On asymptotic behavior of Nadaraya–Watson regression estimator

Abstract

The random field (Xi, Yi), i∈ZN${{\bf i}}\in \mathbb {Z}^N$ is dependent and assumed to satisfy some mild mixing conditions. In this article, a Nadaraya–Watson regression estimator (N. W. R. E.) is established and investigated. We show that the distribution of the N. W. R. E. is asymptotically normal under some commonly used conditions.