preliminary test estimation in rayleigh distribution under a squared-log error loss

The problem of pretest estimation in rayleigh type-ii censored data under the squared-log error loss (slel) is considered. the risk-unbiased estimator is derived and its risk is computed under the slel. the pretest estimator based on a point guess about the parameter of interest is constructed and the bias and risk is computed. a comparison study is performed between the pretest estimator and the risk-unbiased estimator. the optimal level of significance and critical values of pretest is obtained using regret minimax method. a real data set is used for illustrative purposes.