Exploratory exponential tilting
In: Muggeo, V. M. R., Capursi, V., Boscaino, G., Lovison, G. (Eds.): Proceedings of the 28th International Workshop on Statistical Modelling, Palermo 8-12 July, 2013: volume 1, part II, 97–102
Palermo, Università di Palermo, Dipartimento di Scienze Statistiche e Matematiche (2013)
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.