MDP for estimators in EV regression models with α-mixing errors

Abstract

In this paper, we consider the following simple linear errors-in-variables regression model: $\begin{array}{l}{\eta }_i=\theta +\beta x_i+{ϵ}_i,\\ {\xi }_i=x_i+{\delta }_i,\end{array}1\le i\le n,$ where θ and β are the unknown parameters, η_i, ξ_i’s are observable and x_i’s are unobservable. We assume the error variables {(ε₁, δ_i), 1≤i≤n} form a L₂ stationary α-mixing sequences. In this paper, we obtained the moderate deviation principles for the least-square estimators of the unknown parameters θ and β.

Keywords:

• EV models
• LS estimator
• moderate deviation principle
• α-mixing

2010 Mathematics Subject Classifications:

• 60F10
• 62F12

Acknowledgements

The author is very grateful to the editor, associate editor and anonymous referee for helpful comments and suggestions, which have improved the presentation of the paper. This research is supported by the National Natural Science Foundation of China (NSFC) (Grant No.11171262) and ‘the Fundamental Research Funds for the Central Universities’ (Grant No.2012201020201).