NONPARAMETRIC BINARY REGRESSION - A BAYESIAN-APPROACH

The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let xi be a vector of binary covariates and let eta be a binary response variable, with P{eta = 1\xi} = f(xi). Here, f is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural ''balance'' condition. Define a prior distribution on f as SIGMA(k)omega(k)pi(k)/SIGMA(k)omega(k), where pi(k) is uniform on the set of f which only depend on the first k covariates and omega(k) > 0 for infinitely many k. Bayes estimates are consistent at all f if omega(k) decreases rapidly as k increase. Otherwise, the estimates are inconsistent at f = 1/2.