Cover image for Nonparametric statistics with applications to science and engineering
Title:
Nonparametric statistics with applications to science and engineering
Personal Author:
Series:
Wiley series in probability and statistics
Publication Information:
Hoboken, NJ : Wiley-Interscience, 2007
Physical Description:
xiv, 420 p. : ill. ; 24 cm.
ISBN:
9780470081471

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30000010178037 QA278.8 K82 2007 Open Access Book
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Summary

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


Table of Contents

Prefacep. xi
1 Introductionp. 1
1.1 Efficiency of Nonparametric Methodsp. 3
1.2 Overconfidence Biasp. 5
1.3 Computing with MATLABp. 5
1.4 Exercisesp. 7
Referencesp. 7
2 Probability Basicsp. 9
2.1 Helpful Functionsp. 9
2.2 Events, Probabilities and Random Variablesp. 11
2.3 Numerical Characteristics of Random Variablesp. 12
2.4 Discrete Distributionsp. 14
2.5 Continuous Distributionsp. 17
2.6 Mixture Distributionsp. 23
2.7 Exponential Family of Distributionsp. 25
2.8 Stochastic Inequalitiesp. 26
2.9 Convergence of Random Variablesp. 28
2.10 Exercisesp. 31
Referencesp. 32
3 Statistics Basicsp. 33
3.1 Estimationp. 33
3.2 Empirical Distribution Functionp. 34
3.3 Statistical Testsp. 36
3.4 Exercisesp. 45
Referencesp. 46
4 Bayesian Statisticsp. 47
4.1 The Bayesian Paradigmp. 47
4.2 Ingredients for Bayesian Inferencep. 48
4.3 Bayesian Computation and Use of WinBUGSp. 61
4.4 Exercisesp. 63
Referencesp. 67
5 Order Statisticsp. 69
5.1 Joint Distributions of Order Statisticsp. 70
5.2 Sample Quantilesp. 72
5.3 Tolerance Intervalsp. 73
5.4 Asymptotic Distributions of Order Statisticsp. 75
5.5 Extreme Value Theoryp. 76
5.6 Ranked Set Samplingp. 76
5.7 Exercisesp. 77
Referencesp. 80
6 Goodness of Fitp. 81
6.1 Kolmogorov-Smirnov Test Statisticp. 82
6.2 Smirnov Test to Compare Two Distributionsp. 86
6.3 Specialized Testsp. 89
6.4 Probability Plottingp. 97
6.5 Runs Testp. 100
6.6 Meta Analysisp. 106
6.7 Exercisesp. 109
Referencesp. 113
7 Rank Testsp. 115
7.1 Properties of Ranksp. 117
7.2 Sign Testp. 118
7.3 Spearman Coefficient of Rank Correlationp. 122
7.4 Wilcoxon Signed Rank Testp. 126
7.5 Wilcoxon (Two-Sample) Sum Rank Testp. 129
7.6 Mann-Whitney U Testp. 131
7.7 Test of Variancesp. 133
7.8 Exercisesp. 135
Referencesp. 139
8 Designed Experimentsp. 141
8.1 Kruskal-Wallis Testp. 141
8.2 Friedman Testp. 145
8.3 Variance Test for Several Populationsp. 148
8.4 Exercisesp. 149
Referencesp. 152
9 Categorical Datap. 153
9.1 Chi-Square and Goodness-of-Fitp. 155
9.2 Contingency Tablesp. 159
9.3 Fisher Exact Testp. 163
9.4 MC Nemar Testp. 164
9.5 Cochran's Testp. 167
9.6 Mantel-Haenszel Testp. 167
9.7 CLT for Multinomial Probabilitiesp. 171
9.8 Simpson's Paradoxp. 172
9.9 Exercisesp. 173
Referencesp. 180
10 Estimating Distribution Functionsp. 183
10.1 Introductionp. 183
10.2 Nonparametric Maximum Likelihoodp. 184
10.3 Kaplan-Meier Estimatorp. 185
10.4 Confidence Interval for Fp. 192
10.5 Plug-in Principlep. 193
10.6 Semi-Parametric Inferencep. 195
10.7 Empirical Processesp. 197
10.8 Empirical Likelihoodp. 198
10.9 Exercisesp. 201
Referencesp. 203
11 Density Estimationp. 205
11.1 Histogramp. 206
11.2 Kernel and Bandwidthp. 207
11.3 Exercisesp. 213
Referencesp. 215
12 Beyond Linear Regressionp. 217
12.1 Least Squares Regressionp. 218
12.2 Rank Regressionp. 219
12.3 Robust Regressionp. 221
12.4 Isotonic Regressionp. 227
12.5 Generalized Linear Modelsp. 230
12.6 Exercisesp. 237
Referencesp. 240
13 Curve Fitting Techniquesp. 241
13.1 Kernel Estimatorsp. 243
13.2 Nearest Neighbor Methodsp. 247
13.3 Variance Estimationp. 249
13.4 Splinesp. 251
13.5 Summaryp. 257
13.6 Exercisesp. 258
Referencesp. 260
14 Waveletsp. 263
14.1 Introduction to Waveletsp. 263
14.2 How Do the Wavelets Work?p. 266
14.3 Wavelet Shrinkagep. 273
14.4 Exercisesp. 281
Referencesp. 283
15 Bootstrapp. 285
15.1 Bootstrap Samplingp. 285
15.2 Nonparametric Bootstrapp. 287
15.3 Bias Correction for Nonparametric Intervalsp. 292
15.4 The Jackknifep. 295
15.5 Bayesian Bootstrapp. 296
15.6 Permutation Testsp. 298
15.7 More on the Bootstrapp. 302
15.8 Exercisesp. 302
Referencesp. 304
16 EM Algorithmp. 307
16.1 Fisher's Examplep. 309
16.2 Mixturesp. 311
16.3 EM and Order Statisticsp. 315
16.4 MAP via EMp. 317
16.5 Infection Pattern Estimationp. 318
16.6 Exercisesp. 319
Referencesp. 321
17 Statistical Learningp. 323
17.1 Discriminant Analysisp. 324
17.2 Linear Classification Modelsp. 326
17.3 Nearest Neighbor Classificationp. 329
17.4 Neural Networksp. 333
17.5 Binary Classification Treesp. 338
17.6 Exercisesp. 346
Referencesp. 346
18 Nonparametric Bayesp. 349
18.1 Dirichlet Processesp. 350
18.2 Bayesian Categorical Modelsp. 357
18.3 Infinitely Dimensional Problemsp. 360
18.4 Exercisesp. 364
Referencesp. 366
A MATLABp. 369
A.1 Using MATLABp. 369
A.2 Matrix Operationsp. 372
A.3 Creating Functions in MATLABp. 374
A.4 Importing and Exporting Datap. 375
A.5 Data Visualizationp. 380
A.6 Statisticsp. 386
B WinBUGSp. 397
B.1 Using WinBUGSp. 398
B.2 Built-in Functionsp. 401
MATLAB Indexp. 405
Author Indexp. 409
Subject Indexp. 413