Checking Adequacy of Variance Function in Nonparametric Regression with Unknown Mean Function

doi:10.1007/s11424-026-5100-4

Checking Adequacy of Variance Function in Nonparametric Regression with Unknown Mean Function

2026-02-05

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DOI：10.1007/s11424-026-5100-4

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In this paper, the authors propose a class of test procedures to check the fitness of parametric forms of the variance function in regression models when the mean function is unknown. By evaluating the unknown mean function with the classical kernel estimator, the proposed test statistics are built upon a modified minimum distance between a nonparametric fit and a parametric estimator under the null hypothesis for the variance function. Asymptotic properties of the estimator of the parameters in the variance function are discussed, and the large sample distribution of the test statistics under the null hypothesis is established, as well as the consistency and the power under some local alternative hypotheses. Extensive numerical studies demonstrate that the proposed test procedures have satisfactory finite sample performance. Finally, two real data examples further showcase the effectiveness of the proposed test in real applications.

Keywords:

Consistency and local power

heterogeneity test

minimum distance

variance function

Checking Adequacy of Variance Function in Nonparametric Regression with Unknown Mean Function

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