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Statistica Sinica 21 (2011), 1913-1929
doi:10.5705/ss.2009.201





IDENTIFICATION OF THE CONSTANT COMPONENTS

IN GENERALISED SEMIVARYING COEFFICIENT

MODELS BY CROSS-VALIDATION


Wenyang Zhang


Southwestern University of Finance and Economics
and The University of Bath


Abstract: In practice, some coefficients in generalised varying coefficient models may be constant. We pay a price on the variance side of an estimator when constant coefficients are treated as special functions. This prompts the question of how to identify the constant coefficients. This is basically a model selection problem. In this paper, we use cross-validation (CV) as a criterion for model selection to identify the constant coefficients. We investigate the asymptotic properties of the proposed CV-based model selection approach. We report on a simulation study conducted to show how well the proposed method works when sample size is finite. Finally, the proposed method is used to analyse a data set from China about contraceptive use, which leads to some interesting findings.



Key words and phrases: Cross-validation, generalised semivarying-coefficient models, generalised varying-coefficient models, local linear modelling, local maximum likelihood estimation.



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