Sequential point estimation procedures for the parameter of a family of distributions

Abstract

For the family of distributions considered by Chaturvedi and Alam, the problems of minimum risk point estimation and bounded risk point estimation of the parameter are handled. Consideration is given to squared-error loss function. The failure of fixed sample size procedure is established. Sequential procedures are proposed to deal with the situation. For both the estimation problems,the uniformly minimum variance unbiased estimator/maximum likelihood estimator and minimum mean square estimator are utilized to develop the fixed sample size procedures. Second-order approximations are derived for the sequential procedures and �improved� estimators are proposed. First-order properties are also discussed. The negative �regret� [see Starr and Woodroofe] is achieved. � 2019, � 2019 Taylor & Francis Group, LLC.