = sigma2 + n SIGMAai= 1 alpha2i /(a - 1).A.3.2 To Show EMS(MSr) = sigma2.A.4 Balanced One-Way ANOVA, Random Effects.A.5 Balanced Nested Model.A.6 Mixed Model.A.6.1 Variances and Covariances of Yijk.A.6.2 Variance of Yi.A.6.3 Variance of Yi. - Yi'..A.7 Simple Linear Regression-Derivation of Least Squares Estimators.A.8 Derivation of Variance Estimates from Simple Linear Regression.Appendix B.Index.

Inference based on conditional speclfication

Abstract: The first bibliography in the area of inference based on conditional specification was published in 1977, A second bibliography is compiled, and a combined subject index is given.

A unified framework for connectionist systems.

Abstract: Pattern classification using connectionist (i.e., neural network) models is viewed within a statistical framework. A connectionist network's subjective beliefs about its statistical environment are derived. This belief structure is the network's "subjective" probability distribution. Stimulus classification is interpreted as computing the "most probable" response for a given stimulus with respect to the subjective probability distribution. Given the subjective probability distribution, learning algorithms can be analyzed and designed using maximum likelihood estimation techniques, and statistical tests can be developed to evaluate and compare network architectures. The framework is applicable to many connectionist networks including those of Hopfield (1982, 1984), Cohen and Grossberg (1983), Anderson et al. (1977), and Rumelhart et al. (1986b).

Validity Generalization and Situational Specificity: A Second Look at the 75% Rule and Fisher's z Transformation

Abstract: In this article we analyzed the James, Demaree, and Mulaik (1986) critique of validity generalization. We demonstrated that the James et al. article (a) is not relevant to the real-world use of validity generalization in organizations, (b) has overlooked the bulk of the evidence against the situational specificity hypothesis and, therefore, the substantive conclusion that the situational specificity hypothesis is "alive and well" cannot be supported, and (c) has confused the processes of hypothesis testing and parameter estimation in validity generalization and has made incorrect statements about the assumptions underlying both. In addition, (d) James et al.'s critique of the 75% rule is a statistical power argument and, as such, does not add to earlier statistical power studies; (e) the procedures for use of confidence intervals that they advocate are erroneous; (f) there is no double correction of artifacts in validity generalization, as they contend; (g) the bias in the correlation (r) and the sampling error formula for r that they discuss is well-known, trivial in magnitude, and has no empirical significance; and (h) the use of the Fisher's z transformation of r in validity generalization studies and other meta-analyses (which they advocate) creates an unnecessary inflationary bias in estimates of true validities and provides no benefits. In light of these facts, we conclude that the James et al. substantive conclusions and methodological recommendations are seriously flawed. This article is an analysis of the James, Demaree, and Muliak (1986) critique of validity generalization methods and conclusions, a long and detailed article. In the interests of brevity, we will focus only on those portions of James et al. that we judge to be most in need of critical evaluation. Their remaining arguments are left to the reader to evaluate in light of the analysis presented here.

A versatile method for simultaneous analysis of families of curves.

Abstract: We have developed a versatile new approach to the simultaneous analysis of families of curves, which combines the simplicity of empirical methods with several of the advantages of mathematical modeling, including objective comparison of curves and statistical hypothesis testing. The method uses weighted smoothing cubic splines; the degree of smoothing is adjusted automatically to satisfy constraints on curve chape (monotonicity, number of inflection points). By simultaneous analysis of a family of curves, one can extract the shape common to all the curves. Up to four linear scaling parameters are used to match the shape to each curve, and to provide optimal superimposition of the several curves. By applying constraints to these scaling factors, one can test a variety of hypotheses concerning comparisons of curves (e.g., identity, parallelism, or similarity of shape of two or more curves), and thus evaluate the effects of experimental manipulation. By optimal pooling of data one can avoid the need for arbitrary selection of a typical experiment, and can detect subtle but reproducible effects that might otherwise be overlooked. This approach can facilitate the development of an appropriate model. The method has been implemented in a Turbo-Pascal program for IBM-PC compatible microcomputers, and in FORTRAN-77 for the DEC-10 mainframe, and has been utilized successfully in a wide variety of applications.

Implementation of the hypothesis testing identification in power system state estimation

Abstract: The authors consider the online implementation of a general, reliable and efficient bad-data analysis procedure for power system state estimation. It is based on hypothesis testing identification, which was previously proposed and subsequently improved by the authors. The procedure involves a sequential measurement error estimator along with adequate sparsity programming techniques. Both make the procedure easy to implement on any state estimator. A criterion for multiple noninteracting bad-data identification is also proposed, which is applicable to any bad-data analysis method. Simulations are reported on systems of up to 700 buses. A thorough comparison with classical methods is also included. >

Hypothesis Testing for Cointegration Vectors: with Application to the Demand for Money in Denmark and Finland

Abstract: The purpose of this paper is to give a systematic account of the maximum likelihood inference concerning cointegration vectors in non-stationary vector value autoregressive time series with Gaussian errors. The hypothesis of r cointegration vectors is given a simple parametric formulation in terms of cointegration vectors and their weights. We then estimate and test linear hypotheses about these. We find that the asymptotic inference for the linear hypotheses can be performed by applying the usual ² test. We also give some very simple Wald test and their asymptotic properties. The methids are illustrated by data from the Danish and the Finnish economy on the demand for money.

Estimating the power of the two-sample Wilcoxon test for location shift.

Abstract: SUMMARY Traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution. The distribution shape, however, may be unknown. This paper describes a bootstrap method for using observed data (or pilot data) to approximate the power. No assumptions need be made about the shape of the underlying continuous probability distribution. Simulation evidence shows that, when applied to the Wilcoxon two-sample test for location shift, the suggested method is reliable. The evidence also shows that it is more accurate than a benchmark traditional approach. The bootstrap method is applied to a real-data example. The analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift.

Small Sample Asymptotics

Abstract: An approach for modifying the results of asymptotic theory to improve the performance of statistical procedures in small to moderate sample sizes is described in the context of hypothesis testing. The method is illustrated by a series of examples.

Homogeneity Tests against Central-Mixture Alternatives

Abstract: A test of homogeneity is derived for a general sampling model. The alternative hypothesis is a mixture over a parameter of the sampling model, centered at the null hypothesis. The test statistic is derived through a score test. Its functional form is independent of the particular mixing distribution. Suppose Yi (i = 1, …, n) are independent random variables with respective probability density (or mass) functions fi (yi ‖ λi). Under the null hypothesis, suppose all λ i homogeneous and equal to the common value λ0. Under the alternative hypothesis, suppose the λ i behave as random samples taken from a distribution with mean λ0 and finite third moment. The score statistic for testing these hypotheses rejects the null for large values of , where is the maximum likelihood estimate of λ0 under the null hypothesis and . When the sample size n is large, S is normally distributed under both the null hypothesis and a sequence of alternative hypotheses in which the variance of the mixing distribution tends ...