Convergence Rate for LS Estimator in Simple Linear EV Regression Models

Abstract

In this paper, we consider the following simple linear errorsin-variables regression model ηiThe exponential convergence rate for the least squares estimators of the unknown parameters θ, β in this model are obtained. Mathematics Subject Classification (2000). Primary 60F10; Secondary 62F12.

Central limit theorems for LS estimators in the EV regression model with dependent measurements

“…Miao and Liu (2009) obtained the exponential convergence rate (moderate deviation) for the estimatorsβ n andθ n under the weaker moment assumptions and the stronger moderate deviation scale conditions by the methods of Puhalskii (2001). Miao (2010) proved another moderate deviation principle for the estimatorsβ n andθ n by the Gärtner-Ellis theorem (cf. Dembo & Zeitouni, 1998) under the different conditions from the works in Miao andLiu (2009).…”

“…Miao (2010) proved another moderate deviation principle for the estimatorsβ n andθ n by the Gärtner-Ellis theorem (cf. Dembo & Zeitouni, 1998) under the different conditions from the works in Miao andLiu (2009). Miao, Wang, andZhao (2011) studied the consistency, asymptotic normality and large deviation for the LS estimatorsβ n andθ n , which weaken some known conditions and improve some known results.…”