Open Access
Translator Disclaimer
January, 1976 Consistency in Integral Regression Estimation with a Triangular Array of Observation Points
Gordon Pledger
Ann. Statist. 4(1): 234-236 (January, 1976). DOI: 10.1214/aos/1176343358

Abstract

Let $\mu$ be a continuous mean regression function defined on $U$, the unit cube in $N$-dimensional Euclidean space. Let $F$ be a distribution function with support in $U$, and let $M$ denote the indefinite integral of $\mu$ with respect to $F$. This paper provides consistency results, including rates of convergence, for a certain estimator of $M$ in the case that the $n$th estimate is based on observations at points $\mathbf{t}_{n1},\cdots, \mathbf{t}_{nn}$ of $U$. The estimator is the $N$-dimensional analogue of that considered by Brunk (1970).

Citation

Download Citation

Gordon Pledger. "Consistency in Integral Regression Estimation with a Triangular Array of Observation Points." Ann. Statist. 4 (1) 234 - 236, January, 1976. https://doi.org/10.1214/aos/1176343358

Information

Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0322.62045
MathSciNet: MR397976
Digital Object Identifier: 10.1214/aos/1176343358

Subjects:
Primary: 62G05
Secondary: 60G50

Keywords: consistency , integral regression , multiple regression , triangular array

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
3 PAGES


SHARE
Vol.4 • No. 1 • January, 1976
Back to Top