Statistical Analysis of Counting Processes

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. Language: English