On kalman filtering,posterior mode estimation and fisher scoring in dynamic exponential family regression

Summary Dynamic exponential family regression provides a framework for nonlinear regression analysis with time dependent parametersβ ₀,β ₁, …,β _t, …, dimβ _t=p. In addition to the familiar conditionally Gaussian model, it covers e.g. models for categorical or counted responses. Parameters can be estimated by extended Kalman filtering and smoothing. In this paper, further algorithms are presented. They are derived from posterior mode estimation of the whole parameter vector (β′₀, …,β′_t) by Gauss-Newton resp. Fisher scoring iterations. Factorizing the information matrix into block-bidiagonal matrices, algorithms can be given in a forward-backward recursive form where only inverses of “small”p×p-matrices occur. Approximate error covariance matrices are obtained by an inversion formula for the information matrix, which is explicit up top×p-matrices. Heinz Leo Kaufmann, my friend and coauthor for many years, died in a tragical rock climbing accident in August 1989. This paper is dedicated to his memory.