A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

McMaster University, Department of Economics Working Paper Series 2017-13

35 Pages Posted: 22 Aug 2017

See all articles by Jeffrey Racine

Jeffrey Racine

Department of Economics - McMaster University

Ingrid Van Keilegom

Catholic University of Louvain (UCL)

Date Written: August 16, 2017

Abstract

A number of tests have been proposed for assessing the location-scale assumption that is often invoked by practitioners. Existing approaches include Kolmogorov-Smirnov and Cramer-von-Mises statistics that each involve measures of divergence between unknown joint distribution functions and products of marginal distributions. In practice, the unknown distribution functions embedded in these statistics are approximated using non-smooth empirical distribution functions. We demonstrate how replacing the non-smooth distributions with their kernel-smoothed counter-parts can lead to substantial power improvements. In so doing we extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting thereby extending the reach of existing approaches. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided.

Keywords: Kernel Smoothing, Kolmogorov-Smirnov, Inference

JEL Classification: C14

Suggested Citation

Racine, Jeffrey and Van Keilegom, Ingrid, A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test (August 16, 2017). McMaster University, Department of Economics Working Paper Series 2017-13, Available at SSRN: https://ssrn.com/abstract=3020789 or http://dx.doi.org/10.2139/ssrn.3020789

Jeffrey Racine (Contact Author)

Department of Economics - McMaster University ( email )

Hamilton, Ontario L8S 4M4
Canada

Ingrid Van Keilegom

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium

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