Projection Theorems and Estimating Equations for Power-Law Models
Abstract
We extend projection theorems concerning Hellinger and Jones et al. divergences to the continuous case. These projection theorems reduce certain estimation problems on generalized exponential models to linear problems. We introduce the notion of regularity for generalized exponential models and show that the projection theorems in this case are similar to the ones in discrete and canonical case. We also apply these ideas to solve certain estimation problems concerning Student and Cauchy distributions.
Cite
@article{arxiv.1905.01434,
title = {Projection Theorems and Estimating Equations for Power-Law Models},
author = {Atin Gayen and M. Ashok Kumar},
journal= {arXiv preprint arXiv:1905.01434},
year = {2021}
}
Comments
New simulation results added stating the applicability of the generalized estimators: (1) comparing the robust estimators for Student distributions with maximum likelihood estimators, (2) Hellinger estimators for Cauchy distributions using two kernel density estimates for the sample empirical measure