In this paper we first obtained the classical estimators of the parameter θ of the Minimax distribution, i.e., the Maximum Likelihood Estimator (MLE), the Uniformly Minimum Variance Unbiased Estimator (UMVUE), and the Minimum Mean Squared Error (MinMSE) estimator. Meanwhile, this paper is concerned with the problem of finding the minimax estimators of this parameter under the symmetric (for example: weighted squared error and squared log error) loss functions, the asymmetric (for example: precautionary and MLINEX) loss functions, and the weighted balanced (squared error) type loss function by applying the theorem of Lehmann [1950]. The obtained results have been interpreted in the light of two-person zero sum game. All these estimators are compared empirically using Monte Carlo simulation.
Minimax estimator, Minimax distribution, Precautionary loss function, Weighted Balanced type loss function, Game theory, Monte-Carlo simulation
