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On Second Order Efficiency of Estimators Derived by Generalised χ 2 Distance Functions
Author(s) -
Aruna Rao K.,
Nagnur B.N.,
R. Vidya
Publication year - 1999
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199909)41:5<615::aid-bimj615>3.0.co;2-7
Subject(s) - estimator , mathematics , efficient estimator , function (biology) , taylor series , statistics , multinomial distribution , invariant estimator , variance (accounting) , minimum variance unbiased estimator , mathematical analysis , accounting , evolutionary biology , business , biology
Taylor (1953) proposed a distance function in connection with the logit χ 2 estimator. For product (associated) multinomial distributions, he showed that minimization of the distance function yields BAN estimators. Aithal (1986) and Rao (1989) considered a modified version of Taylor's distance function and showed that a member belonging to this class leads to a second order efficient estimator. In this paper we consider Taylor's distance function and show that a member belonging to this class produces a second order efficient estimator. In addition to the above two, the m.l. estimator is also second order efficient. In order to compare these three second order efficient estimators, the small sample variances of the estimators are estimated through a simulation study. The results indicate that the variance of the m.l. estimator is the smallest in most of the cases.