SURE Estimates For The Parameters Of Weibull Distributions Under Type-? Censored Data

Lifetime data can be defined as one of the most important research objects in survival analysis.Due to the effective portrayal of lifetime data,the Weibull distribution has been widely applied in the various fields such as survival analysis and reliability analysis.As well known,we often need to deal with censored lifetime data influenced by factors such as test time and costs.Therefore,it has important theoretical and practical significance to analyze this type of lifetime data.The thesis is concerned with simultaneously estimating scale parameters of the Weibull distributions under mean squared error loss in case of the high-dimensional type-II censoring scheme.By employing the idea of Stein's unbiased estimate of risk,we give the empirical Bayes shrinkage estimators for the parameters and establish their asymptotic optimality properties.Gamma distribution is another important type of lifetime distribution,we propose a class of SURE estimator for the parameter of Gamma distribution and establish the asymptotic optimality properties under mean squared relative error loss in this thesis.We conduct simulation studies to show the performance of our proposed SURE estimators by comparing them with other existing shrinkage estimates.The methods are also applied to real datasets,and we obtain encouraging results.