RESEARCH OF STATISTICAL INFERENCE PLANS ON THE BASIS OF SOME PRIOR

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This research is concerned with estimating a parameter for the case where one has a prior information about the parameter in the form of preliminary conjectured intervals. It is based on the minimum discrimination information(MDI) approach, intended to propose and develop an estimator that has lower risk than the usual estimator (m.l.e.) in or beyond the conjectured intervals. A MDI estimator and its variants were obtained for the estimation of the parameter about the binomial distribution in 1997 and that of the bivariate normal mean vector in 1998. These yield a class of shrinkage type estimator that shrinks towards the preliminary conjectured interval. Their risks were evaluated and compared with the usual estimator under a quadratic loss function. Favorable properties of the proposed estimators were given and recommendations for their use were also made.