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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 \(Y_{ni}=g(x_{ni})+\epsilon _{ni}\) for \(i=1,\cdots ,n\), where \(g\) is unknown, \(x_{ni}\) are fixed design points, and \(\varepsilon _{ni}\) are negatively associated random errors. Nonparametric estimators \(g_{n}(x)\) of \(g(x)\) will be introduced and their asymptotic properties are studied. In particular, pointwise and uniform convergence of \(g_{n}(x)\) 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 and quantile regression
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0637.62044
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References:

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