On ban estimators for Chi squared test criteria

Wijsman (1959a) developed the theory of BAN estimators of a parameter β under some fairly general conditions assuming that n1/2(yn−g(β))→LNs(0,σ(β)). The present article considers the complementary, but somewhat more general, approach under the constraint equation model that restricts the parameter μ so that f(μ)=0 under general conditions requiring n1/2(yn−μ)→LNs(0,σ∗(μ)). 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.