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 linearly parametrized and part is given as a sum of unspecified functions of the explanatory variables. An important feature of the modelling approach is that it distinguishes between global and category specific variables. In contrast to global variables the effect of the latter may vary across the categories of the response. Continuous variables of both types, global and category specific ones, are modelled nonparametrically. 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.
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