Three methods are proposed for constructing reference prior densities for certain biparametric distribution families. These densities represent approximations to the Bayesian concept of noninformative distribution.
The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.