The Annals of Statistics

An Invariance Principle in Regression Analysis

P. K. Bhattacharya

Full-text: Open access

Abstract

The sample paths of cumulative sums of induced order statistics obtained from $n$ independent two-dimensional random vectors, when appropriately normalized, converge weakly (as $n$ increases indefinitely) to the sum of a Brownian motion with time change and an integrated Brownian bridge which is independent of the Brownian motion. Applications in regression analysis are given.

Article information

Source
Ann. Statist., Volume 4, Number 3 (1976), 621-624.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343468

Digital Object Identifier
doi:10.1214/aos/1176343468

Mathematical Reviews number (MathSciNet)
MR400558

Zentralblatt MATH identifier
0331.62016

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory

Keywords
Induced order statistics regression analysis weak convergence Brownian motion

Citation

Bhattacharya, P. K. An Invariance Principle in Regression Analysis. Ann. Statist. 4 (1976), no. 3, 621--624. doi:10.1214/aos/1176343468. https://projecteuclid.org/euclid.aos/1176343468


Export citation