One-step Estimation for Varying Coefficient Models with Unknown Functions of Different Degrees of Smoothness
系数函数光滑度互不相同的变系数模型的一步估计法

An one-step estimation method is proposed to estimate all the unknown functions in varying coefficient models, of which the degrees of smoothness may be different from each other. In one-step estimation approach, the local estimators of all the unknown functions and their derivatives can be obtained by only one minimization operation. The asymptotic properties of the estimators, including bias, variance and asymptotic distribution, are derived. It is shown that all the one-step estimators achieve the optimal convergence rates.