Semiparametric Modelling of Multicategorical Data

Parametric multicategorical models are an established tool in
statistical data analysis. Alternative semi-parametric models are
introduced where part of the explanatory variables is still
linearly parametrized and the rest is given as a sum of unspecified
functions of the explanatory variables. The modelling approach
distinguishes between global and category specific variables, in
contrast to global variables the latter may have different values
for differing categories of the response. Estimation procedures are
derived which make use of an expansion in basis functions which are
localized on a grid of values of the explanatory variables.
Regularization of the estimates is obtained by penalization.