Adjusted Least Squares Estimates for the Scaled Regression Coefficients with Censored Data
Abstract The ordinary least squares (OLS) method is popular for analyzing linear regression models because of its simplicity in computation. Suppose that the regressor variables are stochastic and the dependent observations are censored; we can prove that under very general design conditions, the least squares (LS) method can still be useful in estimating the scaled regression coefficients of the general regression model Y * = Q (α + βXi, ℰi), i = 1, 2, …, n, provided that the censored response observations are properly weighted. (Here α is a constant, β is a 1 + p row vector, X i are p + 1 column vectors of explanatory variables, ℰi are unobserved random errors, and Q is an arbitrary unknown function.) Particularly, we shall see that under stronger design conditions, such as assuming that the regressor variables have elliptically symmetric distribution, the OLS estimator consistently estimates the scaled β when the response observations are complete. The model discussed here is not the usual nonlinear re...