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.

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同质性，并确定了潜在的半参数建模结构。通过初始核估计，我们将经典的层次聚类方法与信息准则的广义版本相结合，以估计集群的数量，每个集群都有一个共同的函数系数，并确定每个集群的成员资格。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、非零常数系数和函数系数。通过基于非参数核的聚类分析和惩罚方法，我们可以大幅减少模型中未知参数和非参数组件的数量，从而达到降维的目的。在某些规律性条件下，我们为所提出的方法建立了渐近特性，包括同质性追求的一致性。数值研究，包括蒙特卡罗实验和两个经验应用，被用来证明我们方法的有限样本性能。