Open Access
May, 1976 An Invariance Principle in Regression Analysis
P. K. Bhattacharya
Ann. Statist. 4(3): 621-624 (May, 1976). DOI: 10.1214/aos/1176343468


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.


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P. K. Bhattacharya. "An Invariance Principle in Regression Analysis." Ann. Statist. 4 (3) 621 - 624, May, 1976.


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

zbMATH: 0331.62016
MathSciNet: MR400558
Digital Object Identifier: 10.1214/aos/1176343468

Primary: 62E20

Keywords: Brownian motion , induced order statistics , regression analysis , weak convergence

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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