Distributionally Robust Conditional Quantile Prediction with Fixed Design

36 Pages Posted: 12 Jun 2019 Last revised: 18 Oct 2021

See all articles by Meng Qi

Meng Qi

Cornell SC Johnson College of Business

Ying Cao

University of California, Berkeley - Department of Industrial Engineering and Operations Research

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR)

Date Written: June 1, 2019

Abstract

Conditional quantile prediction involves estimating/predicting the quantile of a response random variable conditioned on observed covariates. The existing literature assumes the availability of independent and identically distributed (i.i.d.) samples of both the covariates and the response variable. However, such an assumption often becomes restrictive in many real-world applications. By contrast, we consider a fixed-design setting of the covariates, under which neither the response variable nor the covariates have i.i.d. samples. The present study provides a new data-driven distributionally robust framework under a fixed-design setting. We propose a regress-then-robustify method by constructing a surrogate empirical distribution of the noise. The solution of our framework coincides with a simple yet practical method that involves only regression and sorting, therefore provides an explanation for its empirical success. Measure concentration results are obtained for the surrogate empirical distribution, which further lead to finite-sample performance guarantees and asymptotic consistency. Numerical experiments are conducted to demonstrate the advantages of our approach.

Keywords: quantile prediction, distributionally robust optimization, data-driven Newsvendor problem

JEL Classification: C6

Suggested Citation

Qi, Meng and Cao, Ying and Shen, Zuo-Jun Max, Distributionally Robust Conditional Quantile Prediction with Fixed Design (June 1, 2019). Available at SSRN: https://ssrn.com/abstract=3397450 or http://dx.doi.org/10.2139/ssrn.3397450

Meng Qi (Contact Author)

Cornell SC Johnson College of Business ( email )

Ithaca, NY 14850
United States

HOME PAGE: http://https://alicemengqi.github.io/site/

Ying Cao

University of California, Berkeley - Department of Industrial Engineering and Operations Research ( email )

4141 Etcheverry Hall
Berkeley, CA 94720-1777
United States

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR) ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

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