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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Constrained Polynomial Likelihood
Caio Almeida, Ricardo Masini, Paul Schneider · 2019-10-31 · via math.ST updates on arXiv.org

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.

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