We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. 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 linear return models consistent with no-arbitrage.

翻译：我们开发了一种非负多边最低-北位概率比率(PLR),其中两种分布方式只有瞬间才知道。 PLR 组合成真实的、未知的、可能性的比。我们表现出一致性,获得用样本时间估计的PLR系数的无症状分布,并呈现两种应用。第一种是针对跳跃扩散过程的未知过渡密度开发一个PLR。第二种是修改汉森-贾甘纳汉对内核定价框架,以适应无套利的线性返回模型。