On the Convergence Rate for a Kernel Estimate of the Regression Function

摘要

We give the rate of the uniform convergence for the kernel estimate of the regression function over a sequence of compact sets which increases to $mathbb{R}^{d}$ when $n$ approaches the infinity and when the observed process is $arphi$-mixing. The used estimator for the regression function is the kernel estimator proposed by Nadaraya, Watson (1964).