The Annals of Statistics

The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model

Leon Jay Gleser, Raymond J. Carroll, and Paul P. Gallo

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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)).

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 220-233.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350262

Digital Object Identifier
doi:10.1214/aos/1176350262

Mathematical Reviews number (MathSciNet)
MR885733

Zentralblatt MATH identifier
0623.62015

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62J05: Linear regression 62F10: Point estimation 62H99: None of the above, but in this section

Keywords
Regression functional models structural models instrumental variables ordinary least squares estimators consistency

Citation

Gleser, Leon Jay; Carroll, Raymond J.; Gallo, Paul P. The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model. Ann. Statist. 15 (1987), no. 1, 220--233. doi:10.1214/aos/1176350262. https://projecteuclid.org/euclid.aos/1176350262


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