Consistency of logistic classifier in abstract Hilbert spaces

We study the asymptotic behavior of the logistic classifier in an abstract Hilbert space and require realistic conditions on the distribution of data for its consistency. The number kn of estimated parameters via maximum quasi-likelihood is allowed to diverge so that kn/n → 0 and nτ 4 kn → ∞, where n is the number of observations and τkn is the variance of the last principal component of data used for estimation. This is the only result on the consistency of the logistic classifier we know so far when the data are assumed to come from a Hilbert space