Constrained Polynomial Likelihood

10/30/2019

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by   Paul Schneider, et al.

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Starting from a distribution z, we develop a non-negative polynomial minimum-norm likelihood ratio ξ such that dp=ξ dz satisfies a certain type of shape restrictions. The coefficients of the polynomial are the unique solution of a mixed conic semi-definite program. The approach is widely applicable. For example, it can be used to incorporate expert opinion into a model, or as an objective function in machine learning algorithms.