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396 Pages
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Industry Reviews
"This book contains a large amount of material on resampling methods for dependent data a ] . the book is self-contained and therefore can be used as a text for a graduate level course in resampling methods; at the same time, the book is a valuable reference book for researchers. a ] This is a thorough book going into much detail a ] . an excellent book on resampling methods for dependent data which has filled a long lasting gap in the statistical literature." (Efstathios Paparoditis, Sankhya: The Indian Journal of Statistics, Vol. 65 (4), 2003)
"I found this a useful book that organizes many scattered results in a reasonably concise form. The author states that this book has two main audiences, so the first five chapters are a pedantic introduction aimed at graduate students and the last seven a research monograph aimed at researchers in statistics and econometrics. a ] In summary, I learned quite a bit from reading this book and consider it a good reference book for the mathematically inclined." (D.J. Thomson, Short Book Reviews, Vol. 24 (2), 2004)
"Bootstrap methods have seen vigorous growth over the past twenty years, and the book by Lahiri is extremely timely in its appearance. a ] The first five chapters are written in textbook style and this part is aimed at a postgraduate student audience. a ] The second part of the book (chapters 6 a" 12) is written in the form of a research monograph. It is therefore primarily aimed at researchers a ] . this is a well written book, containing a wealth of information a ] ." (Tertius de Wet, Newsletter of the South African Statistical Association, June, 2004)
"This book is devoted to resampling methods fordependent data, which has been a fast developing area in about the last twenty years. a ] provides an introduction to the area of resampling methods for dependent data and also presents the latest results in the area with quite a long reference list. The first part of the book can be used as a textbook, while the second part, which focuses on the advanced results, can be really useful for researchers in statistics and econometrics." (M. HuAkovA, Mathematical Reviews, 2004f)
From the reviews:
"This book contains a large amount of material on resampling methods for dependent data ??? . the book is self-contained and therefore can be used as a text for a graduate level course in resampling methods; at the same time, the book is a valuable reference book for researchers. ??? This is a thorough book going into much detail ??? . an excellent book on resampling methods for dependent data which has filled a long lasting gap in the statistical literature." (Efstathios Paparoditis, Sankhya: The Indian Journal of Statistics, Vol. 65 (4), 2003)
"I found this a useful book that organizes many scattered results in a reasonably concise form. The author states that this book has two main audiences, so the first five chapters are a pedantic introduction aimed at graduate students and the last seven a research monograph aimed at researchers in statistics and econometrics. ??? In summary, I learned quite a bit from reading this book and consider it a good reference book for the mathematically inclined." (D.J. Thomson, Short Book Reviews, Vol. 24 (2), 2004)
"Bootstrap methods have seen vigorous growth over the past twenty years, and the book by Lahiri is extremely timely in its appearance. ??? The first five chapters are written in textbook style and this part is aimed at a postgraduate student audience. ??? The second part of the book (chapters 6 ??? 12) is written in the form of a research monograph. It is therefore primarily aimed at researchers ??? . this is a well written book, containing a wealth of information ??? ." (Tertius de Wet, Newsletter of the South African StatisticalAssociation, June, 2004)
"This book is devoted to resampling methods for dependent data, which has been a fast developing area in about the last twenty years. ??? provides an introduction to the area of resampling methods for dependent data and also presents the latest results in the area with quite a long reference list. The first part of the book can be used as a textbook, while the second part, which focuses on the advanced results, can be really useful for researchers in statistics and econometrics." (M. Hu??kov??, Mathematical Reviews, 2004f)
| Scope of Resampling Methods for Dependent Data | p. 1 |
| The Bootstrap Principle | p. 1 |
| Examples | p. 7 |
| Concluding Remarks | p. 12 |
| Notation | p. 13 |
| Bootstrap Methods | p. 17 |
| Introduction | p. 17 |
| III) Bootstrap | p. 17 |
| Inadequacy of IID Bootstrap for Dependent Data | p. 21 |
| Bootstrap Based on IID Innovations | p. 23 |
| Moving Block Bootstrap | p. 25 |
| Nonoverlapping Block Bootstrap | p. 30 |
| Generalized Block Bootstrap | p. 31 |
| Circular Block Bootstrap | p. 33 |
| Stationary Block Bootstrap | p. 34 |
| Subsampling | p. 37 |
| Transformation-Based Bootstrap | p. 40 |
| Sieve Bootstrap | p. 41 |
| Properties of Block Bootstrap Methods for the Sample Mean | p. 45 |
| Introduction | p. 45 |
| Consistency of MBB, NBB, CBB: Sample Mean | p. 47 |
| Consistency of Bootstrap Variance Estimators | p. 48 |
| Consistency of Distribution Function Estimators | p. 54 |
| Consistency of the SB: Sample Mean | p. 57 |
| Consistency of SB Variance Estimators | p. 57 |
| Consistency of SB Distribution Function Estimators | p. 63 |
| Extensions and Examples | p. 73 |
| Introduction | p. 73 |
| Smooth Functions of Means | p. 73 |
| M Estimators | p. 81 |
| Differentiable Functionals | p. 90 |
| Bootstrapping the Empirical Process | p. 92 |
| Consistency of the MBB for Differentiable Statistical Functionals | p. 94 |
| Examples | p. 99 |
| Comparison of Block Bootstrap Methods | p. 115 |
| Introduction | p. 115 |
| Empirical Comparisons | p. 116 |
| The Theoretical Framework | p. 118 |
| Expansions for the MSEs | p. 120 |
| Theoretical Comparisons | p. 123 |
| Asymptotic Efficiency | p. 123 |
| Comparison at Optimal Block Lengths | p. 124 |
| Concluding Remarks | p. 126 |
| Proofs | p. 127 |
| Proofs of Theorems 5.1-5.2 for the MBB, the NBB, and the CBB | p. 128 |
| Proofs of Theorems 5.1-5.2 for the SB | p. 135 |
| Second-Order Properties | p. 145 |
| Introduction | p. 145 |
| Edgeworth Expansions for the Mean Under Independence | p. 147 |
| Edgeworth Expansions for the Mean Under Dependence | p. 154 |
| Expansions for Functions of Sample Means | p. 160 |
| Expansions Under the Smooth Function Model Under Independence | p. 160 |
| Expansions for Normalized and Studentized Statistics Under Independence | p. 163 |
| Expansions for Normalized Statistics Under Dependence | p. 164 |
| Expansions for Studentized Statistics Under Dependence | p. 166 |
| Second-Order Properties of Block Bootstrap Methods | p. 168 |
| Empirical Choice of the Block Size | p. 175 |
| Introduction | p. 175 |
| Theoretical Optimal Block Lengths | p. 175 |
| Optimal Block Lengths for Bias and Variance Estimation | p. 177 |
| Optimal Block Lengths for Distribution Function Estimation | p. 179 |
| A Method Based on Subsampling | p. 182 |
| A Nonparametric Plug-in Method | p. 186 |
| Motivation | p. 187 |
| The Bias Estimator | p. 188 |
| The JAB Variance Estimator | p. 189 |
| The Optimal Block Length Estimator | p. 193 |
| Model-Based Bootstrap | p. 199 |
| Introduction | p. 199 |
| Bootstrapping Stationary Autoregressive Processes | p. 200 |
| Bootstrapping Explosive Autoregressive Processes | p. 205 |
| Bootstrapping Unstable Autoregressive Processes | p. 209 |
| Bootstrapping a Stationary ARMA Process | p. 214 |
| Frequency Domain Bootstrap | p. 221 |
| Introduction | p. 221 |
| Bootstrapping Ratio Statistics | p. 222 |
| Spectral Means and Ratio Statistics | p. 222 |
| Frequency Domain Bootstrap for Ratio Statistics | p. 224 |
| Second-Order Correctness of the FDB | p. 226 |
| Bootstrapping Spectral Density Estimators | p. 228 |
| Frequency Domain Bootstrap for Spectral Density Estimation | p. 229 |
| Consistency of the FDB Distribution Function Estimator | p. 231 |
| Bandwidth Selection | p. 233 |
| A Modified FDB | p. 235 |
| Motivation | p. 236 |
| The Autoregressive-Aided FDB | p. 237 |
| Long-Range Dependence | p. 241 |
| Introduction | p. 241 |
| A Class of Long-Range Dependent Processes | p. 242 |
| Properties of the MBB Method | p. 244 |
| Main Results | p. 244 |
| Proofs | p. 246 |
| Properties of the Subsampling Method | p. 251 |
| Results on the Normalized Sample Mean | p. 252 |
| Results on the Studentized Sample Mean | p. 253 |
| Proofs | p. 255 |
| Numerical Results | p. 257 |
| Bootstrapping Heavy-Tailed Data and Extremes | p. 261 |
| Introduction | p. 261 |
| Heavy-Tailed Distributions | p. 262 |
| Consistency of the MBB | p. 265 |
| Invalidity of the MBB | p. 268 |
| Extremes of Stationary Random Variables | p. 271 |
| Results on Bootstrapping Extremes | p. 274 |
| Bootstrapping Extremes With Estimated Constants | p. 277 |
| Resampling Methods for Spatial Data | p. 281 |
| Introduction | p. 281 |
| Spatial Asymptotic Frameworks | p. 282 |
| Block Bootstrap for Spatial Data on a Regular Grid | p. 283 |
| Description of the Block Bootstrap Method | p. 284 |
| Numerical Examples | p. 288 |
| Consistency of Bootstrap Variance Estimators | p. 292 |
| Results on the Empirical Distribution Function | p. 301 |
| Differentiable Functionals | p. 304 |
| Estimation of Spatial Covariance Parameters | p. 307 |
| The Variogram | p. 307 |
| Least Squares Variogram Estimation | p. 308 |
| The RGLS Method | p. 310 |
| Properties of the RGLS Estimators | p. 312 |
| Numerical Examples | p. 315 |
| Bootstrap for Irregularly Spaced Spatial Data | p. 319 |
| A Class of Spatial Stochastic Designs | p. 319 |
| Asymptotic Distribution of M-Estimators | p. 320 |
| A Spatial Block Bootstrap Method | p. 323 |
| Properties of the Spatial Bootstrap Method | p. 325 |
| Resampling Methods for Spatial Prediction | p. 328 |
| Prediction of Integrals | p. 328 |
| Prediction of Point Values | p. 335 |
| p. 339 | |
| p. 345 | |
| References | p. 349 |
| Author Index | p. 367 |
| Subject Index | p. 371 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780387009285
ISBN-10: 0387009280
Series: Springer Texts in Statistics
Published: 1st August 2003
Format: Hardcover
Language: English
Number of Pages: 396
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: GB
Dimensions (cm): 23.39 x 15.6 x 2.24
Weight (kg): 0.73
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