Some Pitman closeness properties pertinent to symmetric populations

In this paper, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter θ. We first consider two symmetric estimators θˆ1 and θˆ2 and obtain necessary and sufficient conditions for θˆ1 to be Pitman closer to the common median θ than θˆ2. We then establish some properties in the context of estimation under the Pitman closeness criterion. We define Pitman closeness probability which …