Testing Stochastic Dominance with Many Conditioning Variables

55 Pages Posted: 7 Mar 2020

See all articles by Oliver B. Linton

Oliver B. Linton

University of Cambridge

Myunghwan Seo

affiliation not provided to SSRN

Yoon-Jae Whang

Seoul National University - School of Economics

Date Written: February 10, 2020

Abstract

We propose a test of the hypothesis of conditional stochastic dominance in the presence of many conditioning variables (whose dimension may grow to infinity as the sample size diverges). Our approach builds on a semiparametric location scale model in the sense that the conditional distribution of the outcome given the covariates is characterized by a nonparametric mean function and a nonparametric skedastic function with an independent innovation whose distribution is unknown. We propose to estimate the nonparametric mean and skedastic regression functions by the ℓ₁-penalized nonparametric series estimation with thresholding. Under the sparsity assumption, where the number of truly relevant series terms are relatively small (but their identities are unknown), we develop the estimation error bounds for the regression functions and series coefficients estimates allowing for the time series dependence. We derive the asymptotic distribution of the test statistic, which is not pivotal asymptotically, and introduce the smooth stationary bootstrap to approximate its sample distribution. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.

Keywords: Bootstrap; Empirical process; Home bias; LASSO; Power boosting; Sparsity

JEL Classification: C10, C12,C15, C15

Suggested Citation

Linton, Oliver B. and Seo, Myunghwan and Whang, Yoon-Jae, Testing Stochastic Dominance with Many Conditioning Variables (February 10, 2020). Available at SSRN: https://ssrn.com/abstract=3535723 or http://dx.doi.org/10.2139/ssrn.3535723

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Myunghwan Seo

affiliation not provided to SSRN

No Address Available

Yoon-Jae Whang

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742
Korea
+82 2 80 6362 (Phone)
+82 2 86 4231 (Fax)

HOME PAGE: http://plaza.snu.ac.kr/~whang

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