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Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences. (English) Zbl 1070.62022
Summary: Consider the nonparametric regression model ${Y}_{ni}=g\left({x}_{ni}\right)+{ϵ}_{ni}$ for $i=1,\cdots ,n$, where $g$ is unknown, ${x}_{ni}$ are fixed design points, and ${\epsilon }_{ni}$ are negatively associated random errors. Nonparametric estimators ${g}_{n}\left(x\right)$ of $g\left(x\right)$ will be introduced and their asymptotic properties are studied. In particular, pointwise and uniform convergence of ${g}_{n}\left(x\right)$ and their asymptotic normality will be investigated. This extends earlier work on independent random errors [see, e.g., A. A. Georgiev J. Multivariate Anal. 25, 100–110 (1988; Zbl 0637.62044)].
##### MSC:
 62G08 Nonparametric regression 62G20 Nonparametric asymptotic efficiency