Key points are not available for this paper at this time.
An estimate ⁿ₈=₁ YᵢK ( (x - Xᵢ) /h) /ⁿ₉=₁ K ( (x - Xⱼ) /h), calculated from a sequence (X₁, Y₁), , (Xₙ, Yₙ) of independent pairs of random variables distributed as a pair (X, Y), converges to the regression E\Y X = x\ as n tends to infinity in probability for almost all () x Rᵈ, provided that E|Y| <, h 0 and nhᵈ as n. The result is true for all distributions of X. If, moreover, |Y| < and nhᵈ/ n as n, a complete convergence holds. The class of applicable kernels includes those having unbounded support.
Greblicki et al. (Sat,) studied this question.