Author | Jacobsen, Martin. author |
---|---|
Title | Statistical Analysis of Counting Processes [electronic resource] / by Martin Jacobsen |
Imprint | New York, NY : Springer US, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-6275-3 |
Descript | VIII, 228 p. online resource |
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