变系数单指标模型的B-样条估计

B-Spline Estimation for Varying-Coefficient Single-Index Model

  • 摘要: 变系数单指标模型结合和单指标和变系数模型的优点, 在许多领域中有着重要的应用. 本文我们基于B-样条逼近, 提出了两种估计方法: 第一种方法是利用Newton-Raphson迭代方法同时获得参数和非参数部分的估计; 第二个方法是剖面方法获得了相应的估计. 当模型中有许多参数时, 我们建议使用第二种估计方法, 而当参数个数较少时采用第一种方法更方便. 两个模拟例子用来验证本文提出的估计方法.

     

    Abstract: The varying-coefficient single-index models (VCSIM) have been applied in many fields since they combine the advantages of single-index models and varying-coefficient models. In this paper, their estimation method is proposed based on B-spline approximation technique and two calculation methods can be used. The first one is to directly calculate the parametric and nonparametric parts simultaneously by Newton-Raphson iteration algorithm. The second one is to calculate the two parts by profile method individually. We suggest that the second method is for our preference when the large amount of parameters are involved, otherwise the first method will be more convenient. Two simulated examples are given to illustrate the performances of the proposed estimation methodologies and calculation procedures.

     

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