Electronic Journal of Statistics

Tests for the equality of conditional variance functions in nonparametric regression

Juan Carlos Pardo-Fernández, María Dolores Jiménez-Gamero, and Anouar El Ghouch

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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.

Article information

Electron. J. Statist., Volume 9, Number 2 (2015), 1826-1851.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties 62G09: Resampling methods

Asymptotics bootstrap comparison of curves empirical characteristic function empirical distribution function kernel smoothing local alternatives regression residuals


Pardo-Fernández, Juan Carlos; Jiménez-Gamero, María Dolores; El Ghouch, Anouar. Tests for the equality of conditional variance functions in nonparametric regression. Electron. J. Statist. 9 (2015), no. 2, 1826--1851. doi:10.1214/15-EJS1058. https://projecteuclid.org/euclid.ejs/1440680328

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