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Nonparametric estimation of conditional expectation. (English) Zbl 1149.62078
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.

62M40Statistics of random fields; image analysis
62G05Nonparametric estimation
62E20Asymptotic distribution theory in statistics
62G08Nonparametric regression
62M10Time series, auto-correlation, regression, etc. (statistics)
Full Text: DOI
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