Muutke küpsiste eelistusi

Nonparametric Statistics with Applications to Science and Engineering with R 2nd edition [Kõva köide]

(University of Richmond, Richmond, VA, USA), (Chosun University, Gwangju, South Korea), (Texas A&M University, College Station, TX, USA)
Teised raamatud teemal:
Nonparametric Statistics with Applications to Science and Engineering with R 2nd editionSuurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781119268130.html
Märksõnad:
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 Rs 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, KolmogorovSmirnov 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, Cochrans test, MantelHaenszel 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.
Preface xiii
Acknowledgments xvii
1 Introduction
1(8)
1.1 Efficiency of Nonparametric Methods
2(2)
1.2 Overconfidence Bias
4(1)
1.3 Computing with R
5(1)
1.4 Exercises
6(3)
References
7(2)
2 Probability Basics
9(26)
2.1 Helpful Functions
9(2)
2.2 Events, Probabilities, and Random Variables
11(1)
2.3 Numerical Characteristics of Random Variables
12(1)
2.4 Discrete Distributions
13(4)
2.4.1 Binomial Distribution
13(1)
2.4.2 Poisson Distribution
14(1)
2.4.3 Negative Binomial Distribution
14(1)
2.4.4 Geometric Distribution
15(1)
2.4.5 Hypergeometric Distribution
15(1)
2.4.6 Multinomial Distribution
16(1)
2.5 Continuous Distributions
17(6)
2.5.1 Exponential Distribution
17(1)
2.5.2 Gamma Distribution
16(2)
2.5.3 Normal Distribution
18(1)
2.5.4 Chi-square Distribution
19(1)
2.5.5 (Student) t-Distribution
19(1)
2.5.6 Beta Distribution
20(1)
2.5.7 Double-Exponential Distribution
20(1)
2.5.8 Cauchy Distribution
21(1)
2.5.9 Inverse Gamma Distribution
21(1)
2.5.10 Dirichlet Distribution
21(1)
2.5.11 F Distribution
22(1)
2.5.12 Pareto Distribution
22(1)
2.5.13 Weibull Distribution
23(1)
2.6 Mixture Distributions
23(2)
2.7 Exponential Family of Distributions
25(1)
2.8 Stochastic Inequalities
25(2)
2.9 Convergence of Random Variables
27(4)
2.10 Exercises
31(4)
References
33(2)
3 Statistics Basics
35(16)
3.1 Estimation
35(1)
3.2 Empirical Distribution Function
36(2)
3.2.1 Convergence for EDF
38(1)
3.3 Statistical Tests
38(3)
3.3.1 Test Properties
39(2)
3.4 Confidence Intervals
41(3)
3.4.1 Intervals Based on Normal Approximation
42(2)
3.5 Likelihood
44(4)
3.5.1 Likelihood Ratio
46(1)
3.5.2 Efficiency
47(1)
3.5.3 Exponential Family of Distributions
47(1)
3.6 Exercises
48(3)
References
50(1)
4 Bayesian Statistics
51(22)
4.1 The Bayesian Paradigm
51(1)
4.2 Ingredients for Bayesian Inference
52(4)
4.2.1 Quantifying Expert Opinion
55(1)
4.3 Point Estimation
56(3)
4.3.1 Conjugate Priors
58(1)
4.4 Interval Estimation: Credible Sets
59(1)
4.5 Bayesian Testing
60(2)
4.5.1 Bayesian Testing of Precise Hypotheses
62(1)
4.6 Bayesian Prediction
62(2)
4.7 Bayesian Computation and Use of WinBUGS
64(3)
4.8 Exercises
67(6)
References
71(2)
5 Order Statistics
73(14)
5.1 Joint Distributions of Order Statistics
75(1)
5.2 Sample Quantiles
76(1)
5.3 Tolerance Intervals
77(2)
5.4 Asymptotic Distributions of Order Statistics
79(1)
5.5 Extreme Value Theory
79(1)
5.6 Ranked Set Sampling
80(1)
5.7 Exercises
81(6)
References
84(3)
6 Goodness of Fit
87(38)
6.1 Kolmogorov--Smirnov Test Statistic
88(5)
6.2 Smirnov Test to Compare Two Distributions
93(3)
6.3 Specialized Tests for Goodness of Fit
96(7)
6.3.1 Anderson--Darling Test
96(2)
6.3.2 Cramer--von Mises Test
98(2)
6.3.3 Shapiro--Wilk Test for Normality
100(1)
6.3.4 Choosing a Goodness-of-Fit Test
100(3)
6.4 Probability Plotting
103(5)
6.5 Runs Test
108(6)
6.6 Meta Analysis
114(3)
6.7 Exercises
117(8)
References
122(3)
7 Rank Tests
125(28)
7.1 Properties of Ranks
126(1)
7.2 Sign Test
127(5)
7.2.1 Paired Samples
129(3)
7.2.2 Treatments of Ties
132(1)
7.3 Spearman Coefficient of Rank Correlation
132(4)
7.3.1 Ties in the Data
134(1)
7.3.2 Kendall's Tau
135(1)
7.4 Wilcoxon Signed Rank Test
136(3)
7.5 Wilcoxon (Two-Sample) Sum Rank Test
139(3)
7.5.1 Ties in the Data
141(1)
7.6 Mann-Whitney U Test
142(1)
7.6.1 Equivalence of Mann--Whitney and Wilcoxon Sum Rank Test
142(1)
7.7 Test of Variances
143(2)
7.7.1 Ties in the Data
144(1)
7.8 Walsh Test for Outliers
145(1)
1.9 Exercises
146(7)
References
151(2)
8 Designed Experiments
153(14)
8.1 Kruskal--Wallis Test
153(4)
8.1.1 Kruskal--Wallis Pairwise Comparisons
155(2)
8.1.2 Jonckheere--Terpstra Ordered Alternative
157(1)
8.2 Friedman Test
157(4)
8.2.1 Friedman Pairwise Comparisons
160(1)
8.2.2 Page Test for Ordered Alternative
161(1)
8.3 Variance Test for Several Populations
161(2)
8.3.1 Multiple Comparisons for Variance Test
162(1)
8.4 Exercises
163(4)
References
166(1)
9 Categorical Data
167(32)
9.1 Chi-Square and Goodness-of-Fit
168(5)
9.2 Contingency Tables: Testing for Homogeneity and Independence
173(4)
9.2.1 Relative Risk
176(1)
9.3 Fisher Exact Test
177(2)
9.4 McNemar Test
179(2)
9.5 Cochran's Test
181(2)
9.6 Mantel-Haenszel Test
183(2)
9.7 Central Limit Theorem for Multinomial Probabilities
185(1)
9.8 Simpson's Paradox
186(2)
9.9 Exercises
188(11)
References
196(3)
10 Estimating Distribution Functions
199(24)
10.1 Introduction
199(1)
10.2 Nonparametric Maximum Likelihood
200(1)
10.3 Kaplan--Meier Estimator
201(7)
10.4 Confidence Interval for F
208(1)
10.5 Plug-in Principle
209(2)
10.6 Semi-Parametric Inference
211(2)
10.7 Empirical Processes
213(1)
10.8 Empirical Likelihood
214(3)
10.8.1 Confidence Interval for the Mean
215(2)
10.8.2 Confidence Interval for the Median
217(1)
10.9 Exercises
217(6)
References
220(3)
11 Density Estimation
223(12)
11.1 Histogram
223(3)
11.2 Kernel and Bandwidth
226(7)
11.2.1 Bivariate Density Estimators
232(1)
11.3 Exercises
233(2)
References
234(1)
12 Beyond Linear Regression
235(26)
12.1 Least-Squares Regression
236(1)
12.2 Rank Regression
236(4)
12.2.1 Sen--Theil Estimator of Regression Slope
239(1)
12.3 Robust Regression
240(6)
12.3.1 Least Absolute Residuals Regression
240(1)
12.3.2 Huber Estimate
241(1)
12.3.3 Least Trimmed Squares Regression
241(1)
12.3.4 Weighted Least-Squares Regression
241(1)
12.3.5 Least Median Squares Regression
242(4)
12.4 Isotonic Regression
246(3)
12.4.1 Graphical Solution to Regression
247(2)
12.4.2 Pool Adjacent Violators Algorithm
249(1)
12.5 Generalized Linear Models
249(7)
12.5.1 GLM Algorithm
251(1)
12.5.2 Link Functions
251(2)
12.5.3 Deviance Analysis in GLM
253(3)
12.6 Exercises
256(5)
References
258(3)
13 Curve Fitting Techniques
261(22)
13.1 Kernel Estimators
263(4)
13.1.1 Nadaraya--Watson Estimator
263(2)
13.1.2 Gasser--Muller Estimator
265(1)
13.1.3 Local Polynomial Estimator
265(2)
13.2 Nearest Neighbor Methods
267(3)
13.2.1 LOESS
267(3)
13.3 Variance Estimation
270(1)
13.4 Splines
270(7)
13.4.1 Interpolating Splines
271(2)
13.4.2 Smoothing Splines
273(1)
13.4.2.1 Smoothing Splines as Linear Estimators
274(1)
13.4.3 Selecting and Assessing the Regression Estimator
275(1)
13.4.4 Spline Inference
276(1)
13.5 Summary
277(1)
13.6 Exercises
277(6)
References
280(3)
14 Wavelets
283(22)
14.1 Introduction to Wavelets
283(3)
14.2 How Do the Wavelets Work?
286(8)
14.2.1 The Haar Wavelet
286(4)
14.2.2 Wavelets in the Language of Signal Processing
290(4)
14.3 Wavelet Shrinkage
294(7)
14.3.1 Universal Threshold
295(6)
14.4 Exercises
301(4)
References
303(2)
15 Bootstrap
305(22)
15.1 Bootstrap Sampling
305(2)
15.2 Nonparametric Bootstrap
307(4)
15.2.1 Parametric Case
307(4)
15.2.2 Estimating Standard Error
311(1)
15.3 Bias Correction for Nonparametric Intervals
311(3)
15.4 The Jackknife
314(1)
15.5 Bayesian Bootstrap
315(2)
15.6 Permutation Tests
317(4)
15.7 More on the Bootstrap
321(1)
15.8 Exercises
322(5)
References
324(3)
16 EM Algorithm
327(16)
Definition
328(1)
16.1 Fisher's Example
328(3)
16.2 Mixtures
331(5)
16.3 EM and Order Statistics
336(1)
16.4 MAP via EM
337(2)
16.5 Infection Pattern Estimation
339(1)
16.6 Exercises
340(3)
References
341(2)
17 Statistical Learning
343(26)
17.1 Discriminant Analysis
344(2)
17.1.1 Bias Versus Variance
344(1)
17.1.2 Cross-Validation
345(1)
17.1.3 Bayesian Decision Theory
346(1)
17.2 Linear Classification Models
346(5)
17.2.1 Logistic Regression as Classifier
347(4)
17.3 Nearest Neighbor Classification
351(2)
17.3.1 The Curse of Dimensionality
351(1)
17.3.2 Constructing the Nearest-Neighbor Classifier
352(1)
17.4 Neural Networks
353(5)
17.4.1 Back-Propagation
355(2)
17.4.2 Implementing the Neural Network
357(1)
17.4.3 Projection Pursuit
357(1)
17.5 Binary Classification Trees
358(8)
17.5.1 Growing the Tree
361(1)
17.5.2 Pruning the Tree
362(3)
17.5.3 General Tree Classifiers
365(1)
17.6 Exercises
366(3)
References
367(2)
18 Nonparametric Bayes
369(20)
18.1 Dirichlet Processes
369(8)
18.1.1 Updating Dirichlet Process Priors
373(3)
18.1.2 Generalized Dirichlet Processes
376(1)
18.2 Bayesian Contingency Tables and Categorical Models
377(4)
18.3 Bayesian Inference in Infinitely Dimensional Nonparametric Problems
381(3)
18.3.1 BAMS Wavelet Shrinkage
381(3)
18.4 Exercises
384(5)
References
386(3)
Appendix A WinBUGS
389(8)
A.1 Using WinBUGS
389(4)
A.2 Built-in Functions and Common Distributions in BUGS
393(4)
Appendix B R Coding
397(10)
B.1 Programming in R
397(2)
B.1.1 Vectors
398(1)
B.1.2 Missing Values
399(1)
B.1.3 Logical Arguments
399(1)
B.2 Basics of R
399(1)
B.3 R Commands
400(2)
B.4 R for Statistics
402(5)
R Index 407(4)
Author Index 411(6)
Subject Index 417
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.