Open Access
March, 1983 On Ban Estimators for Chi Squared Test Criteria
Kerry G. Bemis, Vasant P. Bhapkar
Ann. Statist. 11(1): 183-196 (March, 1983). DOI: 10.1214/aos/1176346068


Wijsman (1959a) developed the theory of BAN estimators of a parameter $\beta$ under some fairly general conditions assuming that $n^{1/2}(y_n - g(\beta)) \rightarrow_L N_s(0, \sigma(\beta))$. The present article considers the complementary, but somewhat more general, approach under the constraint equation model that restricts the parameter $\mu$ so that $f(\mu) = 0$ under general conditions requiring $n^{1/2}(y_n - \mu) \rightarrow_L N_s(0, \sigma^\ast(\mu))$. At the same time, this article weakens Wijsman's differentiability requirement by introducing a $p$-differentiability condition for regular estimators. Next the theory of BAN estimation is developed for a model combining features of both of these approaches. As a special case of the model above, weighted least squares estimators for a general linear model are shown to be BAN.


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Kerry G. Bemis. Vasant P. Bhapkar. "On Ban Estimators for Chi Squared Test Criteria." Ann. Statist. 11 (1) 183 - 196, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0521.62026
MathSciNet: MR684875
Digital Object Identifier: 10.1214/aos/1176346068

Primary: 62F12
Secondary: 62F05

Keywords: BAN estimation , Chi squared test criteria , regular estimators , weighted least squares criterion

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • March, 1983
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