Abstract
The varying coefficient model is a useful extension of linear models and has many advantages in practical use. To estimate the unknown functions in the model, the kernel type with local linear least-squares (L 2) estimation methods has been proposed by several authors. When the data contain outliers or come from population with heavy-tailed distributions, L 1-estimation should yield better estimators. In this article, we present the local linear L 1-estimation method and derive the asymptotic distributions of the L 1-estimators. The simulation results for two examples, with outliers and heavy-tailed distribution, respectively, show that the L 1-estimators outperform the L 2-estimators.
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