## Introduction to Empirical Processes and Semiparametric InferenceThe goal of this book is to introduce statisticians, and other researchers with a background in mathematical statistics, to empirical processes and semiparametric inference. These powerful research techniques are surpr- ingly useful for studying large sample properties of statistical estimates from realistically complex models as well as for developing new and - proved approaches to statistical inference. This book is more of a textbook than a research monograph, although a number of new results are presented. The level of the book is more - troductory than the seminal work of van der Vaart and Wellner (1996). In fact, another purpose of this work is to help readers prepare for the mathematically advanced van der Vaart and Wellner text, as well as for the semiparametric inference work of Bickel, Klaassen, Ritov and We- ner (1997). These two books, along with Pollard (1990) and Chapters 19 and 25 of van der Vaart (1998), formulate a very complete and successful elucidation of modern empirical process methods. The present book owes much by the way of inspiration, concept, and notation to these previous works.What is perhaps new is the gradual—yetrigorous—anduni?ed way this book introduces the reader to the ?eld. |

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### Contents

3 | |

Overview of Semiparametric Inference 35 | 34 |

Case Studies I | 49 |

Empirical Processes | 75 |

Stochastic Convergence | 103 |

Empirical Process Methods | 127 |

Entropy Calculations 155 | 154 |

Bootstrapping Empirical Processes | 179 |

Case Studies II | 283 |

Introduction to Semiparametric Inference | 319 |

Semiparametric Models and Efficiency | 333 |

Efficient Inference for FiniteDimensional Parameters | 349 |

Efficient Inference for InfiniteDimensional Parameters 379 | 378 |

Semiparametric MEstimation | 397 |

Case Studies III | 424 |

459 | |

Additional Empirical Process Results | 207 |

The Functional Delta Method 235 | 234 |

ZEstimators | 251 |

Author Index | 470 |

477 | |

### Other editions - View all

Introduction to Empirical Processes and Semiparametric Inference Michael R. Kosorok No preview available - 2007 |

Introduction to Empirical Processes and Semiparametric Inference Michael R. Kosorok No preview available - 2008 |

Introduction to Empirical Processes and Semiparametric Inference Michael R. Kosorok No preview available - 2010 |

### Common terms and phrases

apply approach arbitrary arguments assume assumptions asymptotically Banach space bootstrap bounded Chapter closed Combining compact consider consistency constant continuous convergence Corollary covariance defined definition denote depend derivative desired differentiable discussed distribution Donsker efficient empirical process entropy envelope equation equivalent establish estimator example Exercise exists fact finite fixed function Gaussian given Hence holds implies important independent inequality inference integral interest Lemma likelihood limiting linear M-estimators maximizer maximum mean measurable methods metric norm Note observed obtain operator outer parameter present probability proof prove random regression require respect result sample satisfies score Section semiparametric sequence space statistical subset surely Theorem tight tion true uniform uniformly valid values variables verify weak convergence weighted yields zero