Purpose: To address the problem of estimating a vector of regression parameters in the Weibull censored regression model. Summary: In this article, the problem of estimating vector of regression parameters in the Weibull censored regression model is considered. For this purpose, two estimation strategies, adaptive shrinkage estimation strategy and a LASSO-type (least absolute shrinkage and selection operator) estimation strategy are considered. It is observed that the shrinkage estimators have higher efficiency than the classical estimates for a wide class of model. Further, it is observed that the shrinkage strategy performs better than the LASSO strategy when, and only when, there are many inactive predictors in the model that may or may not be associated with the response. In addition to simulations a real data set is also considered to illustrate the usefulness of the procedures in practice.
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