A Class Of Semiparametric Estimators For Linear Error-in-Covariables Models Under Random Censorship

Consider the linear model Y_i=X_i^Tβ+∈_i, i=1, 2,…, n, in which theresponse variable Y_i is censored randomly on the right and what we can see are Z_i=min(Y_i, T_i) andδ_i=I(Y_i≤T_i); and also the covariable X_i is hard or costly tomeasure, what we can do is to find a relative variable (?)_i that is easy to get, anduse the regression function E[X|(?)] to instead X_i. In this article, we adjust Y_i toY_i^*=δ_iφ₁(Z_i)+(1-δ_i)φ₂(Z_i) as similar to Class K estimation, and use the datas{(X_j,(?)_j)}_j=n+1^n+N to estimate the regression function E[X|(?)]. And finally, we give aclass of semiparametric estimators for vectorβ, and prove the asymptomic normalityfor them.In section 1, we give some introduction about censored data,estimators of pa-rameters in linear regression models with censored data, and what's more, the kernelestimation for regression function. In section 2, we give the linear error-in-covariablesmodel under random censorshipand give a class of semiparametric estimators for it. First, we adjust the random cen-sored data Y_i to Y_i^*=δ_iφ₁(Z_i)+(1-δ_i)φ₂(Z_i), and so Y_i^*=μ^T((?)_i)β+e'_i, andthen we get the estimatorsβ_n by the Least Square Estimation. Because the regres-sion function is always unknown, so we use the datas {(X_j, (?)_j)}_j=n+1^n+N to estimateE[X|(?)] inβ_n, and finally we get the estimators (?)_n,N forβ. Under some conditions,we give the asymptomic normality for (?)_n,N. In section 3, we give the proof of theconclusion and section 4, the postscript.