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What is Learnable in Valiant's Theory of the Learnable? 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Statistical inference for piecewise normal distributions and stochastic variational inequalities
Shu Lu, Hongsheng Liu · 2019-07-12 · via math.ST updates on arXiv.org

In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting, and apply this method to compute confidence intervals for the true solution of a stochastic variational inequality based on a solution to a sample average approximation problem. The confidence intervals are computed with simple formulas. Performance of the proposed method is tested with numerical experiments.

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