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March, 1959 On the Theory of Ban Estimates
Robert A. Wijsman
Ann. Math. Statist. 30(1): 185-191 (March, 1959). DOI: 10.1214/aoms/1177706373


The notion of best asymptotically normal estimates--BAN estimates for short--was introduced by Neyman [8] in the multinomial case. Applications have been made in biological problems, notably in bio-assay [2], [4], [5]. Generalizations of Neyman's work have been made by Barankin and Gurland [1], Chiang [3] and Ferguson [5]. The usual theory of BAN estimates requires differentiability of the estimates, and imposes rather strong conditions on certain functions given in advance (the functions $\zeta$ and $\Sigma$ of Section 3). In this note a different definition of BAN estimates is made which does not require differentiability, at the same time relaxing the conditions on $\zeta$ and $\Sigma,$ whereas in essence all important theorems in the theory of BAN estimates are retained.


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Robert A. Wijsman. "On the Theory of Ban Estimates." Ann. Math. Statist. 30 (1) 185 - 191, March, 1959.


Published: March, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0089.14701
MathSciNet: MR105760
Digital Object Identifier: 10.1214/aoms/1177706373

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 1 • March, 1959
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