Nonparametric Statistics with Applications to Science and Engineering with R

ISBN-13: 9781119268130 / Angielski / Twarda / 2022 / 430 str.

Paul H. Kvam;Brani Vidakovic

Opis

This book presents modern nonparametric statistics from a practical point of view. This new edition includes custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible. Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R's powerful graphic systems, such as ggplot2 package and R base graphic system. Following an introduction and a discussion of the basics of probability, statistics, and Bayesian statistics, the book discusses order statistics, Kolmogorov-Smirnov test statistic, rank tests, and designed experiments. Next, categorical data, estimating distribution functions, and density estimation is examined. Least squares regression is covered, along with curve fitting techniques, wavelets, and bootstrap sampling. Other topics examined include EM algorithm, statistical learning, nonparametric Bayes, and WinBUGS. This book will be of interest to graduate students in engineering and the physical and mathematical sciences as well as researchers who need a more comprehensive, but succinct understanding of modern nonparametric statistical methods.

Spis treści

Preface xi1 Introduction 11.1 Efficiency of Nonparametric Methods 21.2 Overconfidence Bias 41.3 Computing with R 51.4 Exercises 6References 72 Probability Basics 92.1 Helpful Functions 102.2 Events, Probabilities and Random Variables 122.3 Numerical Characteristics of Random Variables 132.4 Discrete Distributions 142.5 Continuous Distributions 182.6 Mixture Distributions 242.7 Exponential Family of Distributions 262.8 Stochastic Inequalities 262.9 Convergence of Random Variables 282.10 Exercises 32References 343 Statistics Basics 353.1 Estimation 363.2 Empirical Distribution Function 363.3 Statistical Tests 383.4 Confidence Intervals 413.5 Likelihood 453.6 Exercises 49References 514 Bayesian Statistics 534.1 The Bayesian Paradigm 534.2 Ingredients for Bayesian Inference 544.3 Point Estimation 584.4 Interval Estimation: Credible Sets 604.5 Bayesian Testing 624.6 Bayesian Prediction 654.7 Bayesian Computation and Use of WinBUGS 674.8 Exercises 69References 735 Order Statistics 755.1 Joint Distributions of Order Statistics 775.2 Sample Quantiles 795.3 Tolerance Intervals 795.4 Asymptotic Distributions of Order Statistics 815.5 Extreme Value Theory 825.6 Ranked Set Sampling 835.7 Exercises 84References 876 Goodness of Fit 896.1 KolmogorovSmirnov Test Statistic 906.2 Smirnov Test to Compare Two Distributions 966.3 Specialized Tests 996.4 Probability Plotting 1066.5 Runs Test 1126.6 Meta Analysis 1176.7 Exercises 121References 1257 Rank Tests 1277.1 Properties of Ranks 1287.2 Sign Test 1307.3 Spearman Coefficient of Rank Correlation 1357.4 Wilcoxon Signed Rank Test 1397.5 Wilcoxon (TwoSample) Sum Rank Test 1427.6 MannWhitney U Test 1447.7 Test of Variances 1467.8 Walsh Test for Outliers 1477.9 Exercises 148References 1538 Designed Experiments 1558.1 KruskalWallis Test 1568.2 Friedman Test 1608.3 Variance Test for Several Populations 1658.4 Exercises 166References 1699 Categorical Data 1719.1 ChiSquare and GoodnessofFit 1729.2 Contingency Tables 1789.3 Fisher Exact Test 1839.4 Mc Nemar Test 1849.5 Cochran's Test 1869.6 MantelHaenszel Test 1889.7 CLT for Multinomial Probabilities 1909.8 Simpson's Paradox 1919.9 Exercises 193References 20010 Estimating Distribution Functions 20310.1 Introduction 20310.2 Nonparametric Maximum Likelihood 20410.3 KaplanMeier Estimator 20510.4 Confidence Interval for F 21310.5 Plugin Principle 21410.6 SemiParametric Inference 21510.7 Empirical Processes 21710.8 Empirical Likelihood 21810.9 Exercises 221References 22311 Density Estimation 22511.1 Histogram 22611.2 Kernel and Bandwidth 22811.3 Exercises 235References 23612 Beyond Linear Regression 23712.1 Least Squares Regression 23812.2 Rank Regression 23912.3 Robust Regression 24312.4 Isotonic Regression 24912.5 Generalized Linear Models 25212.6 Exercises 259References 26113 Curve Fitting Techniques 26313.1 Kernel Estimators 26513.2 Nearest Neighbor Methods 26913.3 Variance Estimation 27213.4 Splines 27313.5 Summary 27913.6 Exercises 279References 28214 Wavelets 28514.1 Introduction to Wavelets 28514.2 How Do the Wavelets Work? 28814.3 Wavelet Shrinkage 29514.4 Exercises 304References 30515 Bootstrap 30715.1 Bootstrap Sampling 30715.2 Nonparametric Bootstrap 30915.3 Bias Correction for Nonparametric Intervals 31515.4 The Jackknife 31715.5 Bayesian Bootstrap 31815.6 Permutation Tests 32015.7 More on the Bootstrap 32415.8 Exercises 325References 32716 EM Algorithm 32916.1 Fisher's Example 33116.2 Mixtures 33316.3 EM and Order Statistics 33816.4 MAP via EM 33916.5 Infection Pattern Estimation 34116.6 Exercises 342References 34317 Statistical Learning 34517.1 Discriminant Analysis 34617.2 Linear Classification Models 34917.3 Nearest Neighbor Classification 35317.4 Neural Networks 35517.5 Binary Classification Trees 36117.6 Exercises 368References 36918 Nonparametric Bayes 37118.1 Dirichlet Processes 37218.2 Bayesian Categorical Models 38018.3 Infinitely Dimensional Problems 38318.4 Exercises 387References 389A WinBUGS 392A.1 Using WinBUGS 393A.2 BuiltinFunctions 396B R Coding 400B.1 Programming in R 400B.2 Basics of R 402B.3 R Commands 403B.4 R for Statistics 405R Index 411Author Index 414Subject Index 418

O autorze

Paul Kvam is professor in the Department of Mathematics, University of Richmond, USA. He received his Ph.D. from University of California, Davis.Brani Vidakovic is professor in the Department of Statistics, Texas A&M University, USA. He received his Ph.D from Purdue University.Seong-joon Kim is assistant professor in Department of Industrial Engineering, Chosun University, South Korea. He received his Ph.D. from Hanyang University.