Universal Prediction Band Via Semi-Definite Programming

16 Pages Posted: 8 Apr 2021

See all articles by Tengyuan Liang

Tengyuan Liang

University of Chicago - Booth School of Business

Date Written: April 6, 2021


We propose a computationally efficient method to construct nonparametric, heteroskedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, with strong non-asymptotic coverage properties, and easy to implement using standard convex programs. Our approach can be viewed as a novel variance interpolation with confidence and further leverages techniques from semi-definite programming and sum-of-squares optimization. Theoretical and numerical performances for the proposed approach for uncertainty quantification are analyzed.

Keywords: Uncertainty quantification, variance interpolation, nonparametric prediction band, semi-definite programming, sum-of-squares.

Suggested Citation

Liang, Tengyuan, Universal Prediction Band Via Semi-Definite Programming (April 6, 2021). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2021-41, Available at SSRN: https://ssrn.com/abstract=3821212 or http://dx.doi.org/10.2139/ssrn.3821212

Tengyuan Liang (Contact Author)

University of Chicago - Booth School of Business ( email )

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