出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：Varying-coefficient linear models arise from multivariate nonparametricregression, nonlinear time series modelling and forecasting, functional dataanalysis, longitudinal data analysis, and others. It has been a commonpractice to assume that the vary-coefficients are functions of a given variablewhich is often called an index. A frequently asked question is which variableshould be used as the index. In this paper, we explore the class of thevarying-coefficient linear models in which the index is unknown and isestimated as a linear combination of regression and/or other variables. Thiswill enlarge the modelling capacity substantially. We search for the index suchthat the derived varying-coefficient model provides the best approximation tothe underlying unknown multi-dimensional regression function in the leastsquare sense. The search is implemented through the newly proposed hybridbackfitting algorithm. The core of the algorithm is the alternative iterationbetween estimating the index through a one-step scheme and estimatingcoefficient functions through a one-dimensional local linear smoothing. Thegeneralised cross-validation method for choosing bandwidth is efficientlyincorporated into the algorithm. The locally significant variables are selectedin terms of the combined use of t-statistic and Akaike information criterion. Wefurther extend the algorithm for the models with two indices. Simulation showsthat the proposed methodology has appreciable flexibility to model complexmultivariate nonlinear structure and is practically feasible with averagemodern computers. The methods are further illustrated through the Canadianmink-muskrat data in 1925-1994 and the pound/dollar exchange rates in1974-1983
关键词：Akaike information criterion; backfitting algorithm; generalised;cross-validation; local linear regression; local significant variable selection;one-step estimation; smoothing index; varying-coefficient linear models
