An Invariance Principle in Regression Analysis

P. K. Bhattacharya

doi:10.1214/aos/1176343468

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Home > Journals > Ann. Statist. > Volume 4 > Issue 3 > Article

May, 1976 An Invariance Principle in Regression Analysis

P. K. Bhattacharya

Ann. Statist. 4(3): 621-624 (May, 1976). DOI: 10.1214/aos/1176343468

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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.

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P. K. Bhattacharya. "An Invariance Principle in Regression Analysis." Ann. Statist. 4 (3) 621 - 624, May, 1976. https://doi.org/10.1214/aos/1176343468