Randomization and statistical expert information methods

Seminar in Insurance and Economics

SPEAKER: Martin Bladt (University of Lausanne)

TITLE: Randomization and statistical expert information methods

KEYWORDS: Randomization, expert information, smoothed distributions, informed estimation.

ABSTRACTWe consider the introduction of exogenous random variables into the statistical modeling framework. The first aim is to show that such a setting can produce robust estimators in the case of few or heterogeneous data, and in that case, the exogenous variables will be fully independent and regarded as a smoothing mechanism. The second aim is to incorporate expert information into maximum likelihood estimation through informed randomization. This mechanism allows incorporating expert guesses into a loss function even before any observation has been made, or when only partial information is present. The latter method has the potential to bridge statistical rigor with certain actuarial traditions, by casting both into the same framework and outputting a balanced result. The third and final aim is to present a nonparametric approach to incorporating expert information into the KaplanMeier estimator. We provide conditions for recovering the asymptotic distribution of the presented estimators, generalizing GlivenkoCantelli and Donsker type results for the independent case, and M- and Z- estimator-type asymptotics for the informed case. Asymptotic theory for the modified KaplanMeier estimators is also provided. The results are not limited to actuarial applications and may be used whenever exogeneous information requires to be taken into account in statistical analysis. The talk is partially based on joint research with Hansjörg Albrecher and Christian Furrer.