One of the advantages for the varying-coefficient model is to allow the coefficients to vary as smooth functions of other variables and the coefficients functions can be estimated easily through a simple B-spline approximations method. This leads to a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when some coefficient functions possess different degrees of smoothness. Under the regularity conditions, the consistency and asymptotic normality of the two step B-spline estimators are also derived. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an AIDS data set.

中文翻译：

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具有两步结数选择的变系数模型的新有效样条估计

变系数模型的优点之一是允许系数随着其他变量的平滑函数而变化，并且可以通过简单的 B 样条近似方法轻松估计系数函数。这导致一个简单的一步估计过程。我们表明，当一些系数函数具有不同程度的平滑度时，这种一步法不能是最优的。在正则条件下，也推导出了两步B样条估计量的一致性和渐近正态性。一些模拟研究表明，两步程序的增益可能相当可观。该方法由艾滋病数据集说明。