Beitrag in einem Sammelband

Exploratory exponential tilting

Abstract

We propose a new technique to summarize several distributions parsimoniously by employing ideas from Exponential Tilting (ET). We assume that the observed data are generated by densities that can be derived from a single (latent) reference distribution by ET, i.e., while preserving the sample means they have minimal Kullback-Leibler distance to the reference distribution. We show how the reference densitiy and the resulting Lagrange multipliers can be estimated by penalized likelihood in a GLM setting. We also suggest an extension of the model, if simple ET does not lead to a satisfactory summary. We illustrate the methodology by two applications.