Nonparametric statistics with applications to science and engineering

This book presents a practical approach to nonparametric statistical analysis and provides comprehensive coverage of both established and newly developed methods. With the use of MATLAB, the authors present information on theorems and rank tests in an applied fashion, with an emphasis on modern methods in regression and curve fitting, bootstrap confidence intervals, splines, wavelets, empirical likelihood, and goodness-of-fit testing.

Nonparametric Statistics with Applications to Science and Engineering begins with succinct coverage of basic results for order statistics, methods of

categorical data analysis, nonparametric regression, and curve fitting methods. The authors then focus on nonparametric procedures that are becoming more relevant to engineering researchers and practitioners. The important fundamental materials needed to effectively learn and apply the discussed methods are also provided throughout the book.

Complete with exercise sets, chapter reviews, and a related Web site that features downloadable MATLAB applications, this book is an essential textbook for graduate courses in engineering and the physical sciences and also serves as a valuable reference for researchers who seek a more comprehensive understanding of modern nonparametric statistical methods.

Author Notes

Paul H. Kvam, PhD, is Professor of Industrial and Systems Engineering at Georgia Institute of Technology
Brani Vidakovic, PhD, is Professor of Statistics and Director of the Center for Bioengineering Statistics at The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology

Preface	p. xi
1 Introduction	p. 1
1.1 Efficiency of Nonparametric Methods	p. 3
1.2 Overconfidence Bias	p. 5
1.3 Computing with MATLAB	p. 5
1.4 Exercises	p. 7
References	p. 7
2 Probability Basics	p. 9
2.1 Helpful Functions	p. 9
2.2 Events, Probabilities and Random Variables	p. 11
2.3 Numerical Characteristics of Random Variables	p. 12
2.4 Discrete Distributions	p. 14
2.5 Continuous Distributions	p. 17
2.6 Mixture Distributions	p. 23
2.7 Exponential Family of Distributions	p. 25
2.8 Stochastic Inequalities	p. 26
2.9 Convergence of Random Variables	p. 28
2.10 Exercises	p. 31
References	p. 32
3 Statistics Basics	p. 33
3.1 Estimation	p. 33
3.2 Empirical Distribution Function	p. 34
3.3 Statistical Tests	p. 36
3.4 Exercises	p. 45
References	p. 46
4 Bayesian Statistics	p. 47
4.1 The Bayesian Paradigm	p. 47
4.2 Ingredients for Bayesian Inference	p. 48
4.3 Bayesian Computation and Use of WinBUGS	p. 61
4.4 Exercises	p. 63
References	p. 67
5 Order Statistics	p. 69
5.1 Joint Distributions of Order Statistics	p. 70
5.2 Sample Quantiles	p. 72
5.3 Tolerance Intervals	p. 73
5.4 Asymptotic Distributions of Order Statistics	p. 75
5.5 Extreme Value Theory	p. 76
5.6 Ranked Set Sampling	p. 76
5.7 Exercises	p. 77
References	p. 80
6 Goodness of Fit	p. 81
6.1 Kolmogorov-Smirnov Test Statistic	p. 82
6.2 Smirnov Test to Compare Two Distributions	p. 86
6.3 Specialized Tests	p. 89
6.4 Probability Plotting	p. 97
6.5 Runs Test	p. 100
6.6 Meta Analysis	p. 106
6.7 Exercises	p. 109
References	p. 113
7 Rank Tests	p. 115
7.1 Properties of Ranks	p. 117
7.2 Sign Test	p. 118
7.3 Spearman Coefficient of Rank Correlation	p. 122
7.4 Wilcoxon Signed Rank Test	p. 126
7.5 Wilcoxon (Two-Sample) Sum Rank Test	p. 129
7.6 Mann-Whitney U Test	p. 131
7.7 Test of Variances	p. 133
7.8 Exercises	p. 135
References	p. 139
8 Designed Experiments	p. 141
8.1 Kruskal-Wallis Test	p. 141
8.2 Friedman Test	p. 145
8.3 Variance Test for Several Populations	p. 148
8.4 Exercises	p. 149
References	p. 152
9 Categorical Data	p. 153
9.1 Chi-Square and Goodness-of-Fit	p. 155
9.2 Contingency Tables	p. 159
9.3 Fisher Exact Test	p. 163
9.4 MC Nemar Test	p. 164
9.5 Cochran's Test	p. 167
9.6 Mantel-Haenszel Test	p. 167
9.7 CLT for Multinomial Probabilities	p. 171
9.8 Simpson's Paradox	p. 172
9.9 Exercises	p. 173
References	p. 180
10 Estimating Distribution Functions	p. 183
10.1 Introduction	p. 183
10.2 Nonparametric Maximum Likelihood	p. 184
10.3 Kaplan-Meier Estimator	p. 185
10.4 Confidence Interval for F	p. 192
10.5 Plug-in Principle	p. 193
10.6 Semi-Parametric Inference	p. 195
10.7 Empirical Processes	p. 197
10.8 Empirical Likelihood	p. 198
10.9 Exercises	p. 201
References	p. 203
11 Density Estimation	p. 205
11.1 Histogram	p. 206
11.2 Kernel and Bandwidth	p. 207
11.3 Exercises	p. 213
References	p. 215
12 Beyond Linear Regression	p. 217
12.1 Least Squares Regression	p. 218
12.2 Rank Regression	p. 219
12.3 Robust Regression	p. 221
12.4 Isotonic Regression	p. 227
12.5 Generalized Linear Models	p. 230
12.6 Exercises	p. 237
References	p. 240
13 Curve Fitting Techniques	p. 241
13.1 Kernel Estimators	p. 243
13.2 Nearest Neighbor Methods	p. 247
13.3 Variance Estimation	p. 249
13.4 Splines	p. 251
13.5 Summary	p. 257
13.6 Exercises	p. 258
References	p. 260
14 Wavelets	p. 263
14.1 Introduction to Wavelets	p. 263
14.2 How Do the Wavelets Work?	p. 266
14.3 Wavelet Shrinkage	p. 273
14.4 Exercises	p. 281
References	p. 283
15 Bootstrap	p. 285
15.1 Bootstrap Sampling	p. 285
15.2 Nonparametric Bootstrap	p. 287
15.3 Bias Correction for Nonparametric Intervals	p. 292
15.4 The Jackknife	p. 295
15.5 Bayesian Bootstrap	p. 296
15.6 Permutation Tests	p. 298
15.7 More on the Bootstrap	p. 302
15.8 Exercises	p. 302
References	p. 304
16 EM Algorithm	p. 307
16.1 Fisher's Example	p. 309
16.2 Mixtures	p. 311
16.3 EM and Order Statistics	p. 315
16.4 MAP via EM	p. 317
16.5 Infection Pattern Estimation	p. 318
16.6 Exercises	p. 319
References	p. 321
17 Statistical Learning	p. 323
17.1 Discriminant Analysis	p. 324
17.2 Linear Classification Models	p. 326
17.3 Nearest Neighbor Classification	p. 329
17.4 Neural Networks	p. 333
17.5 Binary Classification Trees	p. 338
17.6 Exercises	p. 346
References	p. 346
18 Nonparametric Bayes	p. 349
18.1 Dirichlet Processes	p. 350
18.2 Bayesian Categorical Models	p. 357
18.3 Infinitely Dimensional Problems	p. 360
18.4 Exercises	p. 364
References	p. 366
A MATLAB	p. 369
A.1 Using MATLAB	p. 369
A.2 Matrix Operations	p. 372
A.3 Creating Functions in MATLAB	p. 374
A.4 Importing and Exporting Data	p. 375
A.5 Data Visualization	p. 380
A.6 Statistics	p. 386
B WinBUGS	p. 397
B.1 Using WinBUGS	p. 398
B.2 Built-in Functions	p. 401
MATLAB Index	p. 405
Author Index	p. 409
Subject Index	p. 413

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Table of Contents