Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code
Nonparametric Statistics with Applications to Science and Engineering with R presents modern nonparametric statistics from a practical point of view, with the newly revised edition including 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.
The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. New examples and exercises that enable readers to gain a deeper insight into nonparametric statistics and increase their comprehension are also included.
Some of the sample topics discussed in Nonparametric Statistics with Applications to Science and Engineering with R include: - Basics of probability, statistics, Bayesian statistics, order statistics, Kolmogorov-Smirnov test statistics, rank tests, and designed experiments - Categorical data, estimating distribution functions, density estimation, least squares regression, curve fitting techniques, wavelets, and bootstrap sampling - EM algorithms, statistical learning, nonparametric Bayes, WinBUGS, properties of ranks, and Spearman coefficient of rank correlation - Chi-square and goodness-of-fit, contingency tables, Fisher exact test, MC Nemar test, Cochran’s test, Mantel-Haenszel test, and Empirical Likelihood
Nonparametric Statistics with Applications to Science and Engineering with R is a highly valuable resource for 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.
Table of Contents
Preface xi
1 Introduction 1
1.1 Efficiency of Nonparametric Methods 2
1.2 Overconfidence Bias 4
1.3 Computing with R 5
1.4 Exercises 6
References 7
2 Probability Basics 9
2.1 Helpful Functions 10
2.2 Events, Probabilities and Random Variables 12
2.3 Numerical Characteristics of Random Variables 13
2.4 Discrete Distributions 14
2.5 Continuous Distributions 18
2.6 Mixture Distributions 24
2.7 Exponential Family of Distributions 26
2.8 Stochastic Inequalities 26
2.9 Convergence of Random Variables 28
2.10 Exercises 32
References 34
3 Statistics Basics 35
3.1 Estimation 36
3.2 Empirical Distribution Function 36
3.3 Statistical Tests 38
3.4 Confidence Intervals 41
3.5 Likelihood 45
3.6 Exercises 49
References 51
4 Bayesian Statistics 53
4.1 The Bayesian Paradigm 53
4.2 Ingredients for Bayesian Inference 54
4.3 Point Estimation 58
4.4 Interval Estimation: Credible Sets 60
4.5 Bayesian Testing 62
4.6 Bayesian Prediction 65
4.7 Bayesian Computation and Use of WinBUGS 67
4.8 Exercises 69
References 73
5 Order Statistics 75
5.1 Joint Distributions of Order Statistics 77
5.2 Sample Quantiles 79
5.3 Tolerance Intervals 79
5.4 Asymptotic Distributions of Order Statistics 81
5.5 Extreme Value Theory 82
5.6 Ranked Set Sampling 83
5.7 Exercises 84
References 87
6 Goodness of Fit 89
6.1 KolmogorovSmirnov Test Statistic 90
6.2 Smirnov Test to Compare Two Distributions 96
6.3 Specialized Tests 99
6.4 Probability Plotting 106
6.5 Runs Test 112
6.6 Meta Analysis 117
6.7 Exercises 121
References 125
7 Rank Tests 127
7.1 Properties of Ranks 128
7.2 Sign Test 130
7.3 Spearman Coefficient of Rank Correlation 135
7.4 Wilcoxon Signed Rank Test 139
7.5 Wilcoxon (TwoSample) Sum Rank Test 142
7.6 MannWhitney U Test 144
7.7 Test of Variances 146
7.8 Walsh Test for Outliers 147
7.9 Exercises 148
References 153
8 Designed Experiments 155
8.1 KruskalWallis Test 156
8.2 Friedman Test 160
8.3 Variance Test for Several Populations 165
8.4 Exercises 166
References 169
9 Categorical Data 171
9.1 ChiSquare and GoodnessofFit 172
9.2 Contingency Tables 178
9.3 Fisher Exact Test 183
9.4 Mc Nemar Test 184
9.5 Cochran’s Test 186
9.6 MantelHaenszel Test 188
9.7 CLT for Multinomial Probabilities 190
9.8 Simpson’s Paradox 191
9.9 Exercises 193
References 200
10 Estimating Distribution Functions 203
10.1 Introduction 203
10.2 Nonparametric Maximum Likelihood 204
10.3 KaplanMeier Estimator 205
10.4 Confidence Interval for F 213
10.5 Plugin Principle 214
10.6 SemiParametric Inference 215
10.7 Empirical Processes 217
10.8 Empirical Likelihood 218
10.9 Exercises 221
References 223
11 Density Estimation 225
11.1 Histogram 226
11.2 Kernel and Bandwidth 228
11.3 Exercises 235
References 236
12 Beyond Linear Regression 237
12.1 Least Squares Regression 238
12.2 Rank Regression 239
12.3 Robust Regression 243
12.4 Isotonic Regression 249
12.5 Generalized Linear Models 252
12.6 Exercises 259
References 261
13 Curve Fitting Techniques 263
13.1 Kernel Estimators 265
13.2 Nearest Neighbor Methods 269
13.3 Variance Estimation 272
13.4 Splines 273
13.5 Summary 279
13.6 Exercises 279
References 282
14 Wavelets 285
14.1 Introduction to Wavelets 285
14.2 How Do the Wavelets Work? 288
14.3 Wavelet Shrinkage 295
14.4 Exercises 304
References 305
15 Bootstrap 307
15.1 Bootstrap Sampling 307
15.2 Nonparametric Bootstrap 309
15.3 Bias Correction for Nonparametric Intervals 315
15.4 The Jackknife 317
15.5 Bayesian Bootstrap 318
15.6 Permutation Tests 320
15.7 More on the Bootstrap 324
15.8 Exercises 325
References 327
16 EM Algorithm 329
16.1 Fisher’s Example 331
16.2 Mixtures 333
16.3 EM and Order Statistics 338
16.4 MAP via EM 339
16.5 Infection Pattern Estimation 341
16.6 Exercises 342
References 343
17 Statistical Learning 345
17.1 Discriminant Analysis 346
17.2 Linear Classification Models 349
17.3 Nearest Neighbor Classification 353
17.4 Neural Networks 355
17.5 Binary Classification Trees 361
17.6 Exercises 368
References 369
18 Nonparametric Bayes 371
18.1 Dirichlet Processes 372
18.2 Bayesian Categorical Models 380
18.3 Infinitely Dimensional Problems 383
18.4 Exercises 387
References 389
A WinBUGS 392
A.1 Using WinBUGS 393
A.2 Builtin
Functions 396
B R Coding 400
B.1 Programming in R 400
B.2 Basics of R 402
B.3 R Commands 403
B.4 R for Statistics 405
R Index 411
Author Index 414
Subject Index 418
