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.

Keywords:

• Purely sequential
• Point estimation
• Minimum Risk
• Bounded Risk
• Second-order Approximations
• Improved Estimation
• Regret

Mathematics Subject Classification:

• 62L12
• 62F10

Acknowledgments

The authors would like to sincerely thank the editor and the unknown referees for their valuable comments and suggestions, which led to a considerable improvement in this research article.

Additional information

Funding

In particular, Neeraj Joshi is grateful to the Department of Science and Technology, Government of India for their financial support (INSPIRE fellowship IF170889, 2018) to pursue his research.