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March, 1987 The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model
Leon Jay Gleser, Raymond J. Carroll, Paul P. Gallo
Ann. Statist. 15(1): 220-233 (March, 1987). DOI: 10.1214/aos/1176350262

Abstract

It is well-known that the ordinary least squares (OLS) estimator $\hat{\beta}$ of the slope and intercept parameters $\beta$ in a linear regression model with errors of measurement for some of the independent variables (predictors) is inconsistent. However, Gallo (1982) has shown that certain linear combinations of $\beta$. In this paper, it is shown that under reasonable regularity conditions such linear combinations of $\hat{\beta}$ are (jointly) asymptotically normally distributed. Some methodological consequences of our results are given in a companion paper (Carroll, Gallo and Gleser (1985)).

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Leon Jay Gleser. Raymond J. Carroll. Paul P. Gallo. "The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model." Ann. Statist. 15 (1) 220 - 233, March, 1987. https://doi.org/10.1214/aos/1176350262

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0623.62015
MathSciNet: MR885733
Digital Object Identifier: 10.1214/aos/1176350262

Subjects:
Primary: 60F05
Secondary: 62F10, 62H99, 62J05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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