A CLASS OF NONPARAMETRIC RECURSIVE ESTIMATORS OF A MULTIPLE REGRESSION FUNCTION | Zendy

Eiichi Isogai | Zendy

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A CLASS OF NONPARAMETRIC RECURSIVE ESTIMATORS OF A MULTIPLE REGRESSION FUNCTION

Author(s) -

Eiichi Isogai

Publication year - 1983

Publication title -

bulletin of informatics and cybernetics

Language(s) - English

Resource type - Journals

eISSN - 2435-743X

pISSN - 0286-522X

DOI - 10.5109/13343

Subject(s) - estimator , nonparametric statistics , mathematics , class (philosophy) , nonparametric regression , statistics , regression , function (biology) , regression analysis , regression function , recursive partitioning , econometrics , computer science , artificial intelligence , biology , evolutionary biology

Let Z= (X, Y) be a R" x Rvalued random vector having a (unknown) probability density function f* (x, y) with respect to Lebesgue measure. We wish to estimate a regression function m(x) =E[Y1 X=x]. In this paper we propose a class of recursive esti mators {mn (x) } based on a random sample Z1= (X1, Y1) , Z2= (X2, Y2), from Z, and show the strong pointwise consistency and the asymptotic normality of mn (x) at a point x. We also deal with the optimality in the sense of asymptotic minimum variance.

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