Parameter identifiability and redundancy: theoretical considerations

Abstract

Abstract In this paper we outline general considerations on parameter identifiability, and introduce the notion of weak local identifiability and gradient weak local identifiability. These are based on local properties of the likelihood, in particular the rank of the Hessian matrix. We relate these to the notions of parameter identifiability and redundancy previously introduced by Rothenberg (Econometrica 39 (1971) 577-591) and Catchpole and Morgan (Biometrika 84 (1997) 187-196). Within certain special classes of exponential family models, gradient weak local identifiability is shown to be equivalent to lack of parameter redundancy. We consider applications to a recently developed class of cancer models of Littl