Two tests for heteroscedasticity in nonparametric regression |
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Authors: | Mario Francisco-Fernández Juan M Vilar-Fernández |
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Institution: | 1. Facultad de Informática, Universidad de A Coru?a, Campus de Elvi?a s/n, 15071, Corunna, Spain
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Abstract: | In this paper, two new tests for heteroscedasticity in nonparametric regression are presented and compared. The first of these
tests consists in first estimating nonparametrically the unknown conditional variance function and then using a classical
least-squares test for a general linear model to test whether this function is a constant. The second test is based on using
an overall distance between a nonparametric estimator of the conditional variance function and a parametric estimator of the
variance of the model under the assumption of homoscedasticity. A bootstrap algorithm is used to approximate the distribution
of this test statistic. Extended versions of both procedures in two directions, first, in the context of dependent data, and
second, in the case of testing if the variance function is a polynomial of a certain degree, are also described. A broad simulation
study is carried out to illustrate the finite sample performance of both tests when the observations are independent and when
they are dependent. |
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Keywords: | Homoscedasticity Local polynomial estimator Volatility function |
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