Title

Constrained Polynomial Likelihood

Author(s)

Caio Almeida Caio Almeida (Princeton University)

Paul Schneider Paul Schneider (University of Lugano)

Abstract

We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known under shape restrictions. The PLR converges to the true, unknown, likelihood ratio. We show consistency, obtain the asymptotic distribution for the PLR coefficients estimated with sample moments, and present two applications. The first develops a PLR for the unknown transition density of a jump-diffusion process. The second modifies the Hansen-Jagannathan pricing kernel framework to accommodate polynomial return models consistent with no-arbitrage while simultaneously nesting the linear return model.

Creation Date

2021-10

Section URL ID

Paper Number

2021-45

URL

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3851730

File Function

Jel

C13, C51, C61

Keyword(s)

Likelihood ratio, positive polynomial, Reproducing Kernel Hilbert Space (RKHS)

Suppress

false

Series

13