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Consistent nonparametric multiple regression: the fixed design case. (English) Zbl 0637.62044

Consider the nonparametric regression model Y i (n) =g(x i (n) )+ϵ i (n) , i=1,···,n, where g is an unknown function, the design points x i (n) are known and nonrandom, and ϵ i (n) ’s are independent random variables. The regressor is assumed to take values in A p , and the regressand to be real valued. This paper studies the behavior of the general nonparametric estimate

g n (x)= i=1 n w ni (x)Y i (n) ,

where the weight function w ni is of the form w ni (x)=w ni (x;x i (n) ,,x n (n) ). Under suitable conditions, it is shown that the general linear smoother g n for the unknown rendent variable.

62G05Nonparametric estimation
62J02General nonlinear regression
62F15Bayesian inference