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Improved Estimation of the Pareto Location Parameter Under Squared Error Loss |
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| Authors: | Steven T Garren Elizabeth R Hume Glen R Leppert |
| Institution: | 1. Department of Mathematics and Statistics , James Madison University , Harrisonburg, Virginia, USA garrenst@jmu.edu;3. Department of Mathematics and Computer Science , Longwood University , Farmville, Virginia, USA;4. Department of Mathematics and Statistics , James Madison University , Harrisonburg, Virginia, USA |
| Abstract: | Suppose two independent observations are drawn from Pareto distributions with known shape parameters and an order restriction on the unknown location parameters. An isotonic regression estimator of the smaller location parameter dominates a preferred marginal estimator under squared error loss, but fails to dominate under stochastic domination. The results expressed herein advance the theory of order restricted inference. |
| Keywords: | Isotonic regression estimator Order restriction Pareto distribution Stochastic and universal domination |