book

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

Name: Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition
ISBN: 9781119268130

by Paul Kvam, Brani Vidakovic, Seong-joon Kim

October 2022

Intermediate to advanced

448 pages

12h 24m

English

Wiley

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Cover
Title Page
Copyright
Preface
Acknowledgments
1 Introduction
1.1 Efficiency of Nonparametric Methods1.2 Overconfidence Bias1.3 Computing with R1.4 ExercisesReferencesNote
2 Probability Basics
2.1 Helpful Functions2.2 Events, Probabilities, and Random Variables2.3 Numerical Characteristics of Random Variables2.4 Discrete Distributions2.5 Continuous Distributions2.6 Mixture Distributions2.7 Exponential Family of Distributions2.8 Stochastic Inequalities2.9 Convergence of Random Variables2.10 ExercisesReferencesNotes
3 Statistics Basics
3.1 Estimation3.2 Empirical Distribution Function3.3 Statistical Tests3.4 Confidence Intervals3.5 Likelihood3.6 ExercisesReferences
4 Bayesian Statistics
4.1 The Bayesian Paradigm4.2 Ingredients for Bayesian Inference4.3 Point Estimation4.4 Interval Estimation: Credible Sets4.5 Bayesian Testing4.6 Bayesian Prediction4.7 Bayesian Computation and Use of WinBUGS4.8 ExercisesReferencesNote
5 Order Statistics
5.1 Joint Distributions of Order Statistics5.2 Sample Quantiles5.3 Tolerance Intervals5.4 Asymptotic Distributions of Order Statistics5.5 Extreme Value Theory5.6 Ranked Set Sampling5.7 ExercisesReferences

6 Goodness of Fit
6.1 Kolmogorov–Smirnov Test Statistic6.2 Smirnov Test to Compare Two Distributions6.3 Specialized Tests for Goodness of Fit6.4 Probability Plotting6.5 Runs Test6.6 Meta Analysis6.7 ExercisesReferences
7 Rank Tests
7.1 Properties of Ranks7.2 Sign Test7.3 Spearman Coefficient of Rank Correlation7.4 Wilcoxon Signed Rank Test7.5 Wilcoxon (Two‐Sample) Sum Rank Test7.6 Mann–Whitney Test7.7 Test of Variances7.8 Walsh Test for Outliers7.9 ExercisesReferencesNotes
8 Designed Experiments
8.1 Kruskal–Wallis Test8.2 Friedman Test8.3 Variance Test for Several Populations8.4 ExercisesReferencesNote
9 Categorical Data
9.1 Chi‐Square and Goodness‐of‐Fit9.2 Contingency Tables: Testing for Homogeneity and Independence9.3 Fisher Exact Test9.4 Mc Nemar Test9.5 Cochran's Test9.6 Mantel–Haenszel Test9.7 Central Limit Theorem for Multinomial Probabilities9.8 Simpson's Paradox9.9 ExercisesReferencesNotes
10 Estimating Distribution Functions
10.1 Introduction10.2 Nonparametric Maximum Likelihood10.3 Kaplan–Meier Estimator10.4 Confidence Interval for 10.5 Plug‐in Principle10.6 Semi‐Parametric Inference10.7 Empirical Processes10.8 Empirical Likelihood10.9 ExercisesReferences
11 Density Estimation
11.1 Histogram11.2 Kernel and Bandwidth11.3 ExercisesReferences
12 Beyond Linear Regression
12.1 Least‐Squares Regression12.2 Rank Regression12.3 Robust Regression12.4 Isotonic Regression12.5 Generalized Linear Models12.6 ExercisesReferences
13 Curve Fitting Techniques
13.1 Kernel Estimators13.2 Nearest Neighbor Methods13.3 Variance Estimation13.4 Splines13.5 Summary13.6 ExercisesReferencesNotes
14 Wavelets
14.1 Introduction to Wavelets14.2 How Do the Wavelets Work?14.3 Wavelet Shrinkage14.4 ExercisesReferencesNotes
15 Bootstrap
15.1 Bootstrap Sampling15.2 Nonparametric Bootstrap15.3 Bias Correction for Nonparametric Intervals15.4 The Jackknife15.5 Bayesian Bootstrap15.6 Permutation Tests15.7 More on the Bootstrap15.8 ExercisesReferencesNote
16 EM Algorithm
Definition16.1 Fisher's Example16.2 Mixtures16.3 EM and Order Statistics16.4 MAP via EM16.5 Infection Pattern EstimationExercisesReferences
17 Statistical Learning
17.1 Discriminant Analysis17.2 Linear Classification Models17.3 Nearest Neighbor Classification17.4 Neural Networks17.5 Binary Classification TreesExercisesReferencesNote
18 Nonparametric Bayes
18.1 Dirichlet Processes18.2 Bayesian Contingency Tables and Categorical Models18.3 Bayesian Inference in Infinitely Dimensional Nonparametric ProblemsExercisesReferences
Appendix A: WinBUGS
A.1 Using WinBUGSA.2 Built‐in Functions and Common Distributions in BUGS
Appendix B: R Coding
B.1 Programming in RB.2 Basics of RB.3 R CommandsB.4 R for Statistics
R Index
Author Index
Subject Index
End User License Agreement

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

Subject Index

a
Accelerated life testing 212
Adam's rule 13, 32
Almost‐sure convergence 27
Analysis of variance 126, 153
Anderson–Darling test 96
Anscombe's data sets 244
Artificial intelligence 343

b
BAMS wavelet shrinkage 381
Bandwidth
- choice of 228
- optimal 229
Bayes
- nonparametric 369
Bayes classifier 346
Bayes decision rule 346
Bayes factor 61
Bayes formula 11
Bayesian computation 64
Bayesian statistics 51
- prediction 62
- bootstrap 315
- conjugate priors 58
- expert opinion 55
- hyperperameter 52
- hypothesis testing 60
- interval estimation 58
- loss functions 56
- point estimation 56
- posterior distribution 52
- prior distribution 52
- prior predictive 52
Bayesian testing 60
- of precise hypotheses 62
- Lindley paradox 68
Benford's law 172
Bernoulli distribution 13
Bessel functions 11
Beta distribution 20
Beta function 10
Beta‐binomial distribution 24, 32
Bias 345
Binary classification trees 358
- growing 361
- impurity function 359
  - cross entropy 360
  - Gini 360
  - misclassification 360
- pruning 362
Binomial distribution 4, 13, 31
- confidence intervals 41
- normal approximation 42
- relation to Poisson 14
- test of hypothesis 39
Binomial distributions
- tolerance intervals 78
Bootstrap 305, 346
- Bayesian 315
- bias correction 311
- fallibility 321
- nonparametric 307
- percentile 307
Bowman–Shenton test 100
Box kernel function 227
Brownian bridge 213
Brownian motion 213
Byzantine coins 319

c
Cæsarean birth study 254
Categorical data ...

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

by Paul Kvam, Brani Vidakovic, Seong-joon Kim

Subject Index

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