Variable selection for varying coefficient models via kernel based regularized rank regression (Q1987596)

The authors consider the varying coefficient (VC) regression model: \(Y=\alpha(U)+X^Ta(U)+\epsilon\) where \(\alpha(\cdot)\) and \(a(\cdot) = (a_1(\cdot),\dots,a_p{(\cdot)})^T\) are unknown but smooth functions, with true values \(\alpha_0(\cdot)\) and \(a_0(\cdot) = (a_{01}(\cdot),\dots,a_{0p}(\cdot))^T\) respectively, \(\epsilon\) is random error with density function \(f(\cdot)\) and finite Fisher information, i.e., \(\int\frac{(f'(x))^2}{f(x)}\,dx <\infty\) and assume that there is an integer \(d_0\leq p,\) where \(0 < E[a^2_{0j}(U)] <\infty\) for \(j\leq d_0\) but \(E[a^2_{0j}(U)] = 0\) for \(d_0 < j\leq p,\) i. e., the first \(d_0\) variables are truly relevant but the rest are not. For this model they propose a shrinkage method for variable selection. Selection consistency and oracle properties are established and a BIC-type criterion is suggested for shrinkage parameter selection. The performance of the method is illustrated by numerical studies and real data analysis.