Constrained Polynomial Likelihood
Optimization and Control
2023-09-06 v4 Statistics Theory
Statistics Theory
Abstract
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for additional shape restrictions, as we illustrate with two empirical applications. The first develops a PLR for the unknown transition density of a jump-diffusion process, while the second extracts a positive density directly from option prices. In both cases, we show the importance of implementing the non-negativity restriction.
Cite
@article{arxiv.1910.14009,
title = {Constrained Polynomial Likelihood},
author = {Caio Almeida and Ricardo Masini and Paul Schneider},
journal= {arXiv preprint arXiv:1910.14009},
year = {2023}
}