Nonparametric Statistics With Applications to

This book presents modern nonparametric statistics from a practical point of view. It is primarily intended for use with engineers and scientists. While the book covers the necessary theorems and methods of rank tests in an applied fashion, the novelty lies in its emphasis on modern nonparametric methods in regression and curve fitting, bootstrap confidence intervals, splines, wavelets, empirical and nonparametric likelihood, and goodness of fit testing. MATLAB is the computing and programming system of choice throughout the book because of its special applicability for research analysis and simulation.

Paul H. Kvam, PhD, is Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research interests include nonparametric estimation, statistical reliability with applications to engineering, and analysis of complex and dependent systems. He has written over fifty refereed articles and was named a Fellow of the American Statistical Association in 2006.

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. He has authored or co-authored three books and has published more than four dozen refereed articles. His areas of interest include wavelets, Bayesian inference, biostatistics, statistical methods in environmental research, and statistical education.

Preface	p. xi
Introduction	p. 1
Efficiency of Nonparametric Methods	p. 3
Overconfidence Bias	p. 5
Computing with MATLAB	p. 5
Exercises	p. 7
References	p. 7
Probability Basics	p. 9
Helpful Functions	p. 9
Events, Probabilities and Random Variables	p. 11
Numerical Characteristics of Random Variables	p. 12
Discrete Distributions	p. 14
Continuous Distributions	p. 17
Mixture Distributions	p. 23
Exponential Family of Distributions	p. 25
Stochastic Inequalities	p. 26
Convergence of Random Variables	p. 28
Exercises	p. 31
References	p. 32
Statistics Basics	p. 33
Estimation	p. 33
Empirical Distribution Function	p. 34
Statistical Tests	p. 36
Exercises	p. 45
References	p. 46
Bayesian Statistics	p. 47
The Bayesian Paradigm	p. 47
Ingredients for Bayesian Inference	p. 48
Bayesian Computation and Use of WinBUGS	p. 61
Exercises	p. 63
References	p. 67
Order Statistics	p. 69
Joint Distributions of Order Statistics	p. 70
Sample Quantiles	p. 72
Tolerance Intervals	p. 73
Asymptotic Distributions of Order Statistics	p. 75
Extreme Value Theory	p. 76
Ranked Set Sampling	p. 76
Exercises	p. 77
References	p. 80
Goodness of Fit	p. 81
Kolmogorov-Smirnov Test Statistic	p. 82
Smirnov Test to Compare Two Distributions	p. 86
Specialized Tests	p. 89
Probability Plotting	p. 97
Runs Test	p. 100
Meta Analysis	p. 106
Exercises	p. 109
References	p. 113
Rank Tests	p. 115
Properties of Ranks	p. 117
Sign Test	p. 118
Spearman Coefficient of Rank Correlation	p. 122
Wilcoxon Signed Rank Test	p. 126
Wilcoxon (Two-Sample) Sum Rank Test	p. 129
Mann-Whitney U Test	p. 131
Test of Variances	p. 133
Exercises	p. 135
References	p. 139
Designed Experiments	p. 141
Kruskal-Wallis Test	p. 141
Friedman Test	p. 145
Variance Test for Several Populations	p. 148
Exercises	p. 149
References	p. 152
Categorical Data	p. 153
Chi-Square and Goodness-of-Fit	p. 155
Contingency Tables	p. 159
Fisher Exact Test	p. 163
MC Nemar Test	p. 164
Cochran's Test	p. 167
Mantel-Haenszel Test	p. 167
CLT for Multinomial Probabilities	p. 171
Simpson's Paradox	p. 172
Exercises	p. 173
References	p. 180
Estimating Distribution Functions	p. 183
Introduction	p. 183
Nonparametric Maximum Likelihood	p. 184
Kaplan-Meier Estimator	p. 185
Confidence Interval for F	p. 192
Plug-in Principle	p. 193
Semi-Parametric Inference	p. 195
Empirical Processes	p. 197
Empirical Likelihood	p. 198
Exercises	p. 201
References	p. 203
Density Estimation	p. 205
Histogram	p. 206
Kernel and Bandwidth	p. 207
Exercises	p. 213
References	p. 215
Beyond Linear Regression	p. 217
Least Squares Regression	p. 218
Rank Regression	p. 219
Robust Regression	p. 221
Isotonic Regression	p. 227
Generalized Linear Models	p. 230
Exercises	p. 237
References	p. 240
Curve Fitting Techniques	p. 241
Kernel Estimators	p. 243
Nearest Neighbor Methods	p. 247
Variance Estimation	p. 249
Splines	p. 251
Summary	p. 257
Exercises	p. 258
References	p. 260
Wavelets	p. 263
Introduction to Wavelets	p. 263
How Do the Wavelets Work?	p. 266
Wavelet Shrinkage	p. 273
Exercises	p. 281
References	p. 283
Bootstrap	p. 285
Bootstrap Sampling	p. 285
Nonparametric Bootstrap	p. 287
Bias Correction for Nonparametric Intervals	p. 292
The Jackknife	p. 295
Bayesian Bootstrap	p. 296
Permutation Tests	p. 298
More on the Bootstrap	p. 302
Exercises	p. 302
References	p. 304
EM Algorithm	p. 307
Fisher's Example	p. 309
Mixtures	p. 311
EM and Order Statistics	p. 315
MAP via EM	p. 317
Infection Pattern Estimation	p. 318
Exercises	p. 319
References	p. 321
Statistical Learning	p. 323
Discriminant Analysis	p. 324
Linear Classification Models	p. 326
Nearest Neighbor Classification	p. 329
Neural Networks	p. 333
Binary Classification Trees	p. 338
Exercises	p. 346
References	p. 346
Nonparametric Bayes	p. 349
Dirichlet Processes	p. 350
Bayesian Categorical Models	p. 357
Infinitely Dimensional Problems	p. 360
Exercises	p. 364
References	p. 366
MATLAB	p. 369
Using MATLAB	p. 369
Matrix Operations	p. 372
Creating Functions in MATLAB	p. 374
Importing and Exporting Data	p. 375
Data Visualization	p. 380
Statistics	p. 386
WinBUGS	p. 397
Using WinBUGS	p. 398
Built-in Functions	p. 401
MATLAB Index	p. 405
Author Index	p. 409
Subject Index	p. 413
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Nonparametric Statistics With Applications to Science and Engineering

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