Local asymptotics for b-spline estimators of the varying coefficient model

In this paper, the model Studied is the varying coefficient model y = x(1)beta(1)(t) + (...) +x(p)beta(p)(t) + epsilon, where Eepsilon = 0 Eepsilon(2) = sigma(2) and beta(1)(t), l = 1,..., p are smooth coefficient functions, which are approximated by the B-spline function and estimated under the least Squares criterion. The local optimal convergence rate of the B-spline estimators of the coefficient functions is obtained. In addition, the asymptotic normality is established under appropriate conditions. To illuminate our methods a Simulation study is conducted.