Empirical smoothing lack-of-fit tests for variance function. (English) Zbl 1300.62031

Summary: 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 X. Zheng’s nonparametric smoothing test [Metrika 75, No. 4, 455–469 (2012; Zbl 1300.62032)], H. L. Koul and P. Ni’s minimum distance test for the mean function in the classic regression models [J. Stat. Plann. Inference 119, No. 1, 109–141 (2004; Zbl 1032.62036)]. 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.


62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
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