Showing papers on "Nonparametric statistics published in 1993"

Measuring and Testing the Impact of News on Volatility

Abstract: This paper defines the news impact curve which measures how new information is incorporated into volatility estimates. Various new and existing ARCH models including a partially nonparametric one are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented which emphasize the asymmetry of the volatility response to news. Our results suggest that the model by Glosten, Jagannathan, and Runkle is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high.

Multivariate density estimation : theory, practice, and visualization

Abstract: Representation and Geometry of Multivariate Data. Nonparametric Estimation Criteria. Histograms: Theory and Practice. Frequency Polygons. Averaged Shifted Histograms. Kernel Density Estimators. The Curse of Dimensionality and Dimension Reduction. Nonparametric Regression and Additive Models. Special Topics. Appendices. Indexes.

Statistical Analysis of Circular Data

Abstract: Preface 1. The purpose of the book 2. Survey of contents 3. How to use the book 4. Notation, terminology and conventions 5. Acknowledgements Part I. Introduction: Part II. Descriptive Methods: 2.1. Introduction 2.2. Data display 2.3. Simple summary quantities 2.4. Modifications for axial data Part III. Models: 3.1. Introduction 3.2. Notation trigonometric moments 3.3. Probability distributions on the circle Part IV. Analysis of a Single Sample of Data: 4.1. Introduction 4.2. Exploratory analysis 4.3. Testing a sample of unit vectors for uniformity 4.4. Nonparametric methods for unimodal data 4.5. Statistical analysis of a random sample of unit vectors from a von Mises distribution 4.6. Statistical analysis of a random sample of unit vectors from a multimodal distribution 4.7. Other topics Part V. Analysis of Two or More Samples, and of Other Experimental Layouts: 5.1. Introduction 5.2. Exploratory analysis 5.3. Nonparametric methods for analysing two or more samples of unimodal data 5.4. Analysis of two or more samples from von Mises distributions 5.5. Analysis of data from more complicated experimental designs Part VI. Correlation and Regression: 6.1. Introduction 6.2. Linear-circular association and circular-linear association 6.3. Circular-circular association 6.4. Regression models for a circular response variable Part VII. Analysis of Data with Temporal or Spatial Structure: 7.1. Introduction 7.2. Analysis of temporal data 7.3. Spatial analysis Part VIII. Some Modern Statistical Techniques for Testing and Estimation: 8.1. Introduction 8.2. Bootstrap methods for confidence intervals and hypothesis tests: general description 8.3. Bootstrap methods for circular data: confidence regions for the mean direction 8.4. Bootstrap methods for circular data: hypothesis tests for mean directions 8.5. Randomisation, or permutation, tests Appendix A. Tables Appendix B. Data sets References Index.

Biostatistics : The Bare Essentials

Abstract: Section 1: THE NATURE OF DATA AND STATISTICS 1. The Basics 2. Looking at the Data: A First Look at Graphing Data 3. Describing the Data with Numbers: Measures of Central Tendency and Dispersion 4. The Normal Distribution 5. Probability 6. Elements of Statistical Inference C.R.A.P. Detectors Section 2: ANALYSIS OF VARIANCE 7. Comparing Two Groups: The t-Test 8. More than Two Groups: One-Way ANOVA 9. Factorial ANOVA 10. Two Repeated Observations: The Paired t-Test and Alternatives 11. Repeated Measures ANOVA 12. Multivariate ANOVA (MANOVA) C.R.A.P. Detectors Section 3: REGRESSION AND CORRELATION 13. Simple Regression and Correlation 14. Multiple Regression 15. Logistic Regression 16. Advanced Topics in Regression and ANOVA 17. Measuring Change 18. Principal Components and Factor Analysis: Fooling Around with Factors 19. Structural Equation Modeling C.R.A.P. Detectors Section 4: NONPARAMETRIC STATISTICS 20. Tests of Significance for Categorical Frequency Data 21. Measures of Association for Categorical Data 22. Tests of Significance for Ranked Data 23. Measures of Association for Ranked Data 24. Life Table (Survival) Analysis C.R.A.P. Detectors Section 5: REPRISE 25. Screwups, Oddballs, and other Vagaries of Science: Locating Outliers, Handling Missing Data, and Transformations 26. Putting It All Together Test Yourself (Being a Compendium of Questions and Answers) Answers to Chapter Exercises References and Further Readings Unabashed Glossary Appendices

Comparing Nonparametric Versus Parametric Regression Fits

Abstract: In general, there will be visible differences between a parametric and a nonparametric curve estimate. It is therefore quite natural to compare these in order to decide whether the parametric model could be justified. An asymptotic quantification is the distribution of the integrated squared difference between these curves. We show that the standard way of bootstrapping this statistic fails. We use and analyse a different form of bootstrapping for this task. We call this method the wild bootstrap and apply it to fitting Engel curves in expenditure data analysis.

Biostatistics: A Methodology for the Health Sciences

Abstract: Partial table of contents: Biostatistical Design of Medical Studies. Descriptive Statistics. Statistical Inference: Populations and Samples. Counting Data. Categorical Data: Contingency Tables. Nonparametric, Distribution-Free and Permutation Models: Robust Procedures. Analysis of Variance. Association and Prediction: Multiple Regression Analysis, Linear Models with Multiple Predictor Variables. Multiple Comparisons. Discrimination and Classification. Rates and Proportions. Analysis of the Time to an Event: Survival Analysis. Sample Sizes for Observational Studies. A Personal Postscript. Appendix. Indexes.

Conditional Choice Probabilities and the Estimation of Dynamic Models

Abstract: This paper develops a new method for estimating the structural parameters of (discrete choice) dynamic programming problems. The method reduces the computational burden of estimating such models. We show the valuation functions characterizing the expected future utility associated with the choices often can be represented as an easily computed function of the state variables, structural parameters, and the probabilities of choosing alternative actions for states which are feasible in the future. Under certain conditions, nonparametric estimators of these probabilities can be formed from sample information on the relative frequencies of observed choices using observations with the same (or similar) state variables. Substituting the estimators for the true conditional choice probabilities in formulating optimal decision rules, we establish the consistency and asymptotic normality of the resulting structural parameter estimators. To illustrate our new method, we estimate a dynamic model of parental contraceptive choice and fertility using data from the National Fertility Survey.

Nonparametric methods in change-point problems

Abstract: Preface. Introduction: Goals and problems of change point detection. 1. Preliminary considerations. 2. State-of-the-art review. 3. A posteriori change point problems. 4. Sequential change point detection problems. 5. Disorder detection of random fields. 6. Applications of nonparametric change point detection methods. 7. Proofs, new results and technical details. References.

On the Use of Cause-Specific Failure and Conditional Failure Probabilities: Examples from Clinical Oncology Data

Abstract: Nonparametric maximum likelihood estimation of the probability of failing from a particular cause by time t in the presence of other acting causes (i.e., the cause-specific failure probability) is discussed. A commonly used incorrect approach is to take 1 minus the Kaplan-Meier (KM) estimator (1 – KM), whereby patients who fail of extraneous causes are treated as censored observations. Examples showing the extent of bias in using the 1-KM approach are presented using clinical oncology data. This bias can be quite large if the data are uncensored or if a large percentage of patients fail from extraneous causes prior to the occurrence of failures from the cause of interest. Each cause-specific failure probability is mathematically defined as a function of all of the cause-specific hazards. Therefore, nonparametric estimates of the cause-specific failure probabilities may not be able to identify categorized covariate effects on the cause-specific hazards. These effects would be correctly identified ...

Functional-Coefficient Autoregressive Models

Abstract: In this article we propose a new class of models for nonlinear time series analysis, investigate properties of the proposed model, and suggest a modeling procedure for building such a model. The proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics. A consistency result is given to support the procedure. For illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially improve postsample multi-step ahead forecasts over other models.

Detecting Outliers in Deterministic Nonparametric Frontier Models With Multiple Outputs

Abstract: This article provides a statistical methodology for identifying outliers in production data with multiple inputs and outputs used in deterministic nonparametric frontier models. The methodology is useful in identifying observations that may contain some form of measurement error and thus merit closer scrutiny. When data checking is costly, the methodology may be used to rank observations in terms of their dissimilarity to other observations in the data, suggesting a priority for further inspection of the data.

16 Efficient estimation of models with conditional moment restrictions

Abstract: Publisher Summary This chapter aims to discuss (asymptotically) efficient estimation of the parameters of conditional moment restriction models. A useful type of model that imposes few restrictions and can allow for simultaneity is a conditional moment restriction model, where all that is specified is that a vector of residuals, consisting of known, prespecified functions of the data and parameters, has conditional mean zero given known variables. Estimators for the parameters of these models can be constructed by interacting functions of the residuals with functions of the conditioning variables and choosing the parameter estimates so that the sample moments of these interactions are zero. These estimators are conditional, implicit versions of the method of moments that are typically referred to as instrumental variables (IV) estimators, where the instruments are the functions of conditioning variables that interacted with the residuals. These estimators have the usual advantage of method of moments over maximum likelihood that their consistency only depends on correct specification of the residuals and conditioning variables, and not on the correctness of a likelihood function. Maximum likelihood may be more efficient than IV if the distribution is correctly specified, so that the usual bias/efficiency tradeoff is present for IV and maximum likelihood. The chapter discusses the description and motivation for IV estimators, several approaches to efficient estimation, the nearest neighbor nonparametric estimation of the optimal instruments, and estimation via linear combinations of functions.

Is the selection of statistical methods governed by level of measurement

Abstract: The notion that nonparametric methods are required as a replacement of parametric statistical methods when the scale of measurement in a research study does not achieve a certain level was discussed in light of recent developments in representational measurement theory. A new approach to examining the problem via computer simulation was introduced. Some of the beliefs that have been widely held by psychologists for several decades were examined by means of a computer simulation study that mimicked measurement of an underlying empirical structure and performed two - sample Student t - tests on the resulting sample data. It was concluded that there is no need to replace parametric statistical tests by nonparametric methods when the scale of measurement is ordinal and not interval.Stevens' (1946) classic paper on the theory of scales of measurement triggered one of the longest standing debates in behavioural science methodology. The debate -- referred to as the levels of measurement controversy, or measurement - statistics debate -- is over the use of parametric and nonparametric statistics and its relation to levels of measurement. Stevens (1946; 1951; 1959; 1968), Siegel (1956), and most recently Siegel and Castellan (1988) and Conover (1980) argue that parametric statistics should be restricted to data of interval scale or higher. Furthermore, nonparametric statistics should be used on data of ordinal scale. Of course, since each scale of measurement has all of the properties of the weaker measurement, statistical methods requiring only a weaker scale may be used with the stronger scales. A detailed historical review linking Stevens' work on scales of measurement to the acceptance of psychology as a science, and a pedagogical presentation of fundamental axiomatic (i.e., representational) measurement can be found in Zumbo and Zimmerman (1991).Many modes of argumentation can be seen in the debate about levels of measurement and statistics. This paper focusses almost exclusively on an empirical form of rhetoric using experimental mathematics (Ripley, 1987). The term experimental mathematics comes from mathematical physics. It is loosely defined as the mimicking of the rules of a model of some kind via random processes. In the methodological literature this is often referred to as monte carlo simulation. However, for the purpose of this paper, the terms experimental mathematics or computer simulation are preferred to monte carlo because the latter is typically referred to when examining the robustness of a test in relation to particular statistical assumptions. Measurement level is not an assumption of the parametric statistical model (see Zumbo & Zimmerman, 1991 for a discussion of this issue) and to call the method used herein "monte carlo" would imply otherwise. The term experimental mathematics emphasizes the modelling aspect of the present approach to the debate.The purpose of this paper is to present a new paradigm using experimental mathematics to examine the claims made in the levels of measurement controversy. As Michell (1986) demonstrated, the concern over levels of measurement is inextricably tied to the differing notions of measurement and scaling. Michell further argued that fundamental axiomatic measurement or representational theory (see, for example, Narens & Luce, 1986) is the only measurement theory which implies a relation between measurement scales and statistics. Therefore, the approach advocated in this paper is linked closely to representational theory. The novelty of this approach, to the authors knowledge, is in the use of experimental mathematics to mimic representational measurement. Before describing the methodology used in this paper, we will briefly review its motivation.Admissible TransformationsRepresentational theory began in the late 1950's with Scott and Suppes (1958) and later with Suppes and Zinnes (1963), Pfanzagl (1968), and Krantz, Luce, Suppes & Tversky (1971). …

A Fourier Approach to Nonparametric Deconvolution of a Density Estimate

Abstract: We consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f, when a represents the convolution of h and f. Our approach is based on truncated Fourier inversion, in which the truncation point plays the role of a smoothing parameter. We derive the asymptotic mean integrated squared error of the estimate and use this formula to suggest a simple practical method for choosing the truncation point from the data. Strikingly, when the smoothing parameter is chosen in this way then in many circumstances the estimator behaves, to first order, as though the true f were known

Confidence bands in nonparametric regression

Abstract: New bias-corrected confidence bands are proposed for nonparametric kernal regression. These bands are constructed using only a kernel estimator of the regression curve and its data-selected bandwidth. They are shown to have asymptotically correct coverage properties and to behave well in a small-sample study. One consequence of the large-sample developments is that Bonferroni-type bands for the regression curve at the design points also have conservative asymptotic coverage behavior with no bias correction.

Nonparametric Measures of Association

Abstract: Introduction Spearman's Rho and Kendall's Tau as Descriptive Measures of Association Inferences Based on Rho and Tau Kendall's Coefficient of Concordance Partial Correlation Measures of Association in Ordered Contingency Tables Summary

On the Use of Nonparametric Regression for Checking Linear Relationships

Abstract: SUMMARY The problem of checking the linearity of a regression relationship is addressed through the idea of smoothing of a residual plot. A pseudolikelihood ratio test statistic, which measures the distance between the nonparametric and the parametric models, is derived as a ratio of quadratic forms. The distribution of this statistic under the null hypothesis of linearity is calculated numerically by using Johnson curves. A power study shows the new statistic to be more sensitive to non-linearity than the Durbin-Watson statistic.

A non-parametric and scale-independent method for cluster analysis – I. The univariate case

Abstract: The detection and analysis of structure and substructure in systems of galaxies is a well-known problem. Several methods of analysis exist with different ranges of applicability and giving different results. The aim of the present paper is to describe a general procedure of wide applicability that is based on a minimum number of general assumptions and gives an objective, testable, scale-independent and non-parametric estimate of the clustering pattern of a sample of observational data. The method follows the idea that the presence of a cluster in a data sample is indicated by a peak in the probability density underlying the data. There are two steps: the first is estimation of the probability density and the second is identification of the clusters

Exploring Regression Structure Using Nonparametric Functional Estimation

Abstract: Average derivative functionals of regression are proposed for nonparametric model selection and diagnostics. The functionals are of the integral type, which under certain conditions allows their estimation at the usual parametric rate of n –1/2. We analyze asymptotic properties of the estimators of these functionals, based on kernel regression. These estimators can then be used for assessing the validity of various restrictions imposed on the form of regression. In particular, we show how they could be used to reduce the dimensionality of the model, assess the relative importance of predictors, measure the extent of nonlinearity and nonadditivity, and, under certain conditions, help identify projection directions in projection pursuit models and decide on the number of these directions.

Empirical Likelihood in Biased Sample Problems

Abstract: It is well known that we can use the likelihood ratio statistic to test hypotheses and to construct confidence intervals in full parametric models. Recently, Owen introduced the empirical likelihood method in nonparametric models. In this paper, we generalize his results to biased sample problems. A Wilks theorem leading to a likelihood ratio confidence interval for the mean is given. Some extensions, discussion and simulations are presented.

Performance of the Mantel-Haenszel and Simultaneous Item Bias Procedures for Detecting Differential Item Functioning. Laboratory of Psychometric and Evaluative Research Report No. 252.

Abstract: Two nonparametric procedures for detecting differ ential item functioning (DIF)—the Mantel-Haenszel (MH) procedure and the simultaneous item bias (SIB) procedure—were compared with respect to their Type I error rates and power. Data were simulated to reflect conditions varying in sample size, ability distribution differences between the focal and reference groups, pro portion of DIF items in the test, DIF effect sizes, and type of item. 1,296 conditions were studied. The SIB and MH procedures were equally powerful in detecting uniform DIF for equal ability distributions. The SIB procedure was more powerful than the MH procedure in detecting DIF for unequal ability distributions. Both procedures had sufficient power to detect DIF for a sample size of 300 in each group. Ability distribution did not have a significant effect on the SIB procedure but did affect the MH procedure. This is important because ability distribu tion differences between two groups often are found in practice. The Type I error rates for the MH statistic were well within the nominal limits, whereas they were slightly higher than expected for the SIB statistic. Com parisons between the detection rates of the two proce dures were made with respect to the various factors. Index terms: differential item functioning, Mantel- Haenszel statistic, power, simultaneous item bias statis tic, SIBTEST, Type I error rates.

Correlation Curves: Measures of Association as Functions of Covariate Values

Abstract: For experiments where the strength of association between a response variable $Y$ and a covariate $X$ is different over different regions of values for the covariate $X$, we propose local nonparametric dependence functions which measure the strength of association between $Y$ and $X$ as a function of $X = x$ Our dependence functions are extensions of Galton's idea of strength of co-relation from the bivariate normal case to the nonparametric case In particular, a dependence function is obtained by expressing the usual Galton-Pearson correlation coefficient in terms of the regression line slope $\beta$ and the residual variance $\sigma^2$ and then replacing $\beta$ and $\sigma^2$ by a nonparametric regression slope $\beta(x)$ and a nonparametric residual variance $\sigma^2(x) = \operatorname{var}(Y \mid x)$, respectively Our local dependence functions are standardized nonparametric regression curves which provide universal scale-free measures of the strength of the relationship between variables in nonlinear models They share most of the properties of the correlation coefficient and they reduce to the usual correlation coefficient in the bivariate normal case For this reason we call them correlation curves We show that, in a certain sense, they quantify Lehmann's notion of regression dependence Finally, the correlation curve concept is illustrated using data from a study of the relationship between cholesterol levels $x$ and triglyceride concentrations $y$ of heart patients

Statistical Applications for the Behavioral Sciences

Abstract: Partial table of contents: BASIC CONCEPTS OF RESEARCH AND DESCRIPTIVE STATISTICS Basic Concepts in Research Scales of Measurement and Data Display Measures of Central Tendency The Normal Curve and Transformations: Percentiles, z Scores and T Scores INFERENTIAL STATISTICS: PARAMETRIC TESTS Hypothesis Testing and Sampling Distributions Testing the Significance of a Single Mean: The Single-Sample z and t Tests Directional and Nondirectional Testing of the Difference Between Two Means: The Independent-Samples t Test Confidence Intervals and Hypothesis Testing Two-Way Analysis of Variance Repeated-Measures Analysis of Variance Linear Correlation Linear Regression INFERENTIAL STATISTICS: NONPARAMETRIC TESTS The Chi-Square Test Other Nonparametric Tests Appendices Glossary References Index.

Nonparametric methods with applications to hedonic models

Abstract: Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).