Showing papers on "Nonparametric statistics published in 1999"
TL;DR: A nonparametric estimation procedure for assessing the probability weighting function and value function at the level of the individual subject, consistent with a growing body of empirical and theoretical work attempting to establish a psychological rationale for the probabilityWeighting function.
1,328 citations
Book•
01 Jan 1999TL;DR: In this paper, the authors take the more modern definition of "nonparametric" and cover a large range of smoothing methods which can be applied in econometrics.
Abstract: The description “nonparametric” seems to be used in two different ways in the statistical and econometric literature. The older use of the word refers to tests (such as Wilcoxon, Mann-Whitney, etc.) which don’t rely on classical normality assumptions, and which are often based on ranks rather than raw data. More recently, the term has been used to refer to smoothing techniques, especially in density estimation and regression. This book takes the more modern definition of “nonparametric” and covers a large range of smoothing methods which can be applied in econometrics.
1,288 citations
TL;DR: In this article, the authors define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case, and provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator for the bivariate case.
Abstract: Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situations. Consequently, statistical inference based on DEA/FDH-type estimators is now possible. These techniques allow correction for the bias of the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes.
1,099 citations
Book•
17 May 1999
TL;DR: In this article, the authors describe the nature of the design process of measuring and collecting factual data, measuring attitudes, opinions and views, measuring achievement, and evaluating data quality, and determining instrument reliability and validity.
Abstract: PART ONE: INTRODUCTION TO RESEARCH DESIGN The Nature of Enquiry Beginning the Design Process Initial Sources of Invalidity and Confounding Basic Designs Identifying Populations and Samples Additional Sources of Confounding by the Measurement Process and Interactions Refining the Designs PART TWO: MEASUREMENT DESIGN Principles of Measurement and Collecting Factual Data Measuring Attitudes, Opinions and Views Measuring Achievement Evaluating Data Quality Determining Instrument Reliability and Validity PART THREE: TURNING DATA INTO INFORMATION USING STATISTICS Descriptive Statistics Using a Spreadsheet Probability and Statistical Significance Power, Errors and Choosing a PART FOUR: EX POST FACTO, EXPERIMENTAL AND QUASI-EXPERIMENTAL DESIGNS: PARAMETRIC TESTS Comparing Two Groups t-Test One-Way Analysis of Variance Factorial Designs Randomized Block Designs and Analysis of Covariance PART FIVE: NONPARAMETRIC TESTS: NOMINAL AND ORDINAL VARIABLES Nonparametric Tests One and Two Samples Nonparametric Tests Multiple and Related Samples PART SIX: DESCRIBING NON-CAUSAL RELATIONSHIPS Correlation and Association Regression
941 citations
TL;DR: The principle aim of the paper is to compare the results obtained from the three alternative methods of estimating multi-output distance functions, and the construction of a parametric frontier using linear programming; data envelopment analysis (DEA) and corrected ordinary least squares (COLS).
715 citations
Book•
01 Jul 1999
TL;DR: The JMP Help System as mentioned in this paper is a help system for JMP data tables that allows the user to build a JMP table with both feet, and it can be used for statistical sleuthing.
Abstract: Part I: JMPing IN with both feet: 1. Jump Right In. First Session. Modelling Type. Analyze and Graph. Getting Help: The JMP Help System. 2. JMP Data Tables. The Ins and Outs of a JMP Data Table. Moving Data and Results Out of JMP. Juggling Data Tables. The Group/Summary Command. 3. Calculator Adventures. The Calculator Window. A Quick Example. Calculator Pieces and Parts. Terms Functions. Conditional Expressions and Comparison Operators. Summarize Down a Column or Summarize Across Rows. Random Number Functions. Parameters. Tips on Building Formulas. Caution and Error Messages. Part II Statistical sleuthing: 4. What are Statistics? Ponderings. Preparations. Statistical Terms. 5. Univariate Distribution: One Variable, One Sample. Looking at Distributions. Review: Probability Distributions. Describing Distributions of Values. Statistical Inference on the Man. Special Topic: Testing for Normality. Special Topic: Simulating the Central Limit Theorem. 6. Differences Between Two Means. Two Independent Groups. Testing Means for Matched Pairs. Review. A Nonparametric Approach. 7. Comparing Many Means: One-Way Analysis of Variance. What is a One-Way Layout? Comparing and Testing Means. Special Topic: Adjusting for Multiple Comparisons. Special Topic: Power. Special Topic: Unequal Variances. Special Topic: Nonparametric Methods. 8. Fitting Curves Through Points: Regression. Regression. Why Graphics are Important. Why It's Called Regression. Curiosities. 9. Categorical Distributions. Categorical Situations. Categorical Responses and Count Data: Two Outlooks. A Simulated Categorical Response. The Chi-Square Pearson Chi-Square Test Statistic. The G-Square Likelihood Ratio Chi-Square Test Statistic. Univariate Categorical Chi-Square Tests. 10. Categorical Models. Fitting Categorical Responses to Categorical Factors. Correspondence Analysis: Looking at Data with Many Levels. Continuous Factors for Categorical Responses: Logistic Regression. Special Topics. Surprise: Simpson's Paradox: Aggregate Data versus Grouped Data. 11. Multiple Regression. Parts of a Regression Model. A Multiple Regression Example. Special Topic: Collinearity. Special Topic: The Case of the Hidden Leverage Point. Special Topic: Mining Data with Stepwise Regression. 12. Fitting Linear Models. The General Linear Model. Two-Way Analysis of Variance and Interactions. Optional Topic: Random Effects and Nested Effects. 13. Bivariate and Multivariate Relationships. Bivariate Distributions. Correlations and the Bivariate Normal. Three and More Dimensions. 14. Design of Experiments. Introduction. Generating and Experimental Design in JMP. Two-Level Screening Designs. Screening for Main Effects: The Flour Paste Experiment. Screening for Interactions. Response Surface Designs. 15. Statistical Quality Control. Control Charts and Shewhart Charts. The Control Chart Dialog. Pareto Charts. 16. Time Series Analysis. Introduction. Graphing and Fitting by Time. Lagging and Autocorrelation.
675 citations
TL;DR: In this article, generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs, allowing flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects.
Abstract: Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi-likelihood. Because numerical integration is often required by maximizing the objective functions, double penalized quasi-likelihood is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software. A bias correction procedure is also proposed to improve the performance of double penalized quasi-likelihood for sparse data. We illustrate the method with an application to infectious disease data and we evaluate its performance through simulation.
557 citations
TL;DR: In this article, a simple two-step nonparametric estimator for a triangular simultaneous equation model is presented, which employs series approximations that exploit the additive structure of the model.
Abstract: This paper presents a simple two-step nonparametric estimator for a triangular simultaneous equation model. Our approach employs series approximations that exploit the additive structure of the model. The first step comprises the nonparametric estimation of the reduced form and the corresponding residuals. The second step is the estimation of the primary equation via nonparametric regression with the reduced form residuals included as a regressor. We derive consistency and asymptotic normality results for our estimator, including optimal convergence rates. Finally we present an empirical example, based on the relationship between the hourly wage rate and annual hours worked, which illustrates the utility of our approach.
522 citations
TL;DR: It is demonstrated that it is possible to approximate the mutual information arbitrarily closely in probability by calculating the relative frequencies on appropriate partitions and achieving conditional independence on the rectangles of which the partitions are made.
Abstract: We demonstrate that it is possible to approximate the mutual information arbitrarily closely in probability by calculating the relative frequencies on appropriate partitions and achieving conditional independence on the rectangles of which the partitions are made. Empirical results, including a comparison with maximum-likelihood estimators, are presented.
482 citations
Book•
01 May 1999
TL;DR: How to Use SPSS® as mentioned in this paper is designed with the novice computer user in mind and for people who have no previous experience using SPSs and is divided into short sections that describe the statistic being used, important underlying assumptions, and how to interpret the results and express them in a research report.
Abstract: How to Use SPSS® is designed with the novice computer user in mind and for people who have no previous experience using SPSS. Each chapter is divided into short sections that describe the statistic being used, important underlying assumptions, and how to interpret the results and express them in a research report.
The book begins with the basics, such as starting SPSS, defining variables, and entering and saving data. It covers all major statistical techniques typically taught in beginning statistics classes, such as descriptive statistics, graphing data, prediction and association, parametric inferential statistics, nonparametric inferential statistics and statistics for test construction.
More than 270 screenshots (including sample output) throughout the book show students exactly what to expect as they follow along using SPSS. The book includes a glossary of statistical terms and practice exercises. A complete set of online resources including video tutorials and output files for students, and PowerPoint slides and test bank questions for instructors, make How to Use SPSS® the definitive, field-tested resource for learning SPSS.
New to this edition:
Now in full color with additional screenshots
Fully updated to the reflect SPSS version 26 (and prior versions)
Changes in nonparametric tests Model View incorporated
Data and real output are now available for all Phrasing Results sections – eliminating hypothetical output or hypothetical data
430 citations
TL;DR: In this paper, a multivariate, nonparametric time series simulation method is provided to generate random sequences of daily weather variables that "honor" the statistical properties of the historical data of the same weather variables at the site.
Abstract: A multivariate, nonparametric time series simulation method is provided to generate random sequences of daily weather variables that "honor" the statistical properties of the historical data of the same weather variables at the site. A vector of weather variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, average wind speed, and precipitation) on a day of interest is resampled from the historical data by conditioning on the vector of the same variables (feature vector) on the preceding day. The resampling is done from the k nearest neighbors in state space of the feature vector using a weight function. This approach is equivalent to a nonparametric approximation of a multivariate, lag 1 Markov process. It does not require prior assumptions as to the form of the joint probability density function of the variables. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, is provided. Results are compared with those from the application of a multivariate autoregressive model similar to that of Richardson (1981).
TL;DR: In this paper, the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely, assuming that the prior does not put high mass near distributions with very rough densities.
Abstract: We give conditions that guarantee that the posterior probability of every Hellinger neighborhood of the true distribution tends to 1 almost surely. The conditions are (1) a requirement that the prior not put high mass near distributions with very rough densities and (2) a requirement that the prior put positive mass in Kullback-Leibler neighborhoods of the true distribution. The results are based on the idea of approximating the set of distributions with a finite-dimensional set of distributions with sufficiently small Hellinger bracketing metric entropy. We apply the results to some examples.
TL;DR: An EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure is described and a simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm.
Abstract: This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation.
TL;DR: In this paper, the authors present a model that delivers closed-form solutions for bond prices and a concave relationship between the interest rate and the yields, showing that in empirical analyses, their model outperforms the one-factor affine models in both time-series as well as cross-sectional tests.
Abstract: Recent nonparametric estimation studies pioneered by Ait-Sahalia document that the diffusion of the short rate is similar to the parametric function, r[superscript 1.5], estimated by Chan et al., whereas the drift is substantially nonlinear in the short rate. These empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior. This article presents such a model. Our model delivers closed-form solutions for bond prices and a concave relationship between the interest rate and the yields. We show that in empirical analyses, our model outperforms the one-factor affine models in both time-series as well as cross-sectional tests. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
27 Dec 1999
TL;DR: Introduction Summarizing Data Probability Functions of Random Variables Discrete Probability Distributions Continuous Probable Distributions Standard Normal Distribution Estimation Confidence Intervals Hypothesis Testing Regression Analysis Analysis of Variance Experimental Design Nonparametric Statistics Quality Control and Risk Analysis.
Abstract: Introduction Summarizing Data Probability Functions of Random Variables Discrete Probability Distributions Continuous Probability Distributions Standard Normal Distribution Estimation Confidence Intervals Hypothesis Testing Regression Analysis Analysis of Variance Experimental Design Nonparametric Statistics Quality Control and Risk Analysis General Linear Models Miscellaneous Topics Special Functions
Book•
05 Aug 1999
TL;DR: Orthonormal Series and Approximation, nonparametric Regression for Small Samples, and Filtering and Asymptotics.
Abstract: Orthonormal Series and Approximation.- Density Estimation for Small Samples.- Nonparametric Regression for Small Samples.- Nonparametric Time Series Analysis for Small Samples.- Estimation of Multivariate Functions for Small Samples.- Filtering and Asymptotics.- Nonseries Methods.
Book•
18 Oct 1999
TL;DR: In this paper, the authors present a review of Probability, likelihood, Bayesian and decision theory methods for counting and counting data, as well as the analysis of single-factor and multi-factor experiments.
Abstract: 1. Introduction. 2. Review of Probability. 3. Collecting Data. 4. Summarizing and Exploring Data. 5. Sampling Distributions of Statistics. 6. Basic Concepts of Inference. 7. Inferences for Single Samples. 8. Inferences for Two Samples. 9. Inferences for Proportions and Count Data. 10. Simple Linear Regression and Correlation. 11. Multiple Linear Regression. 12. Analysis of Single Factor Experiments. 13. Analysis of Multifactor Experiments. 14. Nonparametric Statistical Methods. 15. Likelihood, Bayesian and Decision Theory Methods. Appendix A: Tables. Appendix B: Abbreviated Answers to Selected Odd Numbered Exercises. Index.
TL;DR: The receiver operator characteristic (ROC) method is used to compare the efficacy of various steps in calculating an activation map in the study of a single subject based on optimizing the ratio of the number of detected activations to thenumber of false-positive findings.
Book•
01 Nov 1999
TL;DR: Theory of nonparametric mixture models algorithms the likelihood ratio test for the number of components C.A.MAN-applications and meta-analysis moment estimators of the variance of the mixing distribution are studied.
Abstract: Theory of nonparametric mixture models algorithms the likelihood ratio test for the number of components C.A.MAN-application - meta-analysis moment estimators of the variance of the mixing distribution C.A.MAN-application - disease mapping other C.A.MAN-applications.
TL;DR: The electronic version of this article is the complete one and can be found online at: http://projecteuclid.org/eaclid/1017939249.
Abstract: © 1999 Institute of Mathematical Statistics. The electronic version of this article is the complete one and can be found online at: http://projecteuclid.org/euclid.aos/1017939249
TL;DR: A Monte Carlo investigation evaluates the comparative power of the independent samples t-test and its nonparametric counterpart, the Wilcoxon Rank-Sum (WRS) test, to violations from population normality, using three commonly occurring distributions and small sample sizes.
Book•
29 Dec 1999
TL;DR: In this paper, the BCA algorithm has been used to estimate the standard error of a BCA CI for a normal population mean and for a Normal Population Mean for a nonparametric population variance.
Abstract: PREFACE: DATA ANALYSIS BY RESAMPLING PART I: RESAMPLING CONCEPTS INTRODUCTION CONCEPTS 1: TERMS AND NOTATION Case, Attributes, Scores, and Treatments / Experimental and Observational Studies / Data Sets, Samples, and Populations / Parameters, Statistics, and Distributions / Distribution Functions APPLICATIONS 1: CASES, ATTRIBUTES, AND DISTRIBUTIONS Attributes, Scores, Groups, and Treatments / Distributions of Scores and Statistics / Exercises CONCEPTS 2: POPULATIONS AND RANDOM SAMPLES Varieties of Populations / Random Samples APPLICATIONS 2: RANDOM SAMPLING Simple Random Samples / Exercises CONCEPTS 3: STATISTICS AND SAMPLING DISTRIBUTIONS Statistics and Estimators / Accuracy of Estimation / The Sampling Distribution / Bias of an Estimator / Standard Error of a Statistic / RMS Error of an Estimator / Confidence Interval APPLICATIONS 3: SAMPLING DISTRIBUTION COMPUTATIONS Exercises CONCEPTS 4: TESTING POPULATION HYPOTHESES Population Statistical Hypotheses / Population Hypothesis Testing APPLICATIONS 4: NULL SAMPLING DISTRIBUTION P-VALUES The p-value of a Directional Test / The p-value of a Nondirectional Test / Exercises CONCEPTS 5: PARAMETRICS, PIVOTALS, AND ASYMPTOTICS The Unrealizable Sampling Distribution / Sampling Distribution of a Sample Mean / Parametric Population Distributions / Pivotal Form Statistics / Asymptotic Sampling Distributions / Limitations of the Mathematical Approach APPLICATIONS 5: CIs FOR NORMAL POPULATION MEAN AND VARIANCE CI for a Normal Population Mean / CI for a Normal Population Variance / Nonparametric CI Estimation / Exercises CONCEPTS 6: LIMITATIONS OF PARAMETRIC INFERENCE Range and Precision of Scores / Size of Population / Size of Sample / Roughness of Population Distribution / Parameters and Statistics of Interests / Scarcity of Random Samples / Resampling Inference APPLICATIONS 6: RESAMPLING APPROACHES TO INFERENCE Exercises CONCEPTS 7: THE REAL AND BOOTSTRAP WORLDS The Real World of Population Inference / The Bootstrap World of Population Inference / Real World Population Distribution Estimates / Nonparametric Population Estimates / Sample Size and Distribution Estimates APPLICATIONS 7: BOOTSTRAP POPULATION DISTRIBUTIONS Nonparametric Population Estimates / Exercises CONCEPTS 8: THE BOOTSTRAP SAMPLING DISTRIBUTION The Bootstrap Conjecture / Complete Bootstrap Sampling Distributions / Monte Carlo Bootstrap Estimate of Standard Error / The Bootstrap Estimate of Bias / Simple Bootstrap CI Estimates APPLICATIONS 8: BOOTSTRAP SE, BIAS, AND CI ESTIMATES Example / Exercises CONCEPTS 9: BETTER BOOTSTRAP CIs: THE BOOTSTRAP-T Pivotal Form Statistics / The Bootstrap-t Pivotal Transformation / Forming Bootstrap-t CIs / Estimating the Standard Error of an Estimate / Range of Applications of the Bootstrap-t / Iterated Bootstrap CIs APPLICATIONS 9: SE AND CIs FOR TRIMMED MEANS Definition of the Trimmed Mean / Importance of the Trimmed Mean / A Note on Outliers / Determining the Trimming Fraction / Sampling Distribution of the Trimmed Mean / Applications / Exercises CONCEPTS 10: BETTER BOOTSTRAP CIs: BCA INTERVALS Bias Corrected and Accelerated CI Estimates / Applications of BCA CI / Better Confidence Interval Estimates APPLICATIONS 10: USING CI CORRECTION FACTORS Requirements for a BCA CI / Implementations of the BCA Algorithm / Exercise CONCEPTS 11: BOOTSTRAP HYPOTHESIS TESTING CIs, Null Hypothesis Tests, and p-values / Bootstrap-t Hypothesis Testing / Bootstrap Hypothesis Testing Alternatives / CI Hypothesis Testing / Confidence Intervals or p-values? APPLICATIONS 11: BOOTSTRAP P-VALUES Computing a Bootstrap-t p-value / Fixed-alpha CIs and Hypothesis Testing / Computing a BCI CI p-Value / Exercise CONCEPTS 12: RANDOMIZED TREATMENT ASSIGNMENT Two Functions of Randomization / Randomization of Sampled Cases / Randomization of Two Available Cases / Statistical Basis for Local Casual Inference / Population Hypothesis Revisited APPLICATIONS 12: MONTE CARLO REFERENCE DISTRIBUTIONS Serum Albumen in Diabetic Mice / Resampling Stats Analysis / SC Analysis / S-Plus Analysis / Exercises CONCEPTS 13: STRATEGIES FOR RANDOMIZING CASES Independent Randomization of Cases / Completely Randomized Designs / Randomized Blocks Designs / Restricted Randomization / Constraints on Rerandomization APPLICATIONS 13: IMPLEMENTING CASE RERANDOMIZATION Completely Randomized Designs / Randomized Blocks Designs / Independent Randomization of Cases / Restricted Randomization / Exercises CONCEPTS 14: RANDOM TREATMENT SEQUENCES Between- and Within-Cases Designs / Randomizing the Sequence of Treatments / Casual Inference for Within-Cases Designs / Sequence of Randomization Strategies APPLICATIONS 14: RERANDOMIZING TREATMENT SEQUENCES Analysis of the AB-BA Design / Sequences of k > 2 Treatments / Exercises CONCEPTS 15: BETWEEN- AND WITHIN-CASE DECISIONS Between/Within Designs / Between/Within Resampling Strategies / Doubly Randomized Available Cases APPLICATIONS 15: INTERACTIONS AND SIMPLE EFFECTS Simple and Main Effects / Exercises CONCEPTS 16: SUBSAMPLES: STABILITY OF DESCRIPTION Nonrandom Studies and Data Sets / Local Descriptive Inference / Descriptive Stability and Case Homogeneity / Subsample Descriptions / Employing Subsample Descriptions / Subsamples and Randomized Studies APPLICATIONS 16: STRUCTURED & UNSTRUCTURED DATA Half-Samples of Unstructured Data / Subsamples of Source-Structured Cases / Exercises PART II: RESAMPLING APPLICATIONS INTRODUCTION APPLICATIONS 17: A SINGLE GROUP OF CASES Random Sample or Set of Available Cases / Typical Size of Score Distribution / Variability of Attribute Scores / Association Between Two Attributes / Exercises APPLICATIONS 18: TWO INDEPENDENT GROUPS OF CASES Constitution of Independent Groups / Location Comparisons for Samples / Magnitude Differences, CR and RB Designs / Magnitude Differences, Nonrandom Designs / Study Size / Exercises APPLICATIONS 19: MULTIPLE INDEPENDENT GROUPS Multiple Group Parametric Comparisons / Nonparametric K-group Comparison / Comparisons among Randomized Groups / Comparisons among Nonrandom Groups / Adjustment for Multiple Comparisons / Exercises APPLICATIONS 20: MULTIPLE FACTORS AND COVARIATES Two Treatment Factors / Treatment and Blocking Factors / Covariate Adjustment of Treatment Scores / Exercises APPLICATIONS 21: WITHIN-CASES TREATMENT COMPARISONS Normal Models, Univariate and Multivariate / Bootstrap Treatment Comparisons / Randomized Sequence of Treatments / Nonrandom Repeated Measures / Exercises APPLICATIONS 22: LINEAR MODELS: MEASURED RESPONSE The Parametric Linear Model / Nonparametric Linear Models / Prediction Accuracy / Linear Models for Randomized Cases / Linear Models for Nonrandom Studies / Exercises APPLICATIONS 23: CATEGORICAL RESPONSE ATTRIBUTES Cross-Classification of Cases / The 2 x 2 Table / Logistic Regression / Exercises POSTSCRIPT: GENERALITY, CAUSALITY & STABILITY Study Design and Resampling / Resampling Tools / REFERENCES / INDEX
TL;DR: A class of nonparametric estimators is introduced that serves as a consistent estimator for standard correlated survival data but not for recurrence time data and the appropriateness of the estimator is confirmed by statistical theory and simulations.
Abstract: Recurrent event data are frequently encountered in studies with longitudinal designs. Let the recurrence time be the time between two successive recurrent events. Recurrence times can be treated as a type of correlated survival data in statistical analysis. In general, because of the ordinal nature of recurrence times, statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data. Specifically, for estimating the marginal survival function, the Kaplan–Meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data. In this article we consider the problem of how to estimate the marginal survival function in nonparametric models. A class of nonparametric estimators is introduced. The appropriateness of the estimators is confirmed by statistical theory and simulations. Simulation and analysis from schizophrenia data are pre...
Journal Article•
TL;DR: It is demonstrated how to use these estimated standard errors for network statistics to compare statistics using an approximate t-test and how statistics can also be compared by another bootstrap approach that is not based on approximate normality.
Abstract: Two procedures are proposed for calculating standard errors for network statistics. Both are based on resampling of vertices: the first follows the bootstrap approach, the second the jackknife approach. In addition, we demonstrate how to use these estimated standard errors to compare statistics using an approximate t-test and how statistics can also be compared by another bootstrap approach that is not based on approximate normality.
TL;DR: A new and more general method to obtain qualitative information about returns to scale for individual observations is defined that is suitable for all reference technologies.
TL;DR: In this paper, a semiparametric estimator of a household equivalence scale under the assumption of base independence without putting any further restrictions on the shape of household Engel curves is presented.
TL;DR: The Partially Linear Additive Cox (PLAC) model as mentioned in this paper is an extension of the linear additive Cox model and allows flexible modeling of covariate effects semiparametrically.
Abstract: The partly linear additive Cox model is an extension of the (linear) Cox model and allows flexible modeling of covariate effects semiparametrically. We study asymptotic properties of the maximum partial likelihood estimator of this model with right-censored data using polynomial splines. We show that, with a range of choices of the smoothing parameter (the number of spline basis functions) required for estimation of the nonparametric components, the estimator of the finite-dimensional regression parameter is root-$n$ consistent, asymptotically normal and achieves the semiparametric information bound. Rates of convergence for the estimators of the nonparametric components are obtained. They are comparable to the rates in nonparametric regression. Implementation of the estimation approach can be done easily and is illustrated by using a simulated example.
Posted Content•
TL;DR: In this paper, a semiparametric regression model is proposed to model the relationship between sales and price discounts. But the model suffers from the curse of dimensionality and cannot capture the nonlinearities and interactions in the relationship.
Abstract: The marketing literature suggests several phenomena that may contribute to the shape of the relationship between sales and price discounts. These phenomena can produce severe nonlinearities and interactions in the curves, and we argue that those are best captured with a flexible approach. Since a fully nonparametric regression model suffers from the curse of dimensionality, we propose a semiparametric regression model. Store-level sales over time is modeled as a nonparametric function of own-and cross-item price discounts, and a parametric function of other predictors (all indicator variables). We compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain better performance on average. The results for three product categories indicate a.o. threshold- and saturation effects for both own- and cross-item temporary price cuts. We also show how the own-item curve depends on other items’ price discounts (flexible interaction effects). In a separate analysis, we show how the shape of the deal effect curve depends on own-item promotion signals. Our results indicate that prevailing methods for the estimation of deal effects on sales are inadequate.
Book•
01 Nov 1999
TL;DR: In this article, the authors discuss the reasons why the social researcher uses statistics and apply statistics to research problems in social science. But they do not discuss how to apply statistics in the context of research problems.
Abstract: Brief Table of Contents: Chapter 1: Why the Social Researcher Uses Statistics PART ONE: Description Chapter 2: Organizing the Data Chapter 3: Measures of Central Tendency Chapter 4: Measures of Variability PART TWO: From Description to Decision Making Chapter 5: Probability and the Normal Curve Chapter 6: Samples and Populations PART THREE: Decision Making Chapter 7: Testing Differences between Means Chapter 8: Analysis of Variance Chapter 9: Nonparametric Tests of Significance PART FOUR: From Decision Making to Association Chapter 10: Correlation Chapter 11: Regression Analysis Chapter 12: Nonparametric Measures of Correlation PART FIVE: Applying Statistics Chapter 13: Choosing Statistical Procedures for Research Problems APPENDICES Appendix A Introduction to SPSS Appendix B A Review of Some Fundamentals of Mathematics Appendix C Tables Appendix D List of Formulas Glossary Answers to Problems Index
TL;DR: In this paper, four different interpolation procedures were evaluated and the accuracy of different procedures was found to vary with size intervals between measured points of the particle-size distribution, and the similarity procedure was capable of giving the most accurate interpolations.