In this paper, we consider the problem of simultaneous variable selection and estimation for varying-coefficient partially linear models in a “small <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation>, large <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p$$</EquationSource> </InlineEquation>” setting, when the number of coefficients in the linear part diverges with sample size while the number of varying...</equationsource></inlineequation></equationsource></inlineequation>

In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s...

We propose the penalized estimator with the smoothly clipped absolute deviation (SCAD) penalty for varying coefficient time series models, which in autoregressive models actually performs lag order selection. Theoretical properties are established. Some numerical examples are also presented.