Uniform Consistency of Kernel Estimators of a Regression Function Under Generalized Conditions

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Abstract
In this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data. In addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous, we consider the cases that some regressors are discrete and the data are either stationary ϕ-mixing themselves or generated by a class of functions of one-sided infinite stationary ϕ-mixing sequences. Moreover, we demonstrate the performance of the kernel estimation method under these generalized conditions by a numerical example.

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