Celebratio Mathematica

P. J. Bickel and D. Blackwell: “A note on Bayes estimates,” Ann. Math. Stat. 38 : 6 (1967), pp. 1907–1911. MR 0219175 Zbl 0155.26103 article

Throughout this paper we are concerned with the problem of estimating a real parameter when the loss function is such that the Bayes estimate exists, is unique, and satisfies a simple Equation, (1.5). If the estimate is unbiased (in the general sense of [Lehmann 1951]) we show under weak conditions that it must satisfy another Equation, (1.14). The main result of Section 1, Theorem 1.3, shows that, in general, these two equations are incompatible unless the Bayes risk is 0. This extends Theorem 11.24 of [Blackwell and Girshick 1954] which states that in estimation with quadratic loss, unbiased Bayes estimates have Bayes risk 0. Some counter-examples at the end of the section indicate the limits of this incompatibility result.

D. Blackwell: “A hypothesis-testing game without a value,” pp. 79–82 in A Festschrift for Erich L. Lehmann. Edited by P. J. Bickel, K. A. Doksum, and J. L. Hodges. Wadsworth Statistics/Probability Series. Wadsworth (Belmont, CA), 1983. MR 689739 Zbl 0525.62006 incollection

Kjell Andreas Doksum	Related
Joseph Lawson Hodges, Jr.	Related
Erich Leo Lehmann	Related
Peter J. Bickel	Related

M. Bhattacharjee, R. Lockhart, J. Rolph, G. Roussas, H. Tucker, R. J.-B. Wets, P. Bickel, T. S. Ferguson, A. Lo, M. L. Puri, S. Stigler, W. Sudderth, Y. Yatracos, D. Brillinger, L. A. Goodman, J. Shaffer, H. Chernoff, P. Diaconis, M. Rosenblatt, and F. J. Samaniego: “A tribute to David Blackwell.” Edited by G. G. Roussas. Notices Am. Math. Soc. 58 : 7 (2011), pp. 912–928. MR 2850553 Zbl 1225.01082 article

Thomas S. Ferguson	Related
Leo A. Goodman	Related
Albert Yee-Lap Lo	Related
George Gregory Roussas	Related
Roger J-B Wets	Related
Madan Lal Puri	Related
Murray Rosenblatt	Related	Volume
Francisco J. Samaniego	Related
Juliet Popper Shaffer	Related
John Rolph	Related
Manish C. Bhattacharjee	Related
Stephen Mack Stigler	Related
William D. Sudderth	Related
Yannis Yatracos	Related
Richard Lockhart	Related
Howard Tucker	Related
Peter J. Bickel	Related
David Brillinger	Related
Herman Chernoff	Related
Persi Diaconis	Related

@article {key2850553m,
	AUTHOR = {Bhattacharjee, Manish and Lockhart,
		 Richard and Rolph, John and Roussas,
		 George and Tucker, Howard and Wets,
		 Roger J.-B. and Bickel, Peter and Ferguson,
		 Thomas S. and Lo, Albert and Puri, Madan
		 L. and Stigler, Stephen and Sudderth,
		 W. and Yatracos, Yannis and Brillinger,
		 David and Goodman, Leo A. and Shaffer,
		 Juliet and Chernoff, Herman and Diaconis,
		 Persi and Rosenblatt, Murray and Samaniego,
		 Francisco J.},
	TITLE = {A tribute to {D}avid {B}lackwell},
	JOURNAL = {Notices Am. Math. Soc.},
	FJOURNAL = {Notices of the American Mathematical
		 Society},
	VOLUME = {58},
	NUMBER = {7},
	YEAR = {2011},
	PAGES = {912--928},
	URL = {http://www.ams.org/notices/201107/rtx110700912p.pdf},
	NOTE = {Edited by G. G. Roussas.
		 MR:2850553. Zbl:1225.01082.},
	ISSN = {0002-9920},
	CODEN = {AMNOAN},
}

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			clear

David H. Blackwell

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