Sparse regression for low-dimensional time-dynamic varying coefficient models with application to air quality data

Time dynamic varying coefficient models play an important role in applications of biology, medicine, environment, finance, etc. Traditional methods, such as kernel smoothing and spline smoothing, are popular. But explicit expressions are unavailable using these methods, and the convergence rate of coefficient function estimators is slow. To address these problems, we expand the varying component with appropriate basis functions. And then we solve a sparse regression problem via a sequential thresholded least-squares estimator. The “parameterization” leads to explicit expressions and fast computation speed. Convergence of the sequential thresholded least squares algorithm is guaranteed. The asymptotic distribution of the coefficient function estimator is derived under certain assumptions. Our simulation shows the proposed method has higher precision and computing speed. Finally, our proposed method is applied to the study of PM $ _{2.5} $ 2.5 concentration in Beijing. We analyze the relationship between PM $ _{2.5} $ 2.5 and other impact factors.