Fixed design regression for negatively associated random fields

Wentao Gu and Lanh Tran

Journal of Nonparametric Statistics, 2009, vol. 21, issue 3, 345-363

Abstract: Data collected on the surface of the earth at different sites often have two- or three-dimensional coordinates associated with it. We assume a simple setting where these sites are integer lattice points, say, 𝒵N, N ≥ 1, in the N-dimensional Euclidean space RN. Denote n = (n1, …, nN)∈𝒵N and In = {i: i∈𝒵N, 1 ≤ ik≤nk, k = 1, …, N}. Consider a simple regression model where the design points xni's and the responses Yni's are related as follows: Yni = g(xni)+ϵni, i∈In, where xni's are fixed design points taking values in a compact subset of Rd and where g is a bounded real-valued function defined on Rd and ϵni are negatively associated random disturbances with zero means and finite variances. The function g(x) is estimated by a general linear smoother gn(x). The asymptotic normality of the estimate gn(x) is established under weak conditions, and general conditions under which the bias gn(x) tends to zero are also determined.

Date: 2009
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DOI: 10.1080/10485250802280218

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