Nonparametric homogeneity pursuit in functional-coefficient models
Nonparametric homogeneity pursuit in functional-coefficient models
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DOI：
10.1080/10485252.2021.1951265
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发表时间：
2021-07
影响因子：
1.2
通讯作者：
Jia Chen;Degui Li;Lingling Wei;Wenyang Zhang
中科院分区：
文献类型：
--
作者：
Jia Chen;Degui Li;Lingling Wei;Wenyang Zhang
摘要本文探讨了具有函数系数的非线性模型中系数函数的齐性，并确定了基本的半参数模型结构。对于初始核估计，我们将经典的层次聚类方法与广义信息准则相结合来估计聚类的数量，每个聚类具有共同的函数系数，并确定每个聚类的隶属度。为了确定可能的半变系数建模框架，我们进一步引入了惩罚局部最小二乘法来确定随指数变量变化的零系数、非零常系数和泛函系数。通过基于非参数核的聚类分析和惩罚方法，可以大大减少模型中未知参数和非参数成分的数量，从而达到降维的目的。在一些正则性条件下，我们建立了所提方法的渐近性质，包括齐性追求的相合性。数值研究，包括蒙特卡罗实验和两个经验应用，证明了我们的方法的有限样本性能。
ABSTRACT This paper explores the homogeneity of coefficient functions in nonlinear models with functional coefficients and identifies the underlying semiparametric modelling structure. With initial kernel estimates, we combine the classic hierarchical clustering method with a generalised version of the information criterion to estimate the number of clusters, each of which has a common functional coefficient, and determine the membership of each cluster. To identify a possible semi-varying coefficient modelling framework, we further introduce a penalised local least squares method to determine zero coefficients, non-zero constant coefficients and functional coefficients which vary with an index variable. Through the nonparametric kernel-based cluster analysis and the penalised approach, we can substantially reduce the number of unknown parametric and nonparametric components in the models, thereby achieving the aim of dimension reduction. Under some regularity conditions, we establish the asymptotic properties for the proposed methods including the consistency of the homogeneity pursuit. Numerical studies, including Monte-Carlo experiments and two empirical applications, are given to demonstrate the finite-sample performance of our methods.