Title: Nonparametric regression estimation in chain graph models
Authors: Mate Baranyi - Institute of Mathematics, Budapest University of Technology and Economics (Hungary) [presenting]
Marianna Bolla - Institute of Mathematics, Technical University of Budapest (Hungary)
Abstract: It is known that a regression graph with a chordal graph for the context variables can be oriented to be Markov equivalent to a DAG on the same skeleton if and only if it does not contain any chordless collision path in four nodes. Constructions for such a DAG and applications of linear, linearized, and logistic regression for prediction along the paths were intensively studied. A nonparametric regression method, using local averaging estimators, is introduced for prediction based on a complete sample. The method makes it possible to perform nonparametric regressions recursively along the DAG, irrespective of the type of the context and response variables. Hence, predictions for the response variables of new-coming cases can be done in the possession of the values of their context variables only. The technique can be extended to undirected graphical models on a chordal graph, where the prediction goes from the separators to the residuals of the cliques ordered in a junction tree structure. We prove consistency under very general conditions on the distribution and the selected kernel. An application to sociological data is also presented.