基于经验似然的Logit模型参数估计及实证研究

发布时间：2018-01-09 19:18

本文关键词：基于经验似然的Logit模型参数估计及实证研究　出处：《兰州财经大学》2016年硕士论文　论文类型：学位论文

【摘要】：广义线性模型(Generalized linear models,GLMs)作为经典线性模型的推广应运而生,它既适用于连续数据,又特别适用于离散数据(如计数数据和属性数据)。在生物、医疗、经济和社会数据的统计分析中发挥了重要作用。根据分布函数、连接函数的不同,又可细分为不同的模型,其中应用最为广泛的就是Logit模型,该模型可以通过一组自变量来预测一组分类形式的因变量中每一个类发生的概率。由于经典Logit模型中的诸多限制条件,在实际应用环境中逐渐产生了一系列对基本假定放宽了的拓展方法,在第二章中在对常用模型优缺点的讨论中可以看到,以往的方法都需要给出误差分布或是方差函数形式。本文基于经验似然方法构造Logit模型,尝试利用经验似然方法的特点来解决这一问题。本文的主要工作分为两部分,第一部分在构造Logit模型后,通过轮廓似然方法求解模型,同时得到参数与分布的估计。接下来讨论估计量的无偏性和渐近正态性,然后使用Monte Carlo方法进行模拟研究,在不同的控制条件下证明了构建模型的稳定性和适用性,最后对已有数据采用多种方法建模分析,通过比较进一步说明了所构建模型确实可以得到有效的拟合结果。第二部分是对上市公司财务危机预警问题的实证分析部分。陷入财务危机的风险是企业面临的所有风险中最为重要的风险之一,尽早地对财务状况进行预警,有助于企业制定措施,减少陷入财务危机的可能性。在这一部分中首先探讨了代表上市公司财务状况的指标选择问题,再搜集2015年全部A股中戴帽公司和其配对公司发生危机前三年的数据,从财务层面的5个方面选取20个财务指标作为研究基础,通过筛选最终保留了5个自变量指标建立预警模型。通过对比,本文模型较相同领域文章给出的预测模型精度较好。本文所提出的模型不需要提前给定待分析数据的误差分布或方差函数。而是将误差分布视作一个无限维的参数,通过极大经验似然方法在得出均值模型的参数估计的同时也得到分布的估计。得到的参数估计量具有一致性,分布具有渐近正态性。在模拟研究中可以看到,本文提出的方法在准确性和灵活性上都表现良好,具有一定的优越性。
[Abstract]:Generalized linear models (GLMs) have emerged as a generalization of classical linear models, which are suitable for continuous data. It is especially suitable for discrete data (such as counting data and attribute data). It plays an important role in the statistical analysis of biological, medical, economic and social data. According to the distribution function, the connection function is different. It can also be subdivided into different models, in which the most widely used model is the Logit model. This model can predict the probability of each class in a set of dependent variables by a set of independent variables, because of the constraints in the classical Logit model. In the practical application environment, a series of extended methods to relax the basic assumptions are gradually produced, which can be seen in the discussion of the advantages and disadvantages of common models in the second chapter. Previous methods need to give the error distribution or the form of variance function. This paper constructs Logit model based on empirical likelihood method. This paper attempts to use the characteristics of empirical likelihood method to solve this problem. The main work of this paper is divided into two parts. In the first part, after constructing the Logit model, the contour likelihood method is used to solve the model. Then the unbiased and asymptotic normality of the estimator are discussed, and then the Monte Carlo method is used to simulate the estimation. The stability and applicability of the model are proved under different control conditions. Finally, various methods are used to model and analyze the existing data. The second part is the empirical analysis of the financial crisis of listed companies. The risk of financial crisis is faced by enterprises. One of the most important of all risks. Early warning of the financial situation will help enterprises formulate measures to reduce the possibility of falling into financial crisis. In this part, we first discuss the choice of indicators representing the financial situation of listed companies. Then collect the data of three years before the crisis of all A-share companies and their matching companies in 2015, and select 20 financial indicators from 5 aspects of the financial level as the research basis. Finally, five independent variables were retained by screening to establish the early warning model. The model in this paper is more accurate than the prediction model given in the same domain. The model presented in this paper does not need to give the error distribution or variance function of the data to be analyzed in advance. Instead, the error distribution is regarded as an infinite dimensional parameter. Count. The maximum empirical likelihood method is used to obtain the parameter estimation of the mean value model as well as the estimation of the distribution. The obtained parameter estimator is consistent and the distribution is asymptotically normal. The method presented in this paper has good accuracy and flexibility, and has some advantages.
【学位授予单位】：兰州财经大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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