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

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  • Jeffrey Racine
  • Ingrid Van Keilegom

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.

Suggested Citation

  • Jeffrey Racine & Ingrid Van Keilegom, 2017. "A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test," Department of Economics Working Papers 2017-13, McMaster University.
    • Handle: RePEc:mcm:deptwp:2017-13
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/McMasterEconWP2017-13.pdf
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    Cited by:

    1. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

    More about this item

    Keywords

    Kernel Smoothing; Kolmogorov-Smirnov; Inference;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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