Exponential Family Nonlinear Models With Linear Constraints Based On The Curvature Of The Statistical Analysis

This paper first presents a MBW geometric framework for nonlinear exponential family regression models with linear restriction.A set of stochastic expansions are given for the restricted maximum likelihood estimator by using the MBW geometric framework. So it is easy to derive the approximations of its moments.The stochastic expansions and the approximations given here depend only on the asymptotically independent normal random variables and curvature arrays , therefore it is convenient to use therm Moreover, this paper studies the relationship between the approximate confidence regions and the statistical curvature in nonlinear exponential family regression models with linear restriction from geometric point of view. And it gives approximate confidence regions for parameters and parameter subsets in this class of models.