The Annals of Statistics

Empirical Processes Based upon Residuals from Errors-in-Variables Regressions

Stephen M. Miller

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Abstract

Multivariate errors-in-variables regression models with normal errors are considered and residuals, similar to those calculated from ordinary least squares regressions, are defined for these models. It is shown that under the assumption of a $n^{1/2}$-consistent estimator of the vector of regression coefficients, certain empirical processes based upon the residuals converge to the same Gaussian process as that of an infinite sequence of normal random variables standardized by their sample mean sample variance.

Article information

Source
Ann. Statist., Volume 17, Number 1 (1989), 282-292.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347016

Digital Object Identifier
doi:10.1214/aos/1176347016

Mathematical Reviews number (MathSciNet)
MR981450

Zentralblatt MATH identifier
0669.62028

JSTOR
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 62E20: Asymptotic distribution theory 62J99: None of the above, but in this section 60F05: Central limit and other weak theorems

Keywords
Errors-in-variables empirical processes regression residuals multivariate normality measurement errors limiting distribution

Citation

Miller, Stephen M. Empirical Processes Based upon Residuals from Errors-in-Variables Regressions. Ann. Statist. 17 (1989), no. 1, 282--292. doi:10.1214/aos/1176347016. https://projecteuclid.org/euclid.aos/1176347016


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