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Statistical Analysis of Counting Processes

BuchKartoniert, Paperback
228 Seiten
Englisch
Springererschienen am01.11.1982Softcover reprint of the original 1st ed. 1982
Since also this process theory is virtually inaccessible to non-probabilists, it would appear useful to have an account of what Aalen has done, that includes exactly the amount of probability required to deal satisfactorily and rigorously with statistical models for counting processes.mehr
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BuchKartoniert, Paperback
EUR53,49
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Produkt

KlappentextSince also this process theory is virtually inaccessible to non-probabilists, it would appear useful to have an account of what Aalen has done, that includes exactly the amount of probability required to deal satisfactorily and rigorously with statistical models for counting processes.
Details
ISBN/GTIN978-0-387-90769-7
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr1982
Erscheinungsdatum01.11.1982
AuflageSoftcover reprint of the original 1st ed. 1982
ReiheLecture Notes in Statistics
Seiten228 Seiten
SpracheEnglisch
Gewicht367 g
IllustrationenVIII, 228 p.
Artikel-Nr.17297815

Inhalt/Kritik

Inhaltsverzeichnis
1. One-Dimensional Counting Processes.- 1.1. Probabilities on (0,?].- 1.2. The definition of one-dimensional counting processes.- 1.3. Construction of canonical counting processes.- 1.4. Intensities for canonical counting processes.- 1.5. Martingale decompositions for canonical counting processes.- 1.6. Statistical models and likelihood ratios.- Notes.- Exercises.- 2. Multivariate Counting Processes.- 2.1. Definition and construction of multivariate counting processes.- 2.2. Intensities and martingale representations.- 2.3. Products of canonical counting processes.- 2.4. Likelihood ratios.- 2.5. Discrete counting processes.- Exercises.- 3. Stochastic Integrals.- 3.1. Processes and martingales on WE.- 3.2. Definition and basic properties of stochastic integrals.- Notes.- Exercises.- 4. The Multiplicative Intensity Model.- 4.1. Definition of the full Aalen model.- 4.2. Product models and sufficient reductions.- 4.3. Estimation in the Aalen Model.- 4.4. Estimation in Markov chains.- 4.5. The Cox regression model.- 4.6. Maximum-likelihood estimation in Aalen models.- Notes.- Exercises.- 5. Asymptotic Theory.- 5.1. A limit theorem for martingales.- 5.2. Asymptotic distributions of Aalen estimators.- 5.3. Asymptotic distributions of product-limit estimators.- 5.4. Comparison of two intensities.- Notes.- Exercises.- 1. The principle of repeated conditioning.- 2. Weak convergence.- References.mehr