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Such that Ci −→ Y and each Ci is locally-λ-recurrent Proof. Obviously (i) implies (ii). The converse is proved in the appendix. ” For an example of the “one-set phenomenon,” see Brown and Hwang (1982). In the current Markov chain context, here is a “one-set” condition that implies local-λ-recurrence for the chain W . 3. 3). Then the Markov chain W is locally-ν-recurrent. Proof. Since λ is σ-finite, there is a sequence of increasing λ-proper sets Bi , i = 1, 2, . . such that Bi −→ Y . Let Ci = Bi ∪ B0 , i = 1, 2, .

1960). Criteria for the recurrence or transience of stochastic processes I. Journal of Math. Anal. Appl. 1, 314–330. MR126872 [21] Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. New York: Springer-Verlag. MR1287609 [22] Revuz, D. (1984). Markov Chains, 2nd Edition. North Holland, Amsterdam. MR415773 [23] Smith, J. Q. (1994). The inadmissibility of certain Bayes decision rules under vague priors in location problems. J. R. S. S. - B. 56, 543–548. MR1278226 [24] Srinivasan, C.

Additional topics and the case of a positive normal mean Other methods have proven useful in assessing the performance of boundary estimators in constrained parameter spaces, as well as providing improvements. As an example, for the model Xi ∼ Bin(ni , θi ); i = 1, . . , k; with θ1 ≤ θ2 ≤ . . ≤ θk , Sackrowitz and Strawderman (1974) investigated the admissibility (for various loss functions) of the MLE of (θ1 , . . , θk ), while Sackrowitz (1982) provided improvements (under sum of squared error losses) to the MLE in the cases above where it is inadmissible.

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