# Projection Theorems and Estimating Equations for Power-Law Models

## TL;DR

This paper extends projection theorems for divergence measures to continuous models, simplifying estimation problems for power-law distributions like Student and Cauchy.

## Contribution

It introduces regularity for generalized exponential models and applies projection theorems to solve estimation problems for specific power-law distributions.

## Key findings

- Projection theorems are extended to continuous models.
- Estimation problems for Student and Cauchy distributions are solved.
- Regularity notion for generalized exponential models is introduced.

## 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.