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Let $ Z = (X, Y) $ be a $ R^p \times R $-valued random vector having a (unknown) probability density function $ f*^ast (x, y) $ with respect to Lebesgue measure. We wish to estimate a regression funct...ion $ m(x) = E[Y mid X = x] $. In this paper we propose a class of recursive estimators $ { m_n (x) } $ based on a random sample $ Z_1 = (X_1, Y_1) $, $ Z_2 = (X_2, Y_2), cdots mathrm{from} Z $, and show the strong pointwise consistency and the asymptotic normality of $ m_n(x) $ at a point $ x $. We also deal with the optimality in the sense of asymptotic minimum variance.続きを見る
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