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Biometrika 2003 90(3):551-566; doi:10.1093/biomet/90.3.551
© 2003 by Biometrika Trust
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Generalised structured models

Enno Mammen1 and Jens Perch Nielsen2

1 Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germanyenno{at}statlab.uni-heidelberg.de 2 Codan, Gammel Kongevej 60 DK 1790 Copenhagen V, Denmark.npj{at}codan.dk

We present a general class of nonlinear regression and time series models that we call generalised structured models.The class is a natural generalisation of generalised additive models, and it includes generalised interaction models, structured volatility models, visual GARCH, generalised autoregressive conditional heteroscedasticity, models and varying coefficient models. We discuss estimation principles including smoothing splines and a generalisation of the projection approach of Mammen et al. (1999). We finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models.

Key Words: Generalised additive model; Generalised structured model; Kernel estimation; Smoothing spline

Received November 2001. Revised November 2002


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