scispace - formally typeset
Search or ask a question

Showing papers on "Nonparametric statistics published in 1985"


Book
01 Jan 1985
TL;DR: In this article, the authors present a model for estimating the effect size from a series of experiments using a fixed effect model and a general linear model, and combine these two models to estimate the effect magnitude.
Abstract: Preface. Introduction. Data Sets. Tests of Statistical Significance of Combined Results. Vote-Counting Methods. Estimation of a Single Effect Size: Parametric and Nonparametric Methods. Parametric Estimation of Effect Size from a Series of Experiments. Fitting Parametric Fixed Effect Models to Effect Sizes: Categorical Methods. Fitting Parametric Fixed Effect Models to Effect Sizes: General Linear Models. Random Effects Models for Effect Sizes. Multivariate Models for Effect Sizes. Combining Estimates of Correlation Coefficients. Diagnostic Procedures for Research Synthesis Models. Clustering Estimates of Effect Magnitude. Estimation of Effect Size When Not All Study Outcomes Are Observed. Meta-Analysis in the Physical and Biological Sciences. Appendix. References. Index.

9,769 citations


Book
30 Jan 1985
TL;DR: In this paper, the authors present a set of tools for the analysis of statistical data, including the use of SPSS and hypothesis testing, to determine whether a given variable is anomalous or not.
Abstract: 1. Introduction. The importance of Context. Basic Terminology. Selection among Statistical Procedures. Using Computers. Summary. Exercises. 2. Basic Concepts. Scales of Measurement. Variables. Random Sampling. Notation. Summary. Exercises. 3. Displaying Data. Plotting Data. Stem-and-Leaf Displays. Histograms. Reading Graphs. Alternative Methods of Plotting Data. Describing Distributions. Using Computer Programs to Display Data. Summary. Exercises. 4. Measures of Central Tendency. The Mode. The Median. The Mean. Relative Advantages of the Mode, the Median, and the Mean. Obtaining Measures of Central Tendency Using SPSS. A Simple Demonstration-Seeing Statistics. Summary. Exercises. 5. Measures of Variability. Range. Interquartile Range and Other Range Statistics. The Average Deviation. The Variance. The Standard Deviation. Computational Formulae for the Variance and the Standard eviation. The Mean and the Variance as Estimators. Boxplots: Graphical Representations of Dispersion and Extreme Scores. A Return to Trimming. Obtaining Measures of Dispersion Using SPSS. A Final Worked Example. Seeing Statistics. Summary. Exercises. 6. The Normal Distribution. The Normal Distribution. The Standard Normal Distribution. Setting Probable Limits on an Observations. Measures Related to z. Seeing Statistics. Summary. Exercises. 7. Basic Concepts of Probability. Probability. Basic Terminology and Rules. The Application of Probability to Controversial Issues. Writing Up the Results. Discrete versus Continuous Variables. Probability Distributions for Discrete Variables. Probability Distributions for Continuous Variables. Summary. Exercises. 8. Sampling Distributions and Hypothesis Testing. Two Simple Examples Involving Course Evaluations and Rude Motorists. Sampling Distributions. Hypothesis Testing. The Null Hypothesis. Test Statistics and Their Sampling Distributions. Using the Normal Distribution to Test Hypotheses. Type I and Type II Errors. One- and Two-Tailed Tests. Seeing Statistics. A Final Worked Example. Back to Course Evaluations and Rude Motorists. Summary. Exercises. 9. Correlation. Scatter Diagrams. The Relationship Between Pace of Life and Heart Disease. The Covariance. The Pearson Product-Moment Correlation Coefficient (r). Correlations with Ranked Data. Factors that Affect the Correlation. Beware Extreme Observations. Correlation and Causation. If Something Looks Too Good to Be True, Perhaps It Is. Testing the Significance of a Correlation Coefficient. Intercorrelation Matrices. Other Correlation Coefficients. Using SPSS to Obtain Correlation Coefficients. Seeing Statistics. A Final Worked Example. Summary . Exercises. 10. Regression. The Relationship Between Stress and Health. The Basic Data. The Regression Line. The Accuracy of Prediction. The Influence of Extreme Values. Hypothesis Testing in Regression. Computer Solutions using SPSS. Seeing Statistics. Summary. Exercises. 11. Multiple Regression. Overview. A Different Data Set. Residuals. The Visual Representation of Multiple Regression. Hypothesis Testing. Refining the Regression Equation. A Second Example: Height and Weight. A Third Example: Psychological Symptoms in Cancer Patients. Summary. Exercises. 12. Hypothesis Testing Applied to Means: One Sample. Sampling Distribution of the Mean. Testing Hypotheses about Means When a is Known. Testing a Sample Mean When a is Unknown (The One-Sample t). Factors that Affect the Magnitude of t and the Decision about H0. A Second Example: The Moon Illusion. How Large is Our Effect?. Confidence Limits on the Mean. Using SPSS to Run One-Sample t tests. A Final Worked Example. Seeing Statistics. Summary. Exercises. 13. Hypothesis Tests Applied to Means: Two Related Samples. Related Samples. Student's t Applied to Difference Scores. A Second Example: The Moon Illusion Again. Advantages and Disadvantages of Using Related Samples. How Large an Effect Have We Found?. Confidence Limits on Changes. Using SPSS for t Tests on Related Samples. Writing Up the Results. Summary. Exercises. 14. Hypothesis Tests Applied to Means: Two Independent Samples. Distribution of Differences Between Means. Heterogeneity of Variance. Nonnormality of Distributions. A Second Example with Two Independent Samples. Effect Sizes Again. Confidence Limits on Y1 V Y2. Writing Up the Results. Use of Computer Programs for Analysis of Two Independent Sample Means. A Final Worked Example. Seeing Statistics. Summary. Exercises. 15. Power. The Basic Concept. Factors that Affect the Power of a Test. Effect Size. Power Calculations for the One-Sample t Test. Power Calculations for Differences Between Two Independent Means. Power Calculations for the t Test for Related Samples. Power Considerations in Terms of Sample Size. You Don't Have to Do It by Hand. Seeing Statistics. Summary. Exercises. 16. One-Way Analysis of Variance. The General Approach. The Logic of the Analysis of Variance. Calculations for the Analysis of Variances. Unequal Sample Sizes. Multiple Comparison Procedures. Violations of Assumptions. The Size of the Effects. Writing Up the Results. The Use of SPSS for a One-Way Analysis of Variance. A Final Worked Example. Seeing Statistics. Summary. Exercises. 17. Factorial Analysis of Variance Factorial Designs. The Extension of the Eysenck Study. Interactions. Simple Effects. Measures of Association and Effect Size. Reporting the Results. Unequal Sample Sizes. A Second Example: Maternal Adaptation Revisited. Using SPSS for Factorial Analysis of Variance. Seeing Statistics. Summary. Exercises. 18. Repeated-Measures Analysis of Variance. An Example: Depression as a Response to an Earthquake. Multiple Comparisons. Effect Size. Assumptions involved in Repeated-Measures Designs. Advantages and Disadvantages of Repeated-Measures Designs. Using SPSS to Analyze Data in a Repeated-Measures Design. Writing Up the Results. A Final Worked Example. Summary. Exercises. 19. Chi-Square. One Classification Variable: The Chi-Square Goodness of Fit Test. Two Classification Variables: Analysis of Contingency Tables. Possible Improvements on Standard Chi-Square. Chi-Square for Larger Contingency Tables. The Problem of Small Expected Frequencies. The Use of Chi-Square as a Test of Proportions. Nonindependent Observations. SPSS Analysis of Contingency Tables. Measures of Effect Size. A Final Worked Example. Writing Up the Results. Seeing Statistics. Summary. Exercises. 20. Nonparametric and Distribution-Free Statistical Tests. The Mann-Whitney Test. Wilcoxon's Matched-Pairs Signed-Ranks Test. Kruskal-Wallis One-Way Analysis of Variance. Friedman's Rank Test for k Correlated Samples. Measures of Effect Size. Writing Up the Results. Summary. Exercises. 21. Choosing the Appropriate Analysis. Exercises and Examples. Appendix A Arithmetic Review. Appendix B Symbols and Notation. Appendix C Basic Statistical Formulae. Appendix D Dataset. Appendix E Statistical Tables. Glossary. References. Answers to Selected Exercises. Index. Index.

987 citations


Book ChapterDOI
01 Jan 1985
TL;DR: In this paper, the authors focus on the study of parametric and nonparametric methods for estimating the effect size (standardized mean difference) from a single experiment, which is based on the belief that the population effect size is actually the same across studies.
Abstract: This chapter focuses on the study of parametric and nonparametric methods for estimating the effect size (standardized mean difference) from a single experiment. It is important to recognize that estimating and interpreting a common effect size is based on the belief that the population effect size is actually the same across studies. Otherwise, estimating a mean effect may obscure important differences between the studies. The chapter discusses several alternative point estimators of the effect size δ from a single two-group experiment. These estimators are based on the sample standardized mean difference but differ by multiplicative constants that depend on the sample sizes involved. Although the estimates have identical large sample properties, they generally differ in terms of small sample properties. The statistical properties of estimators of effect size depend on the model for the observations in the experiment. A convenient and often realistic model is to assume that the observations are independently normally distributed within groups of the experiment.

699 citations


Journal ArticleDOI
TL;DR: In this article, the choice of kernels for nonparametric estimation of regression functions and their derivatives is investigated, and explicit expressions are obtained for kernels minimizing the asymptotic variance or the IMSE (the present proof of the optimality of the latter kernels up to order k = 5).
Abstract: SUMMARY The choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated Explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error, IMSE (the present proof of the optimality of the latter kernels is restricted up to order k = 5) These kernels are also of interest for the nonparametric estimation of probability densities and spectral densities A finite sample study indicates that higher order kernels-asymptotically improving the rate of convergence-may become attractive for realistic finite sample size Suitably modified kernels are considered for estimating at the extremities of the data, in a way which allows to retain the order of the bias found for interior points

486 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a few techniques which may be useful in the analysis of time series when a failure is suspected and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other, of likelihood ratio tests in parametric models which have a nonstandard behaviour in this situation.
Abstract: The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

356 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduce two nonparametric multivariate density estimators that are particularly suitable for application in interactive computing environments, which are statistically comparable to kernel methods and computationally comparable to histogram methods.
Abstract: We introduce two nonparametric multivariate density estimators that are particularly suitable for application in interactive computing environments. These estimators are statistically comparable to kernel methods and computationally comparable to histogram methods. Asymptotic theory of the estimators is presented and examples with univariate and simulated trivariate Gaussian data are illustrated.

263 citations


Journal ArticleDOI
TL;DR: In this article, a class of sequential designs for estimating the percentiles of a quantal response curve is proposed, which can be viewed as a natural analog of the Robbins-Monro procedure in the case of binary data.
Abstract: A class of sequential designs for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all of the data available via a parametric model. The logit-MLE version of the proposed designs can be viewed as a natural analog of the Robbins—Monro procedure in the case of binary data. It is shown to be asymptotically consistent, optimal, and nonparametric via its connection with the latter procedure. For certain choices of initial designs, the proposed method performs very well in a simulation study for sample sizes up to 35. A nonparametric sequential design, via the Spearman—Karber estimator, for estimating the median is also proposed.

224 citations


Journal ArticleDOI
TL;DR: Bootstrap prediction intervals as mentioned in this paper provide a nonparametric measure of the probable error of forecasts from a standard linear regression model without requiring specific assumptions about the sampling distribution, and they are compared to other non-parametric procedures in several Monte Carlo experiments.
Abstract: Bootstrap prediction intervals provide a nonparametric measure of the probable error of forecasts from a standard linear regression model. These intervals approximate the nominal probability content in small samples without requiring specific assumptions about the sampling distribution. Empirical measures of the prediction error rate motivate the choice of these intervals, which are calculated by an application of the bootstrap. The intervals are contrasted to other nonparametric procedures in several Monte Carlo experiments. Asymptotic invariance properties are also investigated.

176 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compare parametric and nonparametric estimators of asset pricing with or without assuming a distribution for security returns and show that the parametric estimator is robust to departures from any particular distribution, and it is more consistent with the spirit underlying utility-based asset pricing models.
Abstract: Utility-based models of asset pricing may be estimated with or without assuming a distribution for security returns; both approaches are developed and compared here The chief strength of a parametric estimator lies in its computational simplicity and statistical efficiency when the added distributional assumption is true In contrast, the nonparametric estimator is robust to departures from any particular distribution, and it is more consistent with the spirit underlying utility-based asset pricing models since the distribution of asset returns remains unspecified even in the empirical work The nonparametric approach turns out to be easy to implement with precision nearly indistinguishable from its parametric counterpart in this particular application The application shows that log utility is consistent with the data over the period 1926-1981 THE DISTRIBUTION OF ASSET returns is a fundamental quantity to be explained by financial economics Consequently, utility-based models of asset pricing are of special interest since they allow the distributions of returns to be explained rather than assumed as in distribution-based models

144 citations



Journal ArticleDOI
TL;DR: In this article, Schipper and Thompson this article showed that under the assumption of normality of residuals, the test statistics reported in ST involving asymptotic chisquared distributions have convenient finite sample distributions which can be used to test some of the hypotheses examined there.
Abstract: In Schipper and Thompson [1983] (henceforth ST), we estimated a pooled cross-section, time-series model of the return-generating process for the common stock in a sample of related firms. Some of the test statistics reported, based on linear constraints across estimated coefficients, are quadratic forms in the sample covariance matrix. Under the structure and assumptions of the model, these test statistics have asymptotic chi-squared distributions (as the number of time-series observations goes to infinity). In that paper, we did not discuss the exact distributions of these test statistics. In this paper, we show that under the assumption of normality of residuals, the test statistics reported in ST involving asymptotic chisquared distributions have convenient finite sample distributions which can be used to test some of the hypotheses examined there.1 In doing so we reaffirm that the average impact on shareholder wealth of the Williams Amendments was negative and statistically significant for the

Journal ArticleDOI
TL;DR: In this article, the kriging method is described and some of its statistical characteristics are explored, and some extensions of the nonparametric regression approach are made so that it too displays the Kriging features.

Book ChapterDOI
01 Aug 1985
TL;DR: In this paper, the form of a regression relationship with respect to some but not all of the explanatory variables is unknown, and the statistician is caught in a quandary: Should parametric models be abandoned altogether, thus losing the opportunity of estimating parameters of real interest and sacrificing efficiency in estimation and prediction, or should the extraneous variables be forced into a parametric model by imposing a possibly inappropriate functional form without adequate justification?
Abstract: When the form of a regression relationship with respect to some but not all of the explanatory variables is unknown, the statistician is caught in a quandary Should parametric models be abandoned altogether, thus losing the opportunity of estimating parameters of real interest and sacrificing efficiency in estimation and prediction, or should the extraneous variables be forced into a parametric model by imposing a possibly inappropriate functional form without adequate justification?

Journal ArticleDOI
TL;DR: In this article, some practical approaches to the problem of choosing parameters which control the smoothness of kernel-based density estimators are investigated, and particularly simple approaches are investigated in the latter case.
Abstract: Some practical approaches to the problem of choosing parameters which control the smoothness of kernel-based density estimators are investigated. Fixed and variable kernels are considered, and particularly simple approaches are investigated in the latter case. The performances of a wide range of estimators are compared in a simulation study.

Journal ArticleDOI
TL;DR: In this paper, a nonparametric procedure for estimating probability distribution function is proposed, which is a viable alternative with the advantage of not requiring a distributional assumption, and has the ability of estimating multimodal distributions.
Abstract: A currently used approach to flood frequency analysis is based on the concept of parametric statistical inference. In this analysis the assumption is made that the distribution function describing flood data is known, for example, a log-Pearson type III distribution. However, such an assumption is not always justified and often leads to other difficulties; it could also result in considerable variability in the estimation of design floods. A new method is developed in this article based on the nonparametric procedure for estimating probability distribution function. The results indicate that design floods computed from the different assumed distribution and from the nonparametric method provide comparable results. However, the nonparametric method is a viable alternative with the advantage of not requiring a distributional assumption, and has the ability of estimating multimodal distributions.


Journal ArticleDOI
TL;DR: In this paper, nonparametric density and regression techniques are employed to infer f(y | x) and m(x) = E[X i + 1 | Xi = x].
Abstract: Let {Xi } be a stationary Markov sequence having a transition probability density function f(y | x) giving the pdf of X i +1 | (Xi = x). In this study, nonparametric density and regression techniques are employed to infer f(y | x) and m(x) = E[X i + 1 | Xi = x]. It is seen that under certain regularity and Markovian assumptions, the asymptotic convergence rate of the nonparametric estimator mn (x) to the predictor m(x) is the same as it would have been had the Xi 's been independently and identically distributed, and this rate is optimal in a certain sense. Consistency can be maintained after differentiability and even the Markovian assumptions are abandoned. Computational and modeling ramifications are explored. I claim that my methodology offers an interesting alternative to the popular ARMA approach.

Book ChapterDOI
01 Jan 1985
TL;DR: In this article, the authors investigate the problem of testing for a change point in stationary statistical models and estimating the change parameters in an off-line framework and provide asymptotic results which emphasize the need for weighting the classical test statistics when the change time is completely unknown.
Abstract: We investigate the problem of testing for a change-point in stationary statistical models and of estimating the change parameters in an off-line framework. This paper provides asymptotic results which emphasize the need for weighting the classical test statistics when the change time is completely unknown. The asymptotic expansions can also give new detectors which are simpler for using.

Journal ArticleDOI
TL;DR: In this paper, the empirical characteristic function (EMF) was used to test the total independence of d (≥2) random variables using empirical characteristic functions, parallel to that of Hoeffding, Blum, Kiefer and Rosenblatt.


Journal ArticleDOI
01 May 1985
TL;DR: In this paper, a nonparametric fitting methodology for multivariate functions is proposed and the mean-square error convergence and the strong convergence are proved, and the methodology is shown to have good performance.
Abstract: The methodology for nonparametric fitting of multivariate functions is proposed. The mean-square error convergence and the strong convergence are proved.

Journal ArticleDOI
TL;DR: In this article, nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc non-parametric analogue of the Newman-Keuls procedure.
Abstract: Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control Type I error levels, and that they have superior pairwise power compared to the commonly used nonstepwise procedures.

Journal ArticleDOI
TL;DR: A complete list of references in non-parametric regression estimation can be found in this article, with a brief introduction of these works according to a classification taking the diversity of problems or methods into account.
Abstract: We attempt to give a complete list of references in non parametric regression estimation (including non parametric time series analysis), with a brief introduction of these works according a classification taking the diversity of problems or methods into account.


Journal ArticleDOI
TL;DR: In this article, the authors examined the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compared them with those of the resubstitution, leave-one-out, and bootstrap estimators.
Abstract: This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.

Journal ArticleDOI
TL;DR: In this paper, distribution-free alternatives to parametric analysis of covariance are presented and demonstrated using a specific data example, and the results of simulation studies investigating these procedures regarding their respective Type I error rate under a null condition and their statistical power are also reviewed.
Abstract: Five distribution-free alternatives to parametric analysis of covariance are presented and demonstrated using a specific data example. The results of simulation studies investigating these procedures regarding their respective Type I error rate under a null condition and their statistical power are also reviewed. The results indicate that the nonparametric procedures have appropriate Type I error rates only for those situations in which para metric A NCO VA is robust to violations of data assumptions. In terms of statistical power, nonparametric alternatives to parametric ANCOVA provide a considerable power advan tage only for situations in which extreme violations of assumptions have occurred and the linear relationship between measures is weak.

Journal ArticleDOI
TL;DR: In clinical research, "samples" are studied in order to get ideas about the characteristics of the larger populations from which the samples are taken, and nonparametric statistical methods are used, which do not require estimates of population parameters.
Abstract: In clinical research, "samples" are studied in order to get ideas about the characteristics of the larger populations from which the samples are taken. Population characteristics are called parameters (the population mean and standard deviation are examples). Parametric statistical methods are those that require estimates of parameters and assumptions about the source populations. Familiar examples of parametric methods are the t test, analysis of variance, and Pearson's correlation coefficient. Nonparametric (NP) methods do not require estimates of population parameters. These methods are sometimes called "distribution-free" because the samples of interest can be evaluated without concern for the shape (distribution) of the values in the populations providing the samples. NP methods also are called "ranking" or "ordering" tests, because the relative size or order of the observations may be evaluated, rather than requiring actual measurements. More than 30% of the research reports that appeared between July 1982 and June 1983, in four pediatric journals, employed at least one nonparametric method. The commonly used tests were chi-square, the Fisher exact test, and various "ranking" methods. An alphabetical list of common nonparametric tests is presented, with brief comments about each. Tables are presented, arranged by types of observations, so that the nature of the data guides the user to the method that might be used.



Journal ArticleDOI
TL;DR: In this article, an estimator which mixes parametric and non-parametric density estimates is proposed to solve the model choice problem for peak annual flows, in the context of flood frequency analysis.
Abstract: Much attention has been invested in the model choice problem for peak annual flows, in the context of flood frequency analysis. The authors would sidestep this dilemma through non-parametric density estimation methodology, but recognize that the standard nonparametric estimators preclude the use of prior information and related data, and furthermore have virtually no tail at all. Here we offer a remedy for these inadequacies by introducing an estimator which mixes parametric and nonparametric density estimates. We prove that our mixture rule is consistent. By this procedure, we do allow incorporation of prior information, experience, and regional data information, but nevertheless provide a safeguard against incorrect model choice.