基于计数过程的统计模型

出版时间：1998-8  出版社：世界图书出版公司  作者：P.K.Andersen等著  页数：767  
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内容概要

One of the most remarkable examples of fast technology transfer from new developments in mathematical probability theory to applied statistical methodology is the use of counting processes, martingales in continuous time, and stochastic integration in event history analysis. By this (or generalized survival analysis), we understand the study of a collection of individuals, each moving among a finite (usually small) number of states. A basic example is moving from alive to dead, which forms the basis of survival analysis. Compared to other branches of statistics, this area is characterized by the dynamic temporal aspect, making modelling via the intensities useful, and by the special patterns of incompleteness of observation, of which right-censoring in survival analysis is the most important and best known example.

书籍目录

Preface I. Introduction 　I.1 General Introduction to the Book 　1.2 Brief Survey of the Development of the Subject 　1.3 Presentation of Practical Examples II. The Mathematical Background 　II.1 An Informal Introduction to the Basic Concepts 　II.2 Preliminaries: Processes， Filtrations， and Stopping Times 　II.3 Martingale Theory 　II.4 Counting Processes 　II.5 Limit Theory 　II.6 Product-Integration and Markov Processes 　II.7 Likelihoods and Partial Likelihoods for Counting Processes 　II.8 The Functional Delta-Method 　II.9 Bibliographic Remarks III. Model Specification and Censoring 　III.1 Examples of Counting Process models for Complete Life 　History Data. The Multiplicative Intensity Model 　III.2 Right-Censoring 　III.3 Left-Truncation 　III.4  General Censorship, Filtering, and Truncation　III.5  Partial Model Specifi ation. Time-Dependent Covariates　III.6  Bibliographic RemarksIV.   Nonparametric Estimation　IV.1  The Nelson-Aalen estimator　IV.2  Smoothing the Nelson-Aalen Estimator　IV.3  The Kaplan-Meier Estimator　IV.4  The Product-Limit Estimator for the Transition Matrix of a      Nonhomogeneous Markov Process　IV.5  Bibliographic RemarksV.   Nonparametric Hypothesis Testing　V.1  One-Sample Tests　V.2  k-Sample Tests　V.3  Other Linear Nonparametric Tests　V.4  Using the Complete Test Statistic Process　V.5  Bibliographic RemarksVI.  Parametric Models　VI.1  Maximum Likelihood Estimation　VI.2  M-Estimators　VI.3  Model Checking　VI.4  Bibliographic RemarksVII.  Regression Models　VII.1  Introduction. Regression Model Formulation　VII.2  Semiparametric Multiplicative Hazard Models　VII.3  Goodness-of-Fit Methods for the Semiparametric       Multiplicative Hazard Model　VII.4  Nonparametric Additive Hazard Models　VII.5  Other Non-and Semi-parametric Regression Models　VII.6  Parametric Regression Models　VII.7  Bibliographic RemarksVIII.  Asymptotic Efficiency　VIII.1  Contiguity and'Local Asymptotic Normality　VIII.2  Local Asymptotic Normality in Counting Process Models　VIII.3  Infinite-dimensional Parameter Spaces: the General Theory　VIll.4  Semiparametric Counting Process Models　VIII.5  Bibliographic RemarksIX.    Frailty Models　IX.1   Introduction　IX.2   Model Construction　IX.3   Likelihoods and Intensities  ……X. Multivariate  Time ScaleAppendixReferencesAuthor IndexSubject Index