Fundamental equations for statistical submanifolds with applications to the Bartlett correction
In the differential geometry literature, there is a set of equations that describe relationships between invariant quantities on the submanifolds and supermanifolds when Riemannian connections are used. The author extends these equations to statistical manifolds, manifolds on which a pair of dual connections is defined. \textit{P. McCullagh} and \textit{D. R. Cox} [Ann. Stat. 14, 1419-1430 (1986; Zbl 0615.62041)] have given geometric interpretations for the Bartlett correction in normal theory regression. In this paper the result is generalized to exponential family regression. Further the author extends this geometric interpretation to statistical manifolds outside of the exponential family. He used a local approximation of the statistical manifold by an exponential family which has locally the same first and second derivatives of the log likelihood function.
derivatives of the log likelihood function
scientific article; zbMATH DE number 4157670
scientific article