Consistency of an estimator of the parameters of a polynomial regression with a known variance relation for errors in the measurement of the regressor and the echo

摘要

We consider an error-in-variables model for a polynomial regression with Gaussian errors. We assume that the covariance matrix of the measurement errors of the regressor and the echo is known up to a scalar factor. We consider the moment estimator of regression coefficients proposed by Cheng and Schneeweiss. Sufficient conditions for the strong consistency of this estimator are given and the rate of convergence is estimated in this paper.