Three Stage Estimation for the Mean of a One-Parameter Exponential Family

  • M. AlMahmeed (Department of Quantitative Methods and Information systems, Kuwait University) ;
  • A. Al-Hessainan (Kuwait University) ;
  • Son, M.S. (Department of Mathematics and Statistics, University of Vermont) ;
  • H. I. Hamdy (Department of Quantitative methods and Information Systems, Kuwait University)
  • Published : 1998.08.01


This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.



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