Download PDF by Dasgupta A. (ed.): A festschrift for Herman Rubin

By Dasgupta A. (ed.)

ISBN-10: 0940600617

ISBN-13: 9780940600614

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J. R. S. S. - B. 56, 543–548. MR1278226 [24] Srinivasan, C. (1981). Admissible generalized Bayes estimators and exterior boundary value problems. Sankhya Ser. A. 43, 1–25. MR656265 [25] Stein, C. (1955). A necessary and sufficient condition for admissibility. Ann. Math. Statist. 76, 518–522. MR70929 [26] Stein, C. (1959). The admissibility of Pitman’s estimator of a single location parameter. Ann. Math. , 30, 970–979. MR109392 [27] Zidek, J. V. (1970). Sufficient conditions for admissibility under squared error loss of formal Bayes estimators.

Marchand and W. E. Strawderman us that the Bayes estimator φUC (Y1 ) of µ1 with respect to a uniform prior on C dominates φ0 (Y1 ) (under squared-error loss). Hence, Proposition 1 applies with φ1 = φUC , producing the following dominating estimator of δ0 (X1 , X2 ): δφUC (X1 , X2 ) = Y2 + φUC (Y1 ). (4) For p = 1 and A = [−m, m], the dominance of δφ0 by the estimator given in (4) was established by van Eeden and Zidek (2001), while for p = 1 and A = [0, ∞) (or A = (−∞, 0]), this dominance result was established by Kubokawa and Saleh (1994).

In all that follows, it is assumed that R is λ-symmetric. Note that the assumption of σ-finiteness for λ is important. Given a λ-symmetric R, consider a real valued measurable function h and let ∆(h) = (h(y) − h(z))2 R(dy|z)λ(dz). 2) The quadratic form ∆ (or sometimes 21 ∆) is often called a Dirichlet form. Such forms are intimately connected with continuous time Markov Process Theory (see Fukushima et al (1994)) and also have played a role in some work on Markov chains (for example, see Diaconis and Strook (1991)).

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A festschrift for Herman Rubin by Dasgupta A. (ed.)


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