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SOME SECOND ORDER ASYMPTOTICS IN EXPONENTIAL FAMILY NON‐LINEAR REGRESSION MODELS (A GEOMETRIC APPROACH)
Author(s) -
Wei BoCheng,
Zhu HongTu
Publication year - 1997
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1997.tb00531.x
Subject(s) - mathematics , independent and identically distributed random variables , exponential family , estimator , covariance , nonlinear system , exponential function , nonlinear regression , regression analysis , mathematical analysis , statistics , random variable , physics , quantum mechanics
summary The differential geometric framework of Amari (1982a, 1985) is applied to the study of some second order asymptotics related to the curvatures for exponential family nonlinear regression models, in which the observations are independent but not necessarily identically distributed. This paper presents a set of reasonable regularity conditions which are needed to study asymptotics from a geometric point of view in regression models. A new stochastic expansion of a first order efficient estimator is derived and used to study several asymptotic problems related to Fisher information in terms of curvatures. The bias and the covariance of the first order efficient estimator are also calculated according to the expansion.