Empirical smoothing lack-of-fit tests for variance function

This paper discusses a nonparametric empirical smoothing lack-of-fit test for the functional form of the variance in regression models. The proposed test can be treated as a nontrivial modification of Zhengʹs nonparametric smoothing test, Koul and Niʹs minimum distance test for the mean function in the classic regression models. The paper establishes the asymptotic normality of the proposed test under the null hypothesis. Consistency at some fixed alternatives and asymptotic power under some local alternatives are also discussed. A simulation study is conducted to assess the finite sample performance of the proposed test. Simulation study also shows that the proposed test is more powerful and computationally more efficient than some existing tests.