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An orthogonal series estimate of time-varying regression

Research paper by Wŀodzimierz Greblicki, Danuta Rutkowska, Leszek Rutkowski

Indexed on: 01 Dec '83Published on: 01 Dec '83Published in: Annals of the Institute of Statistical Mathematics



Abstract

Let (X1,Y1), (X2,Y2),... be independent pairs of random variables according to the modelYn=tn(Xn)R(Xn)+Zn,n=1,2,..., wheretn andR are unknown functions.Zn's are i.i.d. random variables with zero mean and finite variance. The marginal density ofXn is independent ofn. In the paper nonparametric estimates of a nonstationary regression function E{Yn|Xn=x}=tn(x)R(x) are proposed and their asymptotic properties are investigated.