ADAPTING FOR THE MISSING LINK

We consider the fitting of generalized linear models in which the link function is assumed to be unknown, and propose the following computat ional method: First, estimate regression coefficients using the canoni cal link. Then, estimate the link via a kernel smoother, treating the direction in the predictor space determined by the regression coeffici ents as known. Then reestimate the direction using the estimated link and alternate between these two steps. We show that under fairly gener al conditions, n(1/2)-consistent estimates of the direction are obtain ed. A small Monte Carlo study is presented.