## The Annals of Statistics

### An Invariance Principle in Regression Analysis

P. K. Bhattacharya

#### 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

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

Subjects
Primary: 62E20: Asymptotic distribution theory

#### 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