Uniform Consistency of Kernel Estimators of a Regression Function Under Generalized Conditions
本文证明了在数据独立同分布、部分解释变量离散、数据为平稳φ混合序列等广义条件下，多元回归函数核估计量的一致相合性，并通过数值例子展示其表现。
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.