Nonparametric multiple function fitting

Alexander A. Georgiev

Statistics & Probability Letters, 1990, vol. 10, issue 3, 203-211

Abstract: Consider the d-dimensional unit cube [0,1]d and portion it into n regions, A1,..., An. Select and fix a point in each one of these regions so we have x1,..., xn. Consider observable variables Yi, i = 1,..., n, satisfying the multivariate regression model Yi = g(xi) + [var epsilon]i, where g is an unknown real-valued function defined on [0,1]d and [var epsilon]i, i = 1,..., n, are independent random variables with E[var epsilon]i = 0. This paper studies gn(x) = [Sigma]ni=1YiKh(x - xi)[lambda](Ai) as an estimate of g(x), where Kh(·) = h-dK(·/h) is a known function, h = h(n) is a sequence of positive reals converging to zero as n --> [infinity], and [lambda](Ai) is the Lebesgue measure of region Ai. Under suitable conditions, it is shown that gn is asymptotically pointwise weakly, mean square and completely consistent. Asymptotic normality of the estimate is also established. The class of applicable kernel functions {K(·)} includes those discontinuous kernels and kernels with unbounded support. Finally, some global results are stated.

Keywords: Nonparametric estimation; kernel estimate; Priestley--Chao multiple estimate multivariate regression function; law of large numbers; central limit theorem; consistency (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(90)90074-H
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:10:y:1990:i:3:p:203-211

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().