The importance of being able to detect heteroscedasticity in regression is widely recognized because efficient inference for the regression function requires that heteroscedasticity is taken into account. In this paper a simple consistent test for heteroscedasticity is proposed in a nonparametric regression set‐up. The test is based on an estimator for the best L2‐approximation of the variance function by a constant. Under mild assumptions asymptotic normality of the corresponding test statistic is established even under arbitrary fixed alternatives. Confidence intervals are obtained for a corresponding measure of heteroscedasticity. The finite sample performance and robustness of these procedures are investigated in a simulation study and Box‐type corrections are suggested for small sample sizes.
[1]
Peter Hall,et al.
Bootstrap test for difference between means in nonparametric regression
,
1990
.
[2]
Ulrich Stadtmüller,et al.
Estimation of Heteroscedasticity in Regression Analysis
,
1987
.
[3]
J. Cooper,et al.
Theory of Approximation
,
1960,
Mathematical Gazette.
[4]
R. Koenker,et al.
Robust Tests for Heteroscedasticity Based on Regression Quantiles
,
1982
.
[5]
D. Ruppert,et al.
Transformation and Weighting in Regression
,
1988
.