Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 3, 420--441

ASYMPTOTICS FOR NONPARAMETRIC REGRESSION

By

P. K. BHATTACHARYA

And

HANS-GEORGE MÜLLER, University of California at Davis, U. S. A

 

SUMMARY. This paper reviews and compares some of the basic ideas in nonparamatric regression with Mahalanobis' Fractile Graphical Analysis.new results concern a new proof of known properties of the " properties of the "error areas" in Fractile Graphical Analysis using concomitants and a discussion of the properties of Fractile Graphs as a method of nonparametric regression (Fractile Regression). Furthermore, a general result for the local asymptotic distribution of real valued functions with arguments which are functionals formed by weighted averages of the data is provided. This result is applied to derive local distributions for various nonparametric regression type estimates, including estimators for derivatives.

Subject classification. 65G05,62G10,62G20

FULL PAPER.

This article in Mathematical Reviews.