Stepwise BAN estimators for exponential families with multivariate normal applications

Consistent, asymptotically efficient and asymptotically normal stepwise estimators are given for a subclass of the uniparametric and multiparametric exponential families. The estimators are derived by using the Robbins-Monro stochastic approximation procedure with certain families of random variables arising from the normalized log-likelihood. Considered in detail are three multivariate normal examples where the maximum likelihood estimators are not tractable.