Weighted least squares method for censored linear models

For estimation of linear models with randomly censored data, a class of data transformations is used to construct synthetic data. It is shown that the conditional variance of the synthetic data depends on the covariates in the model regardless of the homoscedasticity of the error. Therefore, linear models based on the synthetic data are always heteroscedastic models. To improve efficiency, we propose a weighted least squares (WLS) method, where the conditional variance of the synthetic data is estimated nonparametrically, then the standard WLS principle is applied to the synthetic data in the estimation procedure. The resultant estimator is asymptotically normal and the limiting variance is estimated using the plug-in method. In general, the proposed method improves the existing synthetic data methods for censored linear models, and gains more efficiency. For the censored heteroscedastic linear models, where the Buckley–James (BJ) and rank-based methods cannot be used since the condition of homoscedastic errors is violated, the new method provides a solution for better estimation. Monte Carlo simulations are conducted to compare the proposed method with the unweighted least squares method and the BJ method under different error conditions.