Minimum distance conditional variance function checking in heteroscedastic regression models

This paper discusses a class of minimum distance tests for fitting a parametric variance function in heteroscedastic regression models. These tests are based on certain minimized L2L2 distances between a nonparametric variance function estimator and the parametric variance function estimator. The paper establishes the asymptotic normality of the proposed test statistics and that of the corresponding minimum distance estimator under the fitted model. These estimators turn out to be n-consistent. Consistency of this sequence of tests at some fixed alternatives and asymptotic power under some local nonparametric alternatives are also discussed. Some simulation studies are conducted to assess the finite sample performance of the proposed test.