混合广义部分线性加性模型的参数估计

doi:10.16088/j.issn.1001-6600.2021060909

摘要/Abstract

摘要： 广义部分线性加性模型具有参数和非参数2个部分,并且选择不同连接函数可以得到多种不同加性模型,是一种非常灵活的统计模型。有限混合模型是研究异质性总体的有效工具,扩展性很强,随着计算能力的不断提升,得到越来越广泛应用。本文将这2种模型相结合,提出混合广义部分线性加性模型(MGAPLM)。首先给出模型的定义,并在一些温和条件下证明模型可识别性;然后,使用将样条与核方法相结合的spline-backfitted-kernel(SBK) 方法估计模型中参数和非参数函数,并且证明估计量的渐近性质;此外,给出一种模型检验方法,检验所提出模型有效性,同时在正态分布和二项分布2种情形下进行数值模拟,给出估计量在有限样本下的表现;最后,将提出的方法应用到一组经济数据中,得到此数据下模型的具体形式,并结合实际对建模结果进行分析。

关键词: 广义部分线性加性模型, 样条, 混合模型, EM算法, SBK方法

Abstract: The generalized partially linear additive model has two parts: a parametric part and a non-parametric part. Different link functions can be applied to different situations. So it is a very flexible statistical model. The finite mixture model is an effective tool for studying heterogeneous populations, which has strong expansibility. With the improvement of computing power, it has been widely used. In this paper, mixture of generalized additive partial linear model (MGAPLM) is proposed by combining these two models. First, definition of the model and the identifiability results under some regular conditions are presented. Then the spline-backfitted-kernel (SBK) method that combines the spline and the kernel method is used to estimate the parameters and non-parametric function in the model. Furthermore, the asymptotic property of the estimator is given. In order to test whether the proposed model is effective, a model checking method is proposed under the normal distribution and the binomial distribution. Numerical simulation is carried out to show the performance of the estimator with a finite sample size. Finally, the proposed method is applied to economic data and obtain the specific form of the model.

Key words: generalized additive partial linear models, spline, mixture models, EM algorithm, SBK method

中图分类号:

O212.7

任帅, 程文慧, 周洁. 混合广义部分线性加性模型的参数估计[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 108-124.

REN Shuai, CHENG Wenhui, ZHOU Jie. Estimation of the Mixed Generalized Partially Linear Additive Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 108-124.

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