The Annals of Statistics

The Empirical Distribution Function of Residuals from Generalised Regression

R. M. Loynes

Full-text: Open access

Abstract

Generalised residuals, as defined by Cox and Snell, may be thought of as residuals from generalised regression. Under regularity conditions on the regression and on the estimator of the unknown parameters, the asymptotic behaviour of the empirical distribution of these residuals is determined. The addition of a random adjustment to the maximum likelihood estimator leads to the familiar Brownian bridge as the limit.

Article information

Source
Ann. Statist., Volume 8, Number 2 (1980), 285-298.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344954

Digital Object Identifier
doi:10.1214/aos/1176344954

Mathematical Reviews number (MathSciNet)
MR560730

Zentralblatt MATH identifier
0451.62040

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G10: Hypothesis testing 60F05: Central limit and other weak theorems

Keywords
Generalised residuals empirical distribution function general nonlinear regression random parameter adjustment

Citation

Loynes, R. M. The Empirical Distribution Function of Residuals from Generalised Regression. Ann. Statist. 8 (1980), no. 2, 285--298. doi:10.1214/aos/1176344954. https://projecteuclid.org/euclid.aos/1176344954


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