發(fā)布時(shí)間：2018-05-30 11:16

  本文選題：因子模型 + 懲罰�。� 參考：《浙江工商大學(xué)》2017年碩士論文

【摘要】：在經(jīng)濟(jì)、金融和其他科學(xué)領(lǐng)域,研究者經(jīng)常要面臨大數(shù)據(jù)集,因子模型由于能夠有效地從大數(shù)據(jù)集中提煉信息而被廣泛關(guān)注.研究因子模型的首要問題即為模型中參數(shù)的估計(jì)問題.本文研究近似因子模型的懲罰極大似然估計(jì)并證明了估計(jì)量的相合性.本文對模型做的關(guān)鍵假設(shè)是:特殊因子協(xié)方差陣是稀疏陣.在這樣的假設(shè)下可引進(jìn)懲罰函數(shù)用以懲罰特殊因子協(xié)方差陣中的元素.懲罰函數(shù)采用加權(quán)l(xiāng)1的形式.文中給出三種選擇權(quán)重的方法,每種方法確定的懲罰函數(shù)分別稱為Lasso罰函數(shù)、Adaptive-lasso罰函數(shù)和SCAD罰函數(shù).懲罰極大似然法通過最小化負(fù)的高斯擬似然函數(shù)與懲罰函數(shù)之和得到因子載荷、公共因子和特殊因子協(xié)方差陣.與主成分方法依次得到公共因子、因子載荷及特殊因子協(xié)方差陣不同,懲罰極大似然法同時(shí)得到因子載荷和特殊因子協(xié)方差陣的估計(jì).在數(shù)值模擬部分將該方法分別與傳統(tǒng)主成分方法、加權(quán)主成分方法和極大似然方法做了詳細(xì)對比.模擬結(jié)果表明,懲罰極大似然法的表現(xiàn)優(yōu)于其他方法.本文的結(jié)構(gòu)安排如下.第一章論述研究的背景、意義和現(xiàn)狀.第二章為模型介紹、相關(guān)假設(shè)和本文的主要結(jié)果及其證明.第三章討論計(jì)算與模擬問題.最后一章對全文做出總結(jié)并指出了待解決的問題和今后的研究方向。
[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.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224

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本文編號：1955105