Constrained Polynomial Likelihood

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