Statistica Sinica 19 (2009), 1013-1036

$\mbox{\boldmath $t$}$-TYPE ESTIMATORS FOR A CLASS OF LINEAR

ERRORS-IN-VARIABLES MODELS

Tao Hu and Hengjian Cui

Beijing Normal University

Abstract: This paper discusses $t$-type regression estimators of parameters for linear errors-in-variables model, and the EM algorithm for $t$-type estimators in linear errors-in-variables model is given. When the error variables for both the response and the manifest variables have a joint distribution that is spherically symmetric, but otherwise is unknown, the influence functions of the $t$-type regression estimates based on orthogonal residuals are calculated and the proposed estimators are shown to be consistent and asymptotically normal under some mild conditions. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a dataset is used to illustrate our approach.

Key words and phrases: Asymptotics, errors-in-variables, influence function, M-estimate, t-type regression estimator.