Minimum distance conditional variance function checking in heteroscedastic regression models

Samarakoon, Nishantha Anura; Song, Weixing

doi:10.1016/j.jmva.2010.11.003

Cited by 8 publications

(2 citation statements)

References 26 publications

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“…Wang and Zhou (2007) proposed a nonparametric test based on kernel method for accessing the adequacy of a given parametric variance function. Samarakoon and Song (2011) developed a test for the parametric form of the variance function based on the minimized L 2 distance between a nonparametric variance function estimator and the parametric variance function estimator. Samarakoon and Song (2012) further considered a nonparametric empirical smoothing lack-of-fit test for checking the adequacy of a given parametric variance structure.…”

Section: Introductionmentioning

confidence: 99%

Testing the parametric form of the conditional variance in regressions based on distance covariance

Hu¹,

Li²,

Tan³

2022

Preprint

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In this paper, we propose a new test for checking the parametric form of the conditional variance based on distance covariance in nonlinear and nonparametric regression models. Inherit from the nice properties of distance covariance, our test is very easy to implement in practice and less effected by the dimensionality of covariates. The asymptotic properties of the test statistic are investigated under the null and alternative hypotheses. We show that the proposed test is consistent against any alternative and can detect local alternatives converging to the null hypothesis at the parametric rate 1/ √ n in both the nonlinear and nonparametric settings. As the limiting null distribution of the test statistic is intractable, we propose a residual bootstrap to approximate the limiting null distribution. Simulation studies are presented to assess the finite sample performance of the proposed test. We also apply the proposed test to a real data set for illustration.

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Section: Introductionmentioning

confidence: 99%

Testing the parametric form of the conditional variance in regressions based on distance covariance

Hu¹,

Li²,

Tan³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Specifically, on the basis of independent observations from (1), we wish to test the null hypothesiswhere σ 2 (·; θ) represents a parametric model for the conditional variance function, against the general alternative H 1 : H 0 is not true.Several tests for H 0 have been proposed in the specialised literature. Some of them were designed for testing homoscedasticity (see, for example, Liero, 2003, Dette andMarchlewski, 2010); others assume that the regression function has a known parametric form (see, for example, Koul and Song, 2010, Samarakoon and Song, 2011, 2012; others were built for fixed design points (see, for example, Dette and Hetzler, 2009a,b); others detect contiguous alternatives converging to the null at a rate slower that n −1/2 (see, for example, Wang and Zhou, 2007, Samarakoon and Song, 2011, 2012. Although initially the test in Koul and Song (2010) was designed for parametric regression functions, they also provide the theory for a version where the mean function is nonparametrically estimated.The test in Dette et al (2007) (henceforth DNV) does not possess any of the above cited cons.…”

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confidence: 99%

A model specification test for the variance function in nonparametric regression

Pardo–Fernández

Jiménez-Gamero

2018

AStA Adv Stat Anal

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The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted L 2 -distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.is the conditional variance function and ε is the regression error, which is assumed to be independent of X. Note that, by construction, E(ε) = 0 and V ar(ε)=1. The covariate X is one-dimensional and continuous with probability density function (pdf) f and compact support R. The pdf f is assumed to be positive on R. The regression function, the variance function, the distribution of the error and the distribution of the covariate are unknown and no parametric models are assumed for them.Parametric specifications for either the regression function or the variance function are quite attractive among practitioners since they describe the relation between the response and the covariate in a concise way. Because of this reason, there are a number of papers dealing with the parametric modelling of the conditional mean and the conditional variance of Y , given X. This paper proposes a new goodness-of-fit test for the parametric form of the conditional variance. Specifically, on the basis of independent observations from (1), we wish to test the null hypothesiswhere σ 2 (·; θ) represents a parametric model for the conditional variance function, against the general alternative H 1 : H 0 is not true.Several tests for H 0 have been proposed in the specialised literature. Some of them were designed for testing homoscedasticity (see, for example, Liero, 2003, Dette andMarchlewski, 2010); others assume that the regression function has a known parametric form (see, for example, Koul and Song, 2010, Samarakoon and Song, 2011, 2012; others were built for fixed design points (see, for example, Dette and Hetzler, 2009a,b); others detect contiguous alternatives converging to the null at a rate slower that n −1/2 (see, for example, Wang and Zhou, 2007, Samarakoon and Song, 2011, 2012. Although initially the test in Koul and Song (2010) was designed for parametric regression functions, they also provide the theory for a version where the mean function is nonparametrically estimated.The test in Dette et al. (2007) (henceforth DNV) does not possess any of the above cited cons. The methodology that will be proposed in the present paper is, in a certain sense, close to that in DNV. Next, we describe our proposal and the precise meaning of such closeness. Let ε = {Y − m(X)}/σ(X) be the regression error and let ε 0 = {Y − m(X)}/σ(X; θ)

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Pairwise distance-based heteroscedasticity test for regressions

et al. 2020

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Minimum distance conditional variance function checking in heteroscedastic regression models

Cited by 8 publications

References 26 publications

Testing the parametric form of the conditional variance in regressions based on distance covariance

Testing the parametric form of the conditional variance in regressions based on distance covariance

A model specification test for the variance function in nonparametric regression

Pairwise distance-based heteroscedasticity test for regressions

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