Variable selection for semivarying coefficient models via local averaging

This study aims to provide novel insights into variable selection in the semivarying coefficient model. We focus on the problem of variable selection and screening for the constant coefficient part. A common approach in the existing literature is to infer the constant coefficients by transforming the problem into a linear model scenario, utilizing a fine estimator of the varying coefficients. In this paper, we propose an approximation method for the varying coefficient functions using local averaging, which is characterized by its simplicity, rough and computational efficiency. Additionally, we introduce an adaptive lasso estimator and a forward regression algorithm specifically designed for semivarying coefficient models. Theoretical and experimental results highlight the effectiveness of the local averaging method in extending variable selection techniques from the linear model to the semivarying coefficient model. Our proposed approaches demonstrate a significant improvement in inference speed compared with baseline methods, with little loss of asymptotic efficiency.