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

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A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test. / Racine, Jeffrey S.; Van Keilegom, Ingrid.

In: Journal of Business and Economic Statistics, Vol. 38, No. 4, 2020, p. 784-795.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articlepeer-review

Harvard

Racine, JS & Van Keilegom, I 2020, 'A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test', Journal of Business and Economic Statistics, vol. 38, no. 4, pp. 784-795. https://doi.org/10.1080/07350015.2019.1574227

APA

Racine, J. S., & Van Keilegom, I. (2020). A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test. Journal of Business and Economic Statistics, 38(4), 784-795. https://doi.org/10.1080/07350015.2019.1574227

CBE

Racine JS, Van Keilegom I. 2020. A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test. Journal of Business and Economic Statistics. 38(4):784-795. https://doi.org/10.1080/07350015.2019.1574227

MLA

Racine, Jeffrey S. and Ingrid Van Keilegom. "A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test". Journal of Business and Economic Statistics. 2020, 38(4). 784-795. https://doi.org/10.1080/07350015.2019.1574227

Vancouver

Racine JS, Van Keilegom I. A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test. Journal of Business and Economic Statistics. 2020;38(4):784-795. https://doi.org/10.1080/07350015.2019.1574227

Author

Racine, Jeffrey S. ; Van Keilegom, Ingrid. / A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test. In: Journal of Business and Economic Statistics. 2020 ; Vol. 38, No. 4. pp. 784-795.

Bibtex

@article{9fcdd1888b8d4e3eb5f27a844a65a96b,
title = "A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test",
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 typically approximated using nonsmooth empirical distribution functions (EDFs). In a recent article, Li, Li, and Racine establish the benefits of smoothing the EDF for inference, though their theoretical results are limited to the case where the covariates are observed and the distributions unobserved, while in the current setting some covariates and their distributions are unobserved (i.e., the test relies on population error terms from a location-scale model) which necessarily involves a separate theoretical approach. We demonstrate how replacing the nonsmooth distributions of unobservables with their kernel-smoothed sample counterparts can lead to substantial power improvements, and extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting in the presence of unobservables. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided.",
keywords = "Inference, Kernel smoothing, Kolmogorov–Smirnov, BOOTSTRAP, STATISTICS, Kolmogorov-Smirnov, OF-FIT TESTS, BANDWIDTH SELECTION",
author = "Racine, {Jeffrey S.} and {Van Keilegom}, Ingrid",
year = "2020",
doi = "10.1080/07350015.2019.1574227",
language = "English",
volume = "38",
pages = "784--795",
journal = "Journal of Business and Economic Statistics",
issn = "0735-0015",
publisher = "Taylor & Francis Inc.",
number = "4",

}

RIS

TY - JOUR

T1 - A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

AU - Racine, Jeffrey S.

AU - Van Keilegom, Ingrid

PY - 2020

Y1 - 2020

N2 - 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 typically approximated using nonsmooth empirical distribution functions (EDFs). In a recent article, Li, Li, and Racine establish the benefits of smoothing the EDF for inference, though their theoretical results are limited to the case where the covariates are observed and the distributions unobserved, while in the current setting some covariates and their distributions are unobserved (i.e., the test relies on population error terms from a location-scale model) which necessarily involves a separate theoretical approach. We demonstrate how replacing the nonsmooth distributions of unobservables with their kernel-smoothed sample counterparts can lead to substantial power improvements, and extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting in the presence of unobservables. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided.

AB - 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 typically approximated using nonsmooth empirical distribution functions (EDFs). In a recent article, Li, Li, and Racine establish the benefits of smoothing the EDF for inference, though their theoretical results are limited to the case where the covariates are observed and the distributions unobserved, while in the current setting some covariates and their distributions are unobserved (i.e., the test relies on population error terms from a location-scale model) which necessarily involves a separate theoretical approach. We demonstrate how replacing the nonsmooth distributions of unobservables with their kernel-smoothed sample counterparts can lead to substantial power improvements, and extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting in the presence of unobservables. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided.

KW - Inference

KW - Kernel smoothing

KW - Kolmogorov–Smirnov

KW - BOOTSTRAP

KW - STATISTICS

KW - Kolmogorov-Smirnov

KW - OF-FIT TESTS

KW - BANDWIDTH SELECTION

UR - http://www.scopus.com/inward/record.url?scp=85068178287&partnerID=8YFLogxK

U2 - 10.1080/07350015.2019.1574227

DO - 10.1080/07350015.2019.1574227

M3 - Journal article

AN - SCOPUS:85068178287

VL - 38

SP - 784

EP - 795

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

SN - 0735-0015

IS - 4

ER -