  For a nonlinear regression model the information matrices of designs depend
on the parameter of the model. The adaptive Wynn-algorithm for D-optimal design
estimates the parameter at each step on the basis of the employed design points
and observed responses so far, and selects the next design point as in the
classical Wynn-algorithm for D-optimal design. The name `Wynn-algorithm' is in
honor of Henry P. Wynn who established the latter `classical' algorithm in his
1970 paper. The asymptotics of the sequences of designs and maximum likelihood
estimates generated by the adaptive algorithm is studied for an important class
of nonlinear regression models: generalized linear models whose (univariate)
response variables follow a distribution from a one-parameter exponential
family. Under the assumptions of compactness of the experimental region and of
the parameter space together with some natural continuity assumptions it is
shown that the adaptive ML-estimators are strongly consistent and the design
sequence is asymptotically locally D-optimal at the true parameter point. If
the true parameter point is an interior point of the parameter space then under
some smoothness assumptions the asymptotic normality of the adaptive
ML-estimators is obtained.
