Nonparametric Statistics with Applications to Science and Engineering

Nonparametric Statistics with Applications to Science and Engineering......Page 4
Contents......Page 8
Preface......Page 14
1 Introduction......Page 18
1.1 Efficiency of Nonparametric Methods......Page 20
1.3 Computing with MATLAB......Page 22
References......Page 24
2.1 Helpful Functions......Page 26
2.2 Events, Probabilities and Random Variables......Page 28
2.3 Numerical Characteristics of Random Variables......Page 29
2.4 Discrete Distributions......Page 31
2.5 Continuous Distributions......Page 34
2.6 Mixture Distributions......Page 40
2.7 Exponential Family of Distributions......Page 42
2.8 Stochastic Inequalities......Page 43
2.9 Convergence of Random Variables......Page 45
2.10 Exercises......Page 48
References......Page 49
3.1 Estimation......Page 50
3.2 Empirical Distribution Function......Page 51
3.3 Statistical Tests......Page 53
3.4 Exercises......Page 62
References......Page 63
4.1 The Bayesian Paradigm......Page 64
4.2 Ingredients for Bayesian Inference......Page 65
4.3 Bayesian Computation and Use of WinBUGS......Page 78
4.4 Exercises......Page 80
References......Page 84
5 Order Statistics......Page 86
5.1 Joint Distributions of Order Statistics......Page 87
5.2 Sample Quantiles......Page 89
5.3 Tolerance Intervals......Page 90
5.4 Asymptotic Distributions of Order Statistics......Page 92
5.6 Ranked Set Sampling......Page 93
5.7 Exercises......Page 94
References......Page 97
6 Goodness of Fit......Page 98
6.1 Kolmogorov-Smirnov Test Statistic......Page 99
6.2 Smirnov Test to Compare Two Distributions......Page 103
6.3 Specialized Tests......Page 106
6.4 Probability Plotting......Page 114
6.5 Runs Test......Page 117
6.6 Meta Analysis......Page 123
6.7 Exercises......Page 126
References......Page 130
7 Rank Tests......Page 132
7.1 Properties of Ranks......Page 134
7.2 Sign Test......Page 135
7.3 Spearman Coefficient of Rank Correlation......Page 139
7.4 Wilcoxon Signed Rank Test......Page 143
7.5 Wilcoxon (Two-Sample) Sum Rank Test......Page 146
7.6 Mann-Whitney U Test......Page 148
7.7 Test of Variances......Page 150
7.8 Exercises......Page 152
References......Page 156
8.1 Kruskal-Wallis Test......Page 158
8.2 Friedman Test......Page 162
8.3 Variance Test for Several Populations......Page 165
8.4 Exercises......Page 166
References......Page 169
9 Categorical Data......Page 170
9.1 Chi-square and Goodness-of-Fit......Page 172
9.2 Contingency Tables......Page 176
9.3 Fisher Exact Test......Page 180
9.4 MC Nemar Test......Page 181
9.6 Mantel-Haenszel Test......Page 184
9.7 CLT for Multinomial Probabilities......Page 188
9.8 Simpson’s Paradox......Page 189
9.9 Exercises......Page 190
References......Page 197
10.1 Introduction......Page 200
10.2 Nonparametric Maximum Likelihood......Page 201
10.3 Kaplan-Meier Estimator......Page 202
10.4 Confidence Interval for F......Page 209
10.5 Plug-in Principle......Page 210
10.6 Semi-Parametric Inference......Page 212
10.7 Empirical Processes......Page 214
10.8 Empirical Likelihood......Page 215
10.9 Exercises......Page 218
References......Page 220
11 Density Estimation......Page 222
11.1 Histogram......Page 223
11.2 Kernel and Bandwidth......Page 224
11.3 Exercises......Page 230
References......Page 232
12 Beyond Linear Regression......Page 234
12.1 Least Squares Regression......Page 235
12.2 Rank Regression......Page 236
12.3 Robust Regression......Page 238
12.4 Isotonic Regression......Page 244
12.5 Generalized Linear Models......Page 247
12.6 Exercises......Page 254
References......Page 257
13 Curve Fitting Techniques......Page 258
13.1 Kernel Estimators......Page 260
13.2 Nearest Neighbor Methods......Page 264
13.3 Variance Estimation......Page 266
13.4 Splines......Page 268
13.5 Summary......Page 274
13.6 Exercises......Page 275
References......Page 277
14.1 Introduction to Wavelets......Page 280
14.2 How Do the Wavelets Work?......Page 283
14.3 Wavelet Shrinkage......Page 290
14.4 Exercises......Page 298
References......Page 300
15.1 Bootstrap Sampling......Page 302
15.2 Nonparametric Bootstrap......Page 304
15.3 Bias Correction for Nonparametric Intervals......Page 309
15.4 The Jackknife......Page 312
15.5 Bayesian Bootstrap......Page 313
15.6 Permutation Tests......Page 315
15.8 Exercises......Page 319
References......Page 321
16 EM Algorithm......Page 324
16.1 Fisher’s Example......Page 326
16.2 Mixtures......Page 328
16.3 EM and Order Statistics......Page 332
16.4 MAP via EM......Page 334
16.5 Infection Pattern Estimation......Page 335
16.6 Exercises......Page 336
References......Page 338
17 Statistical Learning......Page 340
17.1 Discriminant Analysis......Page 341
17.2 Linear Classification Models......Page 343
17.3 Nearest Neighbor Classification......Page 346
17.4 Neural Networks......Page 350
17.5 Binary Classification Trees......Page 355
References......Page 363
18 Nonparametric Bayes......Page 366
18.1 Dirichlet Processes......Page 367
18.2 Bayesian Categorical Models......Page 374
18.3 Infinitely Dimensional Problems......Page 377
18.4 Exercises......Page 381
References......Page 383
A.1 Using MATLAB......Page 386
A.2 Matrix Operations......Page 389
A.3 Creating Functions in MATLAB......Page 391
A.4 Importing and Exporting Data......Page 392
A.5 Data Visualization......Page 397
A.6 Statistics......Page 403
B WinBUGS......Page 414
B.1 Using WinBUGS......Page 415
B.2 Built-in Functions......Page 418
MATLAB Index......Page 422
Author Index......Page 426
Subject Index......Page 430