In a book on unbiased estimation I met an example that mentioned an unbiased estimator for the product $\theta_1 \theta_2$ from a sample of a uniform distribution in the interval $(\theta_1, \theta_2)$. The particular reference was: Patel J.K. Complete sufficient statistic and MVU estimators // Commun.Statist., 1973, V.2, Pp.327--336. The paper is out of my reach. My question is actually not mathematical but educational: why does someone ever want to estimate such a product? What use of the quantity was assumed in that paper? Can anyone help me to clarify the point? Thanks
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