Estimating the common hazard rate of two exponential distributions with ordered location parameters |
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Authors: | Lakshmi Kanta Patra Somesh Kumar |
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Affiliation: | 1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India;2. Department of Mathematics, Indian Institute of Information Technology Ranchi, Ranchi, India |
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Abstract: | This paper is concerned with estimating the common hazard rate of two exponential distributions with unknown and ordered location parameters under a general class of bowl-shaped scale invariant loss functions. The inadmissibility of the best affine equivariant estimator is established by deriving an improved estimator. Another estimator is obtained which improves upon the best affine equivariant estimator. A class of improving estimators is derived using the integral expression of risk difference approach of Kubokawa [A unified approach to improving equivariant estimators. Ann Statist. 1994;22(1):290–299]. These results are applied to specific loss functions. It is further shown that these estimators can be derived for four important sampling schemes: (i) complete and i.i.d. sample, (ii) record values, (iii) type-II censoring, and (iv) progressive Type-II censoring. A simulation study is carried out for numerically comparing the risk performance of these proposed estimators. |
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Keywords: | Decision theory best affine equivariant estimator scale invariant loss function smooth improved estimator |
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