Asymptotisch optimale adaptive Auswahlverfahren in semiparametrischen Modellen
Asymptotic optimal adaptive selection procedures for semi-parametric models
140 pages. Lage, Verlag Hans Jacobs (1996)
The thesis focus on two recent developments of modern mathematical statistics. First, the approach of asymptotic decision theory by Le Cam (1986) and Strasser (1985) is used for the derivation of asymptotic optimal selection procedures. Second, models from survival analysis with dependent censoring, which are of great practical relevance, are considered.
Asymptotic optimal non-adaptive selection procedures are derived for specific semi-parametric models. Based on these results adaptive decisions are established. Especially variants of the proportional hazards model considered allow various applications, for example in medicine, epidemiology and demography.
It turns out that despite the very technical derivative asymptotically optimal selection procedures have a very simple structure. A proportional hazards model which includes a infinite dimensional nuisance parameter is assumed. Furthermore, the lifetimes and censoring times are assumed to be conditionally independent given a finite dimensional covariate. For this model we construct a selection procedure without any prior information on the nuisance
parameter. This is done by substituting the unknown nuisance parameter by a kernel estimator. This procedure has the same asymptotic efficiency as the best selection rule with known nuisance parameter. By help of simulations it is shown that these selection procedures have good performance already in the case of moderate sample sizes, which underlines their applicability in practical problems.