5/20/2016, 5/27/2016

Post date: May 24, 2016 8:19:04 PM

Short Course: Biostatistician's User Guide to Empirical Process Theory

Lecturer: Takumi Saegusa, Department of Mathematics, University of Maryland, College Park

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[abstract]

Semi- and non-parametric models play important roles in biostatistical applications. Analysis of these models requires more elaborate mathematical theory than the one needed for parametric models.

Empirical process theory provides sophisticated mathematical tools to study theoretical properties of many statistical procedures in semi- and non-parametric models. Despite its high utility, barriers to entry in empirical process theory seem to be lofty for beginners because required background knowledge such as probability theory and functional analysis is not covered in a standard curriculum in biostatistics. In this short course, we introduce few important concepts in empirical process theory and discuss their use through examples. Specifically we illustrate the uniform law of large numbers, maximal inequalities, and the uniform central limit theorem in the context of establishing consistency, rate of convergence and asymptotic normality of the MLE of the regression parameter in the Cox proportional hazards model with current status data. We rather emphasize applications of empirical process results than proving theorems so that interested applied audience can be motivated to start studying theory itself with concrete applications in mind.