Description
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
