The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model
Gleser, Leon Jay ; Carroll, Raymond J. ; Gallo, Paul P.
Ann. Statist., Tome 15 (1987) no. 1, p. 220-233 / Harvested from Project Euclid
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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)).
Publié le : 1987-03-14
Classification:  Regression,  functional models,  structural models,  instrumental variables,  ordinary least squares estimators,  consistency,  60F05,  62J05,  62F10,  62H99 
@article{1176350262,
     author = {Gleser, Leon Jay and Carroll, Raymond J. and Gallo, Paul P.},
     title = {The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 220-233},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350262}
}

Gleser, Leon Jay; Carroll, Raymond J.; Gallo, Paul P. The Limiting Distribution of Least Squares in an Errors-in-Variables Regression Model. Ann. Statist., Tome 15 (1987) no. 1, pp.  220-233. http://gdmltest.u-ga.fr/item/1176350262/