In this article, a novel adaptive estimation is proposed for varying coefficient models. Unlike
the traditional least squares based methods, the proposed approach can adapt to different
error distributions. An efficient EM algorithm is provided to implement the proposed
estimation. The asymptotic properties of the resulting estimator are established. Both
simulation studies and real data examples are used to illustrate the finite sample
performance of the new estimation procedure. The numerical results show that the gain of …

In this paper, the adaptive estimation for varying coefficient models proposed by Chen,
Wang, and Yao is extended to allowing for nonstationary covariates. The asymptotic
properties of the estimator are obtained, showing different convergence rates for the
integrated covariates and stationary covariates. The nonparametric estimator of the
functional coefficient with integrated covariates has a faster convergence rate than the
estimator with stationary covariates, and its asymptotic distribution is mixed normal …