Asymptotic Statistics

Cambridge University Press, Jun 19, 2000 - Mathematics - 443 pages
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

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p 192 Chapter 14: Asymptotic power functions

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link ve asimtotik kavramı ger�ekten iyi. This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master’s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics. • Based on notes from graduate and master’s level courses taught by the author in Europe and in the US • Mathematically rigorous yet practical • Coverage of a wide range of classical and recent topics Contents 1. Introduction; 2. Stochastic convergence; 3. The delta-method; 4. Moment estimators; 5. M- and Z-estimators; 6. Contiguity; 7. Local asymptotic normality; 8. Efficiency of estimators; 9. Limits of experiments; 10. Bayes procedures; 11. Projections; 12. U-statistics; 13. Rank, sign, and permutation statistics; 14. Relative efficiency of tests; 15. Efficiency of tests; 16. Likelihood ratio tests; 17. Chi-square tests; 18. Stochastic convergence in metric spaces; 19. Empirical processes; 20. The functional delta-method; 21. Quantiles and order statistics; 22. L-statistics; 23. The bootstrap; 24. Nonparametric density estimation; 25. Semiparametric models. Reviews ‘The book is extremely well written and clear … it is comprehensive and has an abundant supply of worked examples … anyone who is genuinely interested in learning about some of the recent developments in asymptotic statistics and their potential applications should have a copy of this book.’ Biometrics ‘I recommend this book to every advanced Master’s student, Ph.D. student or researcher in mathematical statistics.’ Kwantitatieve methoden

Contents

 Stochastic Convergence 5 Delta Method 25 Moment Estimators 35 Contiguity 85 Local Asymptotic Normality 92 Efficiency of Estimators 108 Limits of Experiments 125 Bayes Procedures 138
 Likelihood Ratio Tests 227 ChiSquare Tests 242 Stochastic Convergence in Metric Spaces 255 Empirical Processes 265 Functional Delta Method 291 Quantiles and Order Statistics 304 LStatistics 316 Bootstrap 326

 Projections 153 Statistics 161 Rank Sign and Permutation Statistics 173 Relative Efficiency of Tests 192 Efficiency of Tests 215
 Nonparametric Density Estimation 341 Semiparametric Models 358 References 433 Index 439 Copyright