Author

• N. Sanjari Farsipour

Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Islamic Republic of Iran

Abstract

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant estimator and Bayes estimators are obtained. Fisher’s problem of the Nile as an example is included.

Keywords

• Best invariant estimator
• Bayes estimator
• Scale parameter
• Bounded loss function
• Fisher’s problem of the Nile