回归函数递旧核估计相合的充要条件

NECESSARY AND SUFFICIENT CONSISTENCY CONDITIONS FOR A RECURSIVE KERNEL REGRESSION ESTIMATE

对α-混合,φ-混合样本,本文给出回归函数递归核估计m_a(x)弱、强相合的充要条件.在E|Y|^(1+δ)<∞,δ>0,sum from n=1 to ∞(φ~1 ~2(n))<∞时.得出m_n(x)的强、弱相合是等价的.另外,还给出核估计m_n(x)弱相合的充分条件。

A recursive kernel estimate mn(x) =for a regression m(x)= E(Y|X = x) calculated from α-mixing or (?)-mixing observations (X1 ,Y1),…, (Xn,Yn) of a pair of random variables (X,Y) is examined. For E|Y|< ∞ or E|Y|1+δ <∞,δ > 0 , We obtain the necessary and sufficient conditions for weak or strong consistency of m,(x) for almost all (μ) x ∈Rd, μ is the probability measure of X . Forweak and strong consistences are equivalent. For E|Y|<∞, a sufficient condition for weak consistency for kernelestimate mn(x) =is also given.