Nonparametric Statistics With Applications to Science and - Engineering With

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.

Inhaltsverzeichnis

Preface xi
 
1 Introduction 1
 
1.1 Efficiency of Nonparametric Methods 2
 
1.2 Overconfidence Bias 4
 
1.3 Computing with R 5
 
1.4 Exercises 6
 
References 7
 
2 Probability Basics 9
 
2.1 Helpful Functions 10
 
2.2 Events, Probabilities and Random Variables 12
 
2.3 Numerical Characteristics of Random Variables 13
 
2.4 Discrete Distributions 14
 
2.5 Continuous Distributions 18
 
2.6 Mixture Distributions 24
 
2.7 Exponential Family of Distributions 26
 
2.8 Stochastic Inequalities 26
 
2.9 Convergence of Random Variables 28
 
2.10 Exercises 32
 
References 34
 
3 Statistics Basics 35
 
3.1 Estimation 36
 
3.2 Empirical Distribution Function 36
 
3.3 Statistical Tests 38
 
3.4 Confidence Intervals 41
 
3.5 Likelihood 45
 
3.6 Exercises 49
 
References 51
 
4 Bayesian Statistics 53
 
4.1 The Bayesian Paradigm 53
 
4.2 Ingredients for Bayesian Inference 54
 
4.3 Point Estimation 58
 
4.4 Interval Estimation: Credible Sets 60
 
4.5 Bayesian Testing 62
 
4.6 Bayesian Prediction 65
 
4.7 Bayesian Computation and Use of WinBUGS 67
 
4.8 Exercises 69
 
References 73
 
5 Order Statistics 75
 
5.1 Joint Distributions of Order Statistics 77
 
5.2 Sample Quantiles 79
 
5.3 Tolerance Intervals 79
 
5.4 Asymptotic Distributions of Order Statistics 81
 
5.5 Extreme Value Theory 82
 
5.6 Ranked Set Sampling 83
 
5.7 Exercises 84
 
References 87
 
6 Goodness of Fit 89
 
6.1 KolmogorovSmirnov Test Statistic 90
 
6.2 Smirnov Test to Compare Two Distributions 96
 
6.3 Specialized Tests 99
 
6.4 Probability Plotting 106
 
6.5 Runs Test 112
 
6.6 Meta Analysis 117
 
6.7 Exercises 121
 
References 125
 
7 Rank Tests 127
 
7.1 Properties of Ranks 128
 
7.2 Sign Test 130
 
7.3 Spearman Coefficient of Rank Correlation 135
 
7.4 Wilcoxon Signed Rank Test 139
 
7.5 Wilcoxon (TwoSample) Sum Rank Test 142
 
7.6 MannWhitney U Test 144
 
7.7 Test of Variances 146
 
7.8 Walsh Test for Outliers 147
 
7.9 Exercises 148
 
References 153
 
8 Designed Experiments 155
 
8.1 KruskalWallis Test 156
 
8.2 Friedman Test 160
 
8.3 Variance Test for Several Populations 165
 
8.4 Exercises 166
 
References 169
 
9 Categorical Data 171
 
9.1 ChiSquare and GoodnessofFit 172
 
9.2 Contingency Tables 178
 
9.3 Fisher Exact Test 183
 
9.4 Mc Nemar Test 184
 
9.5 Cochran's Test 186
 
9.6 MantelHaenszel Test 188
 
9.7 CLT for Multinomial Probabilities 190
 
9.8 Simpson's Paradox 191
 
9.9 Exercises 193
 
References 200
 
10 Estimating Distribution Functions 203
 
10.1 Introduction 203
 
10.2 Nonparametric Maximum Likelihood 204
 
10.3 KaplanMeier Estimator 205
 
10.4 Confidence Interval for F 213
 
10.5 Plugin Principle 214
 
10.6 SemiParametric Inference 215
 
10.7 Empirical Processes 217
 
10.8 Empirical Likelihood 218
 
10.9 Exercises 221
 
References 223
 
11 Density Estimation 225
 
11.1 Histogram 226
 
11.2 Kernel and Bandwidth 228
 
11.3 Exercises 235
 
References 236
 
12 Beyond Linear Regression 2

Über den Autor / die Autorin

Paul Kvam is professor in the Department of Mathematics, University of Richmond, USA. He received his Ph.D. from University of California, Davis. Brani Vidakovic is professor in the Department of Statistics, Texas A&M University, USA. He received his Ph.D from Purdue University. Seong-joon Kim is assistant professor in Department of Industrial Engineering, Chosun University, South Korea. He received his Ph.D. from Hanyang University.

Zusammenfassung

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.

Produktdetails

• Autoren: Seong-joon Kim, Kvam, P Kvam, Paul Kvam, Paul (University of Richmond Kvam, Paul H. Kvam, Paul H. Vidakovic Kvam, Paul Vidakovic Kvam, Brani Vidakovic, Vidakovic Brani
• Verlag: Wiley, John and Sons Ltd
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 28.02.2019
• EAN: 9781119268130
• ISBN: 978-1-119-26813-0
• Seiten: 448
• Serien: Wiley Series in Probability and Statistics; Wiley Series in Probability and Statistics; Wiley Probability and Statisti
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Statistik, Statistics, Multivariate Analyse, Statistik in den Ingenieurwissenschaften, Engineering Statistics, Statistiksoftware / R, Statistical Software / R, Nichtparametrische Verfahren, Nonparametric Analysis