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Shrinkage estimation of the varying coefficient model. (English) Zbl 1388.62213
Summary: The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator (LASSO). The new method can do nonparametric estimation and variable selection simultaneously. With a local constant estimator and the adaptive LASSO penalty, the new method can identify the true model consistently, and that the resulting estimator can be as efficient as the oracle estimator. Numerical studies clearly confirm our theories. Extension to other shrinkage methods (e.g., the SCAD, i.e., the Smoothly Clipped Absolute Deviation.) and other smoothing methods is straightforward.

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
62F10 Point estimation
62G05 Nonparametric estimation
62J05 Linear regression; mixed models
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