基于计数过程的统计模型

所属分类:数学  
出版时间:1998-8   出版时间:世界图书出版公司   作者:P.K.Andersen等著   页数:767  
Tag标签:数学  

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

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数学


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