Projection theorems and estimating equations for power-law models

Atin Gayen and M. Ashok Kumar

Journal of Multivariate Analysis, 2021, vol. 184, issue C

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.

Keywords: Cauchy distribution; Divergence; Estimating equation; Power-law family; Projection theorem; Student distribution (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.jmva.2021.104734

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