# Constrained Polynomial Likelihood

arXiv: https://arxiv.org/abs/1910.14009 · HTML: https://mlsanity.com/paper/1910.14009/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Adaptive joint distribution learning](https://mlsanity.com/paper/2110.04829/) (2021)

## Abstract (arXiv)

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.