Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

by Paul Kvam, Brani Vidakovic, Seong-joon Kim
Released October 2022
Publisher(s): Wiley
ISBN: 9781119268130

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Book description

NONPARAMETRIC STATISTICS WITH APPLICATIONS TO SCIENCE AND ENGINEERING WITH R

Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code

Nonparametric Statistics with Applications to Science and Engineering with R presents modern nonparametric statistics from a practical point of view, with the newly revised edition including custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible.

Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R’s powerful graphic systems, such as ggplot2 package and R base graphic system.

The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. New examples and exercises that enable readers to gain a deeper insight into nonparametric statistics and increase their comprehension are also included.

Some of the sample topics discussed in Nonparametric Statistics with Applications to Science and Engineering with R include:

  • Basics of probability, statistics, Bayesian statistics, order statistics, Kolmogorov–Smirnov test statistics, rank tests, and designed experiments
  • Categorical data, estimating distribution functions, density estimation, least squares regression, curve fitting techniques, wavelets, and bootstrap sampling
  • EM algorithms, statistical learning, nonparametric Bayes, WinBUGS, properties of ranks, and Spearman coefficient of rank correlation
  • Chi-square and goodness-of-fit, contingency tables, Fisher exact test, MC Nemar test, Cochran’s test, Mantel–Haenszel test, and Empirical Likelihood

Nonparametric Statistics with Applications to Science and Engineering with R is a highly valuable resource for graduate students in engineering and the physical and mathematical sciences, as well as researchers who need a more comprehensive, but succinct understanding of modern nonparametric statistical methods.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Acknowledgments
  6. 1 Introduction
    1. 1.1 Efficiency of Nonparametric Methods
    2. 1.2 Overconfidence Bias
    3. 1.3 Computing with R
    4. 1.4 Exercises
    5. References
    6. Note
  7. 2 Probability Basics
    1. 2.1 Helpful Functions
    2. 2.2 Events, Probabilities, and Random Variables
    3. 2.3 Numerical Characteristics of Random Variables
    4. 2.4 Discrete Distributions
    5. 2.5 Continuous Distributions
    6. 2.6 Mixture Distributions
    7. 2.7 Exponential Family of Distributions
    8. 2.8 Stochastic Inequalities
    9. 2.9 Convergence of Random Variables
    10. 2.10 Exercises
    11. References
    12. Notes
  8. 3 Statistics Basics
    1. 3.1 Estimation
    2. 3.2 Empirical Distribution Function
    3. 3.3 Statistical Tests
    4. 3.4 Confidence Intervals
    5. 3.5 Likelihood
    6. 3.6 Exercises
    7. References
  9. 4 Bayesian Statistics
    1. 4.1 The Bayesian Paradigm
    2. 4.2 Ingredients for Bayesian Inference
    3. 4.3 Point Estimation
    4. 4.4 Interval Estimation: Credible Sets
    5. 4.5 Bayesian Testing
    6. 4.6 Bayesian Prediction
    7. 4.7 Bayesian Computation and Use of WinBUGS
    8. 4.8 Exercises
    9. References
    10. Note
  10. 5 Order Statistics
    1. 5.1 Joint Distributions of Order Statistics
    2. 5.2 Sample Quantiles
    3. 5.3 Tolerance Intervals
    4. 5.4 Asymptotic Distributions of Order Statistics
    5. 5.5 Extreme Value Theory
    6. 5.6 Ranked Set Sampling
    7. 5.7 Exercises
    8. References
  11. 6 Goodness of Fit
    1. 6.1 Kolmogorov–Smirnov Test Statistic
    2. 6.2 Smirnov Test to Compare Two Distributions
    3. 6.3 Specialized Tests for Goodness of Fit
    4. 6.4 Probability Plotting
    5. 6.5 Runs Test
    6. 6.6 Meta Analysis
    7. 6.7 Exercises
    8. References
  12. 7 Rank Tests
    1. 7.1 Properties of Ranks
    2. 7.2 Sign Test
    3. 7.3 Spearman Coefficient of Rank Correlation
    4. 7.4 Wilcoxon Signed Rank Test
    5. 7.5 Wilcoxon (Two‐Sample) Sum Rank Test
    6. 7.6 Mann–Whitney Test
    7. 7.7 Test of Variances
    8. 7.8 Walsh Test for Outliers
    9. 7.9 Exercises
    10. References
    11. Notes
  13. 8 Designed Experiments
    1. 8.1 Kruskal–Wallis Test
    2. 8.2 Friedman Test
    3. 8.3 Variance Test for Several Populations
    4. 8.4 Exercises
    5. References
    6. Note
  14. 9 Categorical Data
    1. 9.1 Chi‐Square and Goodness‐of‐Fit
    2. 9.2 Contingency Tables: Testing for Homogeneity and Independence
    3. 9.3 Fisher Exact Test
    4. 9.4 Mc Nemar Test
    5. 9.5 Cochran's Test
    6. 9.6 Mantel–Haenszel Test
    7. 9.7 Central Limit Theorem for Multinomial Probabilities
    8. 9.8 Simpson's Paradox
    9. 9.9 Exercises
    10. References
    11. Notes
  15. 10 Estimating Distribution Functions
    1. 10.1 Introduction
    2. 10.2 Nonparametric Maximum Likelihood
    3. 10.3 Kaplan–Meier Estimator
    4. 10.4 Confidence Interval for
    5. 10.5 Plug‐in Principle
    6. 10.6 Semi‐Parametric Inference
    7. 10.7 Empirical Processes
    8. 10.8 Empirical Likelihood
    9. 10.9 Exercises
    10. References
  16. 11 Density Estimation
    1. 11.1 Histogram
    2. 11.2 Kernel and Bandwidth
    3. 11.3 Exercises
    4. References
  17. 12 Beyond Linear Regression
    1. 12.1 Least‐Squares Regression
    2. 12.2 Rank Regression
    3. 12.3 Robust Regression
    4. 12.4 Isotonic Regression
    5. 12.5 Generalized Linear Models
    6. 12.6 Exercises
    7. References
  18. 13 Curve Fitting Techniques
    1. 13.1 Kernel Estimators
    2. 13.2 Nearest Neighbor Methods
    3. 13.3 Variance Estimation
    4. 13.4 Splines
    5. 13.5 Summary
    6. 13.6 Exercises
    7. References
    8. Notes
  19. 14 Wavelets
    1. 14.1 Introduction to Wavelets
    2. 14.2 How Do the Wavelets Work?
    3. 14.3 Wavelet Shrinkage
    4. 14.4 Exercises
    5. References
    6. Notes
  20. 15 Bootstrap
    1. 15.1 Bootstrap Sampling
    2. 15.2 Nonparametric Bootstrap
    3. 15.3 Bias Correction for Nonparametric Intervals
    4. 15.4 The Jackknife
    5. 15.5 Bayesian Bootstrap
    6. 15.6 Permutation Tests
    7. 15.7 More on the Bootstrap
    8. 15.8 Exercises
    9. References
    10. Note
  21. 16 EM Algorithm
    1. Definition
    2. 16.1 Fisher's Example
    3. 16.2 Mixtures
    4. 16.3 EM and Order Statistics
    5. 16.4 MAP via EM
    6. 16.5 Infection Pattern Estimation
    7. Exercises
    8. References
  22. 17 Statistical Learning
    1. 17.1 Discriminant Analysis
    2. 17.2 Linear Classification Models
    3. 17.3 Nearest Neighbor Classification
    4. 17.4 Neural Networks
    5. 17.5 Binary Classification Trees
    6. Exercises
    7. References
    8. Note
  23. 18 Nonparametric Bayes
    1. 18.1 Dirichlet Processes
    2. 18.2 Bayesian Contingency Tables and Categorical Models
    3. 18.3 Bayesian Inference in Infinitely Dimensional Nonparametric Problems
    4. Exercises
    5. References
  24. Appendix A: WinBUGS
    1. A.1 Using WinBUGS
    2. A.2 Built‐in Functions and Common Distributions in BUGS
  25. Appendix B: R Coding
    1. B.1 Programming in R
    2. B.2 Basics of R
    3. B.3 R Commands
    4. B.4 R for Statistics
  26. R Index
  27. Author Index
  28. Subject Index
  29. End User License Agreement

Product information

  • Title: Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition
  • Author(s): Paul Kvam, Brani Vidakovic, Seong-joon Kim
  • Release date: October 2022
  • Publisher(s): Wiley
  • ISBN: 9781119268130