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Zbl 1149.62078
Li, Jiexiang; Tran, Lanh Tat
Nonparametric estimation of conditional expectation.
(English)
[J] J. Stat. Plann. Inference 139, No. 2, 164-175 (2009). ISSN 0378-3758

Summary: Denote the integer lattice points in the $N$-dimensional Euclidean space by $\Bbb Z^N$ and assume that $(X_i,Y_i)$, $i\in\Bbb Z^N$, is a mixing random field. Estimators of the conditional expectation $r(x)=E[Y_i\,|\,X_i=x]$ by nearest neighbor methods are established and investigated. The main analytical result of this study is that, under general mixing assumptions, the estimators considered are asymptotically normal. Many difficulties arise since points in higher dimensional space $N\geqslant 2$ cannot be linearly ordered. Our result applies to many situations where parametric methods cannot be adopted with confidence.
MSC 2000:
*62M40 Statistics of random fields
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
62G08 Nonparametric regression
62M10 Time series, etc. (statistics)

Keywords: random field; conditional expectation; nearest neighbor estimator; asymptotic normality

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