## Asymptotic StatisticsThis 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

link ve asimtotik kavramı gerçekten 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 |

433 | |

439 | |