A Parametricness Index to Help Stop the War Between AIC and BIC?

Abstract

Parametric and nonparametric models are convenient mathematical tools to describe characteristics of data with different degrees of simplification. When a model is to be selected from a number of parametric candidates, not surprisingly, differences occur when the data generating process is assumed to be parametric or nonparametric. In particular, there is the well known "war" between AIC and BIC. In this talk, in a regression context, we will consider the question if and how we can distinguish between parametric and nonparametric situations and discuss feasibility of adaptive estimation to handle both parametric and nonparametric scenarios optimally. This is joint work with Wei Liu.