Consistency of LS estimators in the EV regression model with martingale difference errors

Abstract

In this paper, we consider the following simple linear errors in variables model ${\eta }_i=\theta +\beta x_i+{\epsilon }_i,{\xi }_i=x_i+{\delta }_i,1\le i\le n,$ where θ, β, x₁, x₂, … are unknown constants (parameters) and ξ_i, η_i, i=1, 2, … are observable. The consistency of the least square estimators for the unknown parameters β and θ is established, while the errors { ϵ_i}, {δ_i} are sequences of martingale difference. In order to obtain our results, some limit theorems for weighted sums of martingale differences are proved.

Keywords:

• EV model
• strong consistency
• weak consistency
• LS estimator
• martingale difference sequence

2000 Mathematics Subject Classification:

• 62F12
• 60F05

Acknowledgements

This work is supported by NSFC (11001077), NCET (NCET-11-0945), Plan For Scientific Innovation Talent of Henan Province (124100510014) and Outstanding Youth Talent of Henan Normal University.