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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010178037 | QA278.8 K82 2007 | Open Access Book | Book | Searching... |

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### Summary

### Summary

A thorough and definitive book that fully addresses traditional and modern-day topics of nonparametric statistics

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

### Table of Contents

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 |