By Per Brinch Hansen
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Extra info for Architecture of Concurrent Programs
De Gunst, C. Klaassen, and A. van der Vaart, pp. 223– 243. Volume 36 in the IMS Lecture Note Series, Beachwood, Ohio. , Takeda, M. (1994). Dirichlet Forms and Symmetric Markov Processes. New York: de Gruyter. , Keane, M. and Roynette, B. (1977). March aleatoires sur les Groupes de Lie. Lecture Notes in Math 624, New York: Springer. MR517359  Hobert, J. and Robert, C. (1999). Eaton’s Markov chain, its conjugate partner, and P -admissibility. Ann. Statist. 27, 361–373. MR1701115  James, W.
Canada, E3B 5A3. ca 2 Department of Statistics, Rutgers University, 501 Hill Center, Busch Campus, Piscataway, NJ 08855, USA. edu Keywords and phrases: restricted parameter spaces, minimaxity, admissibility, dominating procedures, maximum likelihood estimation. AMS 2000 subject classifications: 62-02, 62C99, 62C15, 62C20, 62C10, 62F10, 62F30. 1 Department 21 22 E. Marchand and W. E. Strawderman the original space) is non-compact. In this case it often happens that these classical estimators are minimax in both the original problem and the restricted problem.
More precisely, consider the path space W = Y ∞ = Y × Y × · · · with the usual product σ-algebra. Given the initial value w0 , there is a Markov chain W = (w0 , W1 , W2 , . ) so that R(dwi+1 |wi ) is the conditional distribution of Wi+1 given Wi = wi , for i = 0, 1, 2, . .. The unique probability measure on path space that is consistent with this Markov specification, is denoted by S(·|w0 ). Because the space Y is rather general, the definition of recurrence has to be selected with some care. The reader should note that neither irreducibility nor periodicity occur in the discussion that follows (see Meyn and Tweedie (1993) for a discussion of such things in the general state space case).
Architecture of Concurrent Programs by Per Brinch Hansen