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2015 Tests for the equality of conditional variance functions in nonparametric regression
Juan Carlos Pardo-Fernández, María Dolores Jiménez-Gamero, Anouar El Ghouch
Electron. J. Statist. 9(2): 1826-1851 (2015). DOI: 10.1214/15-EJS1058


In this paper we are interested in checking whether the conditional variances are equal in $k\ge2$ location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use of this null hypothesis. We propose four test statistics based on empirical distribution functions (Kolmogorov-Smirnov and Cramér-von Mises type test statistics) and two test statistics based on empirical characteristic functions. The limiting distributions of these six test statistics are established under the null hypothesis and under local alternatives. We show how to approximate the critical values using either an estimated version of the asymptotic null distribution or a bootstrap procedure. Simulation studies are conducted to assess the finite sample performance of the proposed tests. We also apply our tests to data on household expenditures.


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Juan Carlos Pardo-Fernández. María Dolores Jiménez-Gamero. Anouar El Ghouch. "Tests for the equality of conditional variance functions in nonparametric regression." Electron. J. Statist. 9 (2) 1826 - 1851, 2015.


Received: 1 July 2014; Published: 2015
First available in Project Euclid: 27 August 2015

zbMATH: 1327.62294
MathSciNet: MR3391121
Digital Object Identifier: 10.1214/15-EJS1058

Primary: 62G08 , 62G10
Secondary: 62G09 , 62G20

Keywords: asymptotics , bootstrap , comparison of curves , Empirical characteristic function , Empirical distribution function , kernel smoothing , local alternatives , regression residuals

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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