Degrees of freedom and model selection in semiparametric additive monotone regression

The degrees of freedom of semiparametric additive monotone models are derived using results about projections onto sums of order cones. Two important related questions are also studied, namely, the definition of estimators for the parameter of the error term and the formulation of specific Akaike Information Criteria statistics. Several alternatives are proposed to solve both problems and simulation experiments are conducted to compare the behavior of the different candidates. A new selection criterion is proposed that combines the ability to guess the model but also the efficiency to estimate the variance parameter. Finally, the criterion is used to select the model in a regression problem from a well known data set.