Theory of Probability and Mathematical Statistics
Convergence of estimators in the polynomial measurement error model
A. G. Kukush, Ya. V. Tsaregorodtsev
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Abstract: A polynomial measurement error model is considered. The variance of errors in the regressor variable and the covariance between errors in the regressor variable and errors of the response variable are assumed to be known. The adjusted least squares estimator of regression parameters adopts the ordinary least squares estimator to the errors presented in the regressor. Conditions for the strong consistency of the estimator are found. These conditions are weaker as compared to those by Cheng and Schneeweiss (1998) [Journal of the Royal Statistical Society B, no. 1, 189-199]. Sufficient conditions for the asymptotic normality of the estimator are also found.
Keywords: Asymptotic normality, adjusted least squares estimator, consistency of estimators, measurement error model, modification of estimators for small samples, polynomial regression
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