Guo Guangbao
Department of Statistics, Shandong University of Technology, Zibo, People's Republic of China.
J Appl Stat. 2020 Mar 20;48(4):669-692. doi: 10.1080/02664763.2020.1743650. eCollection 2021.
It is a major research topic of limited generalized linear models, namely, generalized linear models with limited dependent variables. The models are developed in many research fields. However, quasi-likelihood estimation of the models is an unresolved issue, due to including limited dependent variables. We propose a novel quasi-likelihood, called Taylor quasi-likelihood, to handle with the unified estimation problem of the limited models. It is based on Taylor expansion of distribution function or likelihood function. We also extend the likelihood to a generalized version and an adaptive version and propose a distributed procedure to obtain the likelihood estimator. In low-dimensional setting, we give selection criteria for the proposed method and make arguments for the consistency and asymptotic normality of the estimator. In high-dimensional setting, we discuss feature selection and oracle properties of the proposed method. Simulation results confirm the advantages of the proposed method.
这是受限广义线性模型的一个主要研究课题，即具有受限因变量的广义线性模型。这些模型在许多研究领域都有发展。然而，由于包含受限因变量，这些模型的拟似然估计是一个未解决的问题。我们提出了一种新颖的拟似然，称为泰勒拟似然，以处理受限模型的统一估计问题。它基于分布函数或似然函数的泰勒展开。我们还将似然扩展到广义版本和自适应版本，并提出一种分布式程序来获得似然估计量。在低维情况下，我们给出了所提方法的选择标准，并论证了估计量的一致性和渐近正态性。在高维情况下，我们讨论了所提方法的特征选择和神谕性质。模拟结果证实了所提方法的优势。
