系数函数光滑度互不相同的变系数模型的一步估计法

One-step Estimation for Varying Coefficient Models with Unknown Functions of Different Degrees of Smoothness

该文提出了一种一步估计方法用以估计变系数模型中具有互不相同光滑度的未知函数,所有未知函数和它们的导数的估计量由一次极小化得到.给出了估计量的渐近性质,包括渐近偏差、方差和渐近分布,一步估计量被证明达到了最优收敛速度.

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.