Adaptive varying co-efficient linear models
AbstractVarying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an "index". To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the "t"-statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate non-linear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink-muskrat data in 1925-1994 and the pound-dollar exchange rates in 1974-1983. Copyright 2003 Royal Statistical Society.
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Bibliographic InfoPaper provided by London School of Economics and Political Science in its series Open Access publications from London School of Economics and Political Science with number http://eprints.lse.ac.uk/5885/.
Date of creation: Feb 2003
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Publication status: Published in Journal of the Royal Statistical Society: series B (statistical methodology) (2003-02) v.65, p.57-80
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