CAJ | 학술논문

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。
변계수단지표모형결합화단지표화변계수모형적우점，재허다영역중유착중요적응용。본문아문기우B-양조핍근，제출료량충고계방법：제일충방법시이용Newton-Raphson질대방법동시획득삼수화비삼수부분적고계；제이개방법시부면방법획득료상응적고계。당모형중유허다삼수시，아문건의사용제이충고계방법，이당삼수개수교소시채용제일충방법경방편。량개모의례자용래험증본문제출적고계방법。
The varying-coeffcient single-index models (VCSIM) have been applied in many fields since they combine the advantages of single-index models and varying-coeffcient models. In this paper, their estimation method is proposed based on B-spline approximation technique and two calcula-tion 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 conve-nient. Two simulated examples are given to illustrate the performances of the proposed estimation methodologies and calculation procedures.