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Nonparametric Statistics with Applications to Science and Engineering with R

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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.

Author(s): Paul Kvam, Brani Vidakovic, Seong-joon Kim
Series: Wiley Series in Probability and Statistics
Edition: 2
Publisher: Wiley
Year: 2022

Language: English
Pages: 449
City: Hoboken

Cover
Title Page
Copyright
Contents
Preface
Acknowledgments
Chapter 1 Introduction
1.1 Efficiency of Nonparametric Methods
1.2 Overconfidence Bias
1.3 Computing with R
1.4 Exercises
References
Chapter 2 Probability Basics
2.1 Helpful Functions
2.2 Events, Probabilities, and Random Variables
2.3 Numerical Characteristics of Random Variables
2.4 Discrete Distributions
2.4.1 Binomial Distribution
2.4.2 Poisson Distribution
2.4.3 Negative Binomial Distribution
2.4.4 Geometric Distribution
2.4.5 Hypergeometric Distribution
2.4.6 Multinomial Distribution
2.5 Continuous Distributions
2.5.1 Exponential Distribution
2.5.2 Gamma Distribution
2.5.3 Normal Distribution
2.5.4 Chi‐square Distribution
2.5.5 (Student) t‐Distribution
2.5.6 Beta Distribution
2.5.7 Double‐Exponential Distribution
2.5.8 Cauchy Distribution
2.5.9 Inverse Gamma Distribution
2.5.10 Dirichlet Distribution
2.5.11 F Distribution
2.5.12 Pareto Distribution
2.5.13 Weibull Distribution
2.6 Mixture Distributions
2.7 Exponential Family of Distributions
2.8 Stochastic Inequalities
2.9 Convergence of Random Variables
2.10 Exercises
References
Chapter 3 Statistics Basics
3.1 Estimation
3.2 Empirical Distribution Function
3.2.1 Convergence for EDF
3.3 Statistical Tests
3.3.1 Test Properties
3.4 Confidence Intervals
3.4.1 Intervals Based on Normal Approximation
3.5 Likelihood
3.5.1 Likelihood Ratio
3.5.2 Efficiency
3.5.3 Exponential Family of Distributions
3.6 Exercises
References
Chapter 4 Bayesian Statistics
4.1 The Bayesian Paradigm
4.2 Ingredients for Bayesian Inference
4.2.1 Quantifying Expert Opinion
4.3 Point Estimation
4.3.1 Conjugate Priors
4.4 Interval Estimation: Credible Sets
4.5 Bayesian Testing
4.5.1 Bayesian Testing of Precise Hypotheses
4.6 Bayesian Prediction
4.7 Bayesian Computation and Use of WinBUGS
4.8 Exercises
References
Chapter 5 Order Statistics
5.1 Joint Distributions of Order Statistics
5.2 Sample Quantiles
5.3 Tolerance Intervals
5.4 Asymptotic Distributions of Order Statistics
5.5 Extreme Value Theory
5.6 Ranked Set Sampling
5.7 Exercises
References
Chapter 6 Goodness of Fit
6.1 Kolmogorov–Smirnov Test Statistic
6.2 Smirnov Test to Compare Two Distributions
6.3 Specialized Tests for Goodness of Fit
6.3.1 Anderson–Darling Test
6.3.2 Cramér–von Mises Test
6.3.3 Shapiro–Wilk Test for Normality
6.3.4 Choosing a Goodness‐of‐Fit Test
6.4 Probability Plotting
6.5 Runs Test
6.6 Meta Analysis
6.7 Exercises
References
Chapter 7 Rank Tests
7.1 Properties of Ranks
7.2 Sign Test
7.2.1 Paired Samples
7.2.2 Treatments of Ties
7.3 Spearman Coefficient of Rank Correlation
7.3.1 Ties in the Data
7.3.2 Kendall's Tau
7.4 Wilcoxon Signed Rank Test
7.5 Wilcoxon (Two‐Sample) Sum Rank Test
7.5.1 Ties in the Data
7.6 Mann–Whitney U Test
7.6.1 Equivalence of Mann–Whitney and Wilcoxon Sum Rank Test
7.7 Test of Variances
7.7.1 Ties in the Data
7.8 Walsh Test for Outliers
7.9 Exercises
References
Chapter 8 Designed Experiments
8.1 Kruskal–Wallis Test
8.1.1 Kruskal–Wallis Pairwise Comparisons
8.1.2 Jonckheere–Terpstra Ordered Alternative
8.2 Friedman Test
8.2.1 Friedman Pairwise Comparisons
8.2.2 Page Test for Ordered Alternative
8.3 Variance Test for Several Populations
8.3.1 Multiple Comparisons for Variance Test
8.4 Exercises
References
Chapter 9 Categorical Data
9.1 Chi‐Square and Goodness‐of‐Fit
9.2 Contingency Tables: Testing for Homogeneity and Independence
9.2.1 Relative Risk
9.3 Fisher Exact Test
9.4 Mc Nemar Test
9.5 Cochran's Test
9.6 Mantel–Haenszel Test
9.7 Central Limit Theorem for Multinomial Probabilities
9.8 Simpson's Paradox
9.9 Exercises
References
Chapter 10 Estimating Distribution Functions
10.1 Introduction
10.2 Nonparametric Maximum Likelihood
10.3 Kaplan–Meier Estimator
10.4 Confidence Interval for F
10.5 Plug‐in Principle
10.6 Semi‐Parametric Inference
10.7 Empirical Processes
10.8 Empirical Likelihood
10.8.1 Confidence Interval for the Mean
10.8.2 Confidence Interval for the Median
10.9 Exercises
References
Chapter 11 Density Estimation
11.1 Histogram
11.2 Kernel and Bandwidth
11.2.1 Bivariate Density Estimators
11.3 Exercises
References
Chapter 12 Beyond Linear Regression
12.1 Least‐Squares Regression
12.2 Rank Regression
12.2.1 Sen–Theil Estimator of Regression Slope
12.3 Robust Regression
12.3.1 Least Absolute Residuals Regression
12.3.2 Huber Estimate
12.3.3 Least Trimmed Squares Regression
12.3.4 Weighted Least‐Squares Regression
12.3.5 Least Median Squares Regression
12.4 Isotonic Regression
12.4.1 Graphical Solution to Regression
12.4.2 Pool Adjacent Violators Algorithm
12.5 Generalized Linear Models
12.5.1 GLM Algorithm
12.5.2 Link Functions
12.5.3 Deviance Analysis in GLM
12.6 Exercises
References
Chapter 13 Curve Fitting Techniques
13.1 Kernel Estimators
13.1.1 Nadaraya–Watson Estimator
13.1.2 Gasser–Müller Estimator
13.1.3 Local Polynomial Estimator
13.2 Nearest Neighbor Methods
13.2.1 LOESS
13.3 Variance Estimation
13.4 Splines
13.4.1 Interpolating Splines
13.4.2 Smoothing Splines
13.4.2.1 Smoothing Splines as Linear Estimators
13.4.3 Selecting and Assessing the Regression Estimator
13.4.4 Spline Inference
13.5 Summary
13.6 Exercises
References
Chapter 14 Wavelets
14.1 Introduction to Wavelets
14.2 How Do the Wavelets Work?
14.2.1 The Haar Wavelet
14.2.2 Wavelets in the Language of Signal Processing
14.3 Wavelet Shrinkage
14.3.1 Universal Threshold
14.4 Exercises
References
Chapter 15 Bootstrap
15.1 Bootstrap Sampling
15.2 Nonparametric Bootstrap
15.2.1 Parametric Case
15.2.2 Estimating Standard Error
15.3 Bias Correction for Nonparametric Intervals
15.4 The Jackknife
15.5 Bayesian Bootstrap
15.6 Permutation Tests
15.7 More on the Bootstrap
15.8 Exercises
References
Chapter 16 EM Algorithm
Definition
16.1 Fisher's Example
16.2 Mixtures
16.3 EM and Order Statistics
16.4 MAP via EM
16.5 Infection Pattern Estimation
16.6 Exercises
References
Chapter 17 Statistical Learning
17.1 Discriminant Analysis
17.1.1 Bias Versus Variance
17.1.2 Cross‐Validation
17.1.3 Bayesian Decision Theory
17.2 Linear Classification Models
17.2.1 Logistic Regression as Classifier
17.3 Nearest Neighbor Classification
17.3.1 The Curse of Dimensionality
17.3.2 Constructing the Nearest‐Neighbor Classifier
17.4 Neural Networks
17.4.1 Back‐Propagation
17.4.2 Implementing the Neural Network
17.4.3 Projection Pursuit
17.5 Binary Classification Trees
17.5.1 Growing the Tree
17.5.2 Pruning the Tree
17.5.3 General Tree Classifiers
17.6 Exercises
References
Chapter 18 Nonparametric Bayes
18.1 Dirichlet Processes
18.1.1 Updating Dirichlet Process Priors
18.1.2 Generalized Dirichlet Processes
18.2 Bayesian Contingency Tables and Categorical Models
18.3 Bayesian Inference in Infinitely Dimensional Nonparametric Problems
18.3.1 BAMS Wavelet Shrinkage
18.4 Exercises
References
Appendix A WinBUGS
A.1 Using WinBUGS
A.2 Built‐in Functions and Common Distributions in BUGS
Appendix B R Coding
B.1 Programming in R
B.1.1 Vectors
B.1.2 Missing Values
B.1.3 Logical Arguments
B.2 Basics of R
B.3 R Commands
B.4 R for Statistics
R Index
Author Index
Subject Index
EULA