Statistical Inference for a Family of Counting Processes

Aalen absolutely continuous adapted to F Assume Assumption 2.1 Asymptotic Theory asymptotically optimal Berkeley Berkeley LIBRARY Berkeley OF CALIFORNIA Billingsley 1968 Boel CALIFORNIA Berkeley Berkeley CALIFORNIA LIBRARY censoring process component process condition constant convergence in probability Corollary defined Definition denote distribution Dolivo Doob-Meyer decomposition theorem forces of transition Hence independent Poisson processes intensity process interval Kaplan and Meier left-continuous Lemma likelihood M₂ Markov chain McLeish Meyer multivariate counting process N₁ N₂ Nonparametric estimation notation number of jumps o-algebras observed orthogonal square integrable P₁ partition Poisson processes probability measure process with intensity proof prove random sample random variable rank tests respect to F result right-continuous right-hand limits s)ds satisfying Section 5A self-exciting sequence square integrable martingales step functions Stieltjes integrals stochastic integrals stochastic process submartingale Theorem 4.1 theory of Section U₁ UNIVERSITY OF CALIFORNIA weak convergence Wiener processes Y₁