Varying coefficient regression: Revisit and parametric help

초록

This paper concerns the estimation of varying coefficient models, which is considered very useful in analyzing the regression relationship between variables. The purpose of this paper is threefold. Firstly, we introduce a new formulation of varying coefficient regression under which a structure-respecting constraint is developed for identifying the model components. Secondly, we develop a full account of locally linear kernel smoothing approach to estimating varying coefficient models which is largely missing in the literature. Thirdly, we address a bias reduction technique applied to locally linear varying coefficient regression which turns out to be successful under mild condition. We develop our methodology and theory for response variables taking values in a general Hilbert space. We discuss relevant theory for the associated projection operators, the convergence of an iterative backfitting algorithm, and the error rates and asymptotic distributions of the estimators. We also include some simulation results demonstrating the success of the proposed approach.

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