近似因子模型的惩罚极大似然估计

发布时间：2018-05-30 11:16

本文选题：因子模型 + 惩罚　；参考：《浙江工商大学》2017年硕士论文

【摘要】：在经济、金融和其他科学领域,研究者经常要面临大数据集,因子模型由于能够有效地从大数据集中提炼信息而被广泛关注.研究因子模型的首要问题即为模型中参数的估计问题.本文研究近似因子模型的惩罚极大似然估计并证明了估计量的相合性.本文对模型做的关键假设是:特殊因子协方差阵是稀疏阵.在这样的假设下可引进惩罚函数用以惩罚特殊因子协方差阵中的元素.惩罚函数采用加权l1的形式.文中给出三种选择权重的方法,每种方法确定的惩罚函数分别称为Lasso罚函数、Adaptive-lasso罚函数和SCAD罚函数.惩罚极大似然法通过最小化负的高斯拟似然函数与惩罚函数之和得到因子载荷、公共因子和特殊因子协方差阵.与主成分方法依次得到公共因子、因子载荷及特殊因子协方差阵不同,惩罚极大似然法同时得到因子载荷和特殊因子协方差阵的估计.在数值模拟部分将该方法分别与传统主成分方法、加权主成分方法和极大似然方法做了详细对比.模拟结果表明,惩罚极大似然法的表现优于其他方法.本文的结构安排如下.第一章论述研究的背景、意义和现状.第二章为模型介绍、相关假设和本文的主要结果及其证明.第三章讨论计算与模拟问题.最后一章对全文做出总结并指出了待解决的问题和今后的研究方向。
[Abstract]:In the fields of economics, finance and other sciences, researchers often face big data sets, and factor models have attracted much attention because of their ability to extract information from big data centralization effectively. The most important problem in the study of factor model is the estimation of parameters in the model. In this paper, we study the penalty maximum likelihood estimation of the approximate factor model and prove the consistency of the estimator. The key assumption of the model is that the special factor covariance matrix is sparse matrix. Under this assumption, the penalty function can be introduced to punish the elements in the covariance matrix of special factors. The penalty function takes the form of weighted l 1. Three methods of selecting weights are given in this paper. The penalty functions determined by each method are called Lasso penalty function Adaptive-lasso penalty function and SCAD penalty function respectively. By minimizing the sum of negative Gao Si quasi-likelihood functions and penalty functions, the penalty maximum likelihood method obtains factor loads, common factors and special factor covariance matrices. Different from the principal component method, the common factor, the factor load and the special factor covariance matrix are obtained in turn. The penalty maximum likelihood method is used to estimate the factor load and the special factor covariance matrix at the same time. In the part of numerical simulation, the method is compared with the traditional principal component method, the weighted principal component method and the maximum likelihood method in detail. The simulation results show that the performance of the penalty maximum likelihood method is better than that of other methods. The structure of this paper is as follows. The first chapter discusses the background, significance and current situation of the research. The second chapter is the introduction of the model, the related assumptions and the main results of this paper and its proof. Chapter three discusses the problem of calculation and simulation. The last chapter summarizes the full text and points out the problems to be solved and the future research direction.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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