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El. knyga: Bootstrap Methods: With Applications in R

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  • Formatas: EPUB+DRM
  • Išleidimo metai: 10-Aug-2021
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030734800
Kitos knygos pagal šią temą:
Bootstrap Methods: With Applications in RDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 10-Aug-2021
  • Leidėjas: Springer Nature Switzerland AG
  • Kalba: eng
  • ISBN-13: 9783030734800
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This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time.





The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
1 Introduction
1(8)
1.1 Basic Idea of the Bootstrap
1(4)
1.2 The R-Project for Statistical Computing
5(1)
1.3 Usage of R in This Book
5(2)
1.3.1 Further Non-Statistical R-Packages
6(1)
References
7(2)
2 Generating Random Numbers
9(12)
2.1 Distributions in the R-Package Stats
9(1)
2.2 Uniform df. on the Unit Interval
10(1)
2.3 The Quantile Transformation
11(4)
2.4 The Normal Distribution
15(1)
2.5 Method of Rejection
16(3)
2.6 Generation of Random Vectors
19(1)
2.7 Exercises
20(1)
References
20(1)
3 The Classical Bootstrap
21(26)
3.1 An Introductory Example
21(6)
3.2 Basic Mathematical Background of the Classical Bootstrap
27(5)
3.3 Discussion of the Asymptotic Accuracy of the Classical Bootstrap
32(2)
3.4 Empirical Process and the Classical Bootstrap
34(2)
3.5 Mathematical Framework of Mallow's Metric
36(8)
3.6 Exercises
44(1)
References
45(2)
4 Bootstrap-Based Tests
47(26)
4.1 Introduction
47(2)
4.2 The One-Sample Test
49(4)
4.3 Two-Sample Tests
53(7)
4.4 Goodness-of-Fit (GOF) Test
60(5)
4.5 Mathematical Framework of the GOF Test
65(5)
4.6 Exercises
70(2)
References
72(1)
5 Regression Analysis
73(92)
5.1 Homoscedastic Linear Regression under Fixed Design
74(16)
5.1.1 Model-Based Bootstrap
77(7)
5.1.2 LSE Asymptotic
84(4)
5.1.3 LSE Bootstrap Asymptotic
88(2)
5.2 Linear Correlation Model and the Bootstrap
90(16)
5.2.1 Classical Bootstrap
93(3)
5.2.2 Wild Bootstrap
96(3)
5.2.3 Mathematical Framework of LSE
99(2)
5.2.4 Mathematical Framework of Classical Bootstrapped LSE
101(3)
5.2.5 Mathematical Framework of Wild Bootstrapped LSE
104(2)
5.3 Generalized Linear Model (Parametric)
106(36)
5.3.1 Mathematical Framework of MLE
121(12)
5.3.2 Mathematical Framework of Bootstrap MLE
133(9)
5.4 Semi-parametric Model
142(20)
5.4.1 Mathematical Framework of LSE
147(6)
5.4.2 Mathematical Framework of Wild Bootstrap LSE
153(9)
5.5 Exercises
162(2)
References
164(1)
6 Goodness-of-Fit Test for Generalized Linear Models
165(66)
6.1 MEP in the Parametric Modeling Context
167(20)
6.1.1 Implementation
168(3)
6.1.2 Bike Sharing Data
171(6)
6.1.3 Artificial Data
177(10)
6.2 MEP in the Semi-parametric Modeling Context
187(7)
6.2.1 Implementation
190(2)
6.2.2 Artificial Data
192(2)
6.3 Comparison of the GOF Tests under the Parametric and Semi-parametric Setup
194(3)
6.4 Mathematical Framework: Marked Empirical Processes
197(17)
6.4.1 The Basic MEP
198(5)
6.4.2 The MEP with Estimated Model Parameters Propagating in a Fixed Direction
203(4)
6.4.3 The MEP with Estimated Model Parameters Propagating in an Estimated Direction
207(7)
6.5 Mathematical Framework: Bootstrap of Marked Empirical Processes
214(15)
6.5.1 Bootstrap of the BMEP
218(3)
6.5.2 Bootstrap of the EMEP
221(8)
6.6 Exercises
229(1)
References
230(1)
Appendix A Boot Package 231(6)
Appendix B SimTool Package 237(12)
Appendix C Bootgof Package 249(4)
Appendix D Session Info 253(2)
Index 255
Gerhard Dikta has been a full-time professor at the Department of Medical Engineering and Technomathematics within the University of Applied Sciences, FH-Aachen, since 1993. He has also been an adjunct professor at the Department of Mathematics of the University of Wisconsin-Milwaukee since 2004. In addition to general problems in mathematical statistics, statistical modeling, simulation and optimization, his research interests and contributions are in survival analysis and, recently, in the development of statistical test methods for model verification.









Marsel Scheer has been a data scientist at Bayer AG since 2019. He was head of biostatistics and software development at Myriad International GmbH (formerly Sividon Diagnostics GmbH) for 5 years and worked as a biometrician in diabetes research at the German Diabetes Center for 6 years. His research interests are in statistical learning and modeling, machine learning, simulation and software development.
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