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Confidence Intervals for Piecewise Normal Distributions and Stochastic Variational Inequalities

Author

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  • Shu Lu

    (Optana L.L.C., Chapel Hill, North Carolina 27516)

Abstract

In this paper, we first show how to obtain easy-to-compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution (assuming that the center belongs to a known affine set parallel to the common lineality space of all cones defining the piecewise normal distribution) by using certain skewed projectors on that space. We then extend this method to an asymptotic setting. Next, we apply this method to compute confidence intervals for the true solution of a stochastic variational inequality given a solution to a sample average approximation (SAA) problem for the general situation in which the asymptotic distribution of SAA solutions is piecewise normal. For stochastic complementarity problems, we obtain asymptotic normality of certain estimators of the true solution when the asymptotic distribution of the SAA solutions is piecewise normal.

Suggested Citation

  • Shu Lu, 2025. "Confidence Intervals for Piecewise Normal Distributions and Stochastic Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1333-1363, May.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:1333-1363
    DOI: 10.1287/moor.2023.0021
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