Generalized smooth monotonic regression

Common approaches to monotonic regression focus on the case of a
unidimensional covariate and continuous dependent variable. Here a
general approach is proposed that allows for additive and
multiplicative structures where one or more variables have monotone
influence on the dependent variable. In addition the approach
allows for dependent variables from an exponential family,
including binary and Poisson distributed dependent variables.
Flexibility of the smooth estimate is gained by expanding the
unknown function in monotonic basis functions. For the estimation
of coefficients and the selection of basis functions a likelihood
based boosting algorithm is proposed which is simply to implement.
Stopping criteria and inference are based on AIC-type measures. The
method is applied to several data sets.