Estimation of Partial Linear Error-in-Variables Models for Negatively Associated Dependence Data

摘要

Consider the partly linear regression model Y = xβ + g(t) + e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is negatively associated dependent. Let x be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of {(Y_j, X_j, t_j)_(j=n+1)~(n+N), which is negatively associated data sets, an independent validation data containing n observations of {(x_j, X_j, t_j)_(i=1)~n} is available. The exact observations on x may be obtained by some expensive or difficult procedures for only a small subset of subjects enrolled in the study. In this paper, a semiparametric method with the primary data is employed to obtain the estimators of β and g(·) based on the least squares criterion with the help of validata data. The proposed estimators are proved to be strongly consistent.