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SECOND ORDER ASYMPTOTIC COMPARISON OF ESTIMATORS UNDER UNIVERSAL DOMINATION CRITERION
Author(s) -
Takagi Yoshiji
Publication year - 2006
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2006.00438.x
Subject(s) - mathematics , estimator , class (philosophy) , value (mathematics) , order (exchange) , basis (linear algebra) , statistics , geometry , finance , artificial intelligence , computer science , economics
Summary The main purpose of this paper is to formulate theories of universal optimality, in the sense that some criteria for performances of estimators are considered over a class of loss functions. It is shown that the difference of the second order terms between two estimators in any risk functions is expressed as a form which is characterized by a peculiar value associated with the loss functions, which is referred to as the loss coefficient. This means that the second order optimal problem is completely characterized by the value of the loss coefficient. Furthermore, from the viewpoint of change of the loss coefficient, the relationship between two estimators is classified into six types. On the basis of this classification, the concept of universal second order admissibility is introduced. Some sufficient conditions are given to determine whether any estimators are universally admissible or not.