区间删失数据下几种分布的统计推断及金融数据实证分析

发布时间：2019-05-09 17:01

【摘要】：在很多实际的统计问题中,由于观测技术或者试验经费等客观条件的限制无法得到观测对象的精确值,只能观测到它所处的范围,统计学称这类数据为删失数据。譬如在医学中,研究某种疾病发病时间时会遇到删失数据;在工程学中,研究产品寿命时会遇到删失数据;在金融经济学中,研究贸易关系持续时长、债券的发行与违约时间、企业生存周期时会遇到删失数据。由于删失数据在医学、工程学、金融经济学、保险精算学、人口统计学等领域中大量存在,因而对删失数据进行统计分析尤为重要。当前对删失数据的研究大多集中在较为简单的右删失数据上,而对更为普遍存在的区间删失数据的研究结果不多。实证分析也多集中在医学和工程学领域,对于金融经济和保险精算领域涉及较少。本文利用生存分析中对寿命数据的研究思路,讨论区间删失数据下几种生存分布的统计推断问题。采用基于删失似然函数的极大似然估计方法、EM算法以及对EM算法的M步进行改进的ECM算法,对区间删失数据下指数分布、Weibull分布、对数Logistic分布进行参数估计。利用Matlab和R软件编程实现区间删失数据下三种分布的参数估计,对不同区间删失样本进行数值模拟,比较三种方法的估计效果,模拟结果表明所给参数估计方法可行且估计效果相近。改进的ECM算法具有良好的收敛性质,比EM算法有更广泛的应用。当样本容量较大、删失比例较小的情况下估计效果最好。另一方面,在参数估计和基于缺失信息原则的期望信息矩阵下,利用方差-协方差矩阵的一致渐近性质,构造参数的置信区间,并利用使期望信息矩阵包含最大信息量的原则,设计最优删失计划,并进行数值模拟。最后,采用本文参数估计、置信区间构造方法,对金融经济领域2004-2014年中国对美国的农产品出口贸易关系持续时长的区间删失数据进行了实证分析,估计得到的Weibull分布生存函数与理论生存函数一致,表明上述统计推断方法在金融经济领域具有较好的理论意义和实际应用价值。
[Abstract]:In many practical statistical problems, due to the limitation of objective conditions such as observation technology or test expenses, the exact value of the observation object can not be obtained, and the scope of the observation object can only be observed. This kind of data is called censored data in statistics. For example, in medicine, censored data will be encountered when studying the onset time of a disease, and in engineering, the deleted data will be encountered when studying the life span of a product. In financial economics, the study of trade relations lasts a long time, the issuance and default time of bonds, the life cycle of enterprises will encounter censored data. Because of the large number of deleted data in medicine, engineering, financial economics, insurance actuary, demographics and other fields, it is particularly important to carry out statistical analysis of deleted data. At present, most of the research on deleted data focuses on the relatively simple right deleted data, but the research results on the more common interval censored data are few. Empirical analysis also focuses on medicine and engineering, but less on financial economy and insurance actuarial field. In this paper, several statistical inference problems of survival distribution under interval censored data are discussed by using the research ideas of life data in survival analysis. The maximum likelihood estimation method based on censored likelihood function, the EM algorithm and the improved ECM algorithm for M-step of EM algorithm are used to estimate the parameters of exponential distribution, Weibull distribution and logarithmic Logistic distribution under interval censored data. Using Matlab and R software programming to realize the parameter estimation of three kinds of distribution under interval censored data, the numerical simulation of different interval censored samples is carried out, and the estimation effects of the three methods are compared. The simulation results show that the given parameter estimation method is feasible and the estimation effect is similar. The improved ECM algorithm has a good convergence property and is more widely used than the EM algorithm. When the sample size is large and the censored ratio is small, the estimation effect is the best. On the other hand, under the parameter estimation and the expected information matrix based on the principle of missing information, the confidence interval of the parameter is constructed by using the uniform asymptotic property of the variance-covariance matrix, and the principle that the expected information matrix contains the maximum amount of information is used. The optimal censored plan is designed and the numerical simulation is carried out. Finally, using the method of parameter estimation and confidence interval construction, this paper makes an empirical analysis of the interval censored data of China's agricultural export trade relationship to the United States from 2004 to 2014 in the financial and economic fields. The estimated survival function of Weibull distribution is consistent with the theoretical survival function, which indicates that the above statistical inference method has good theoretical significance and practical application value in the field of finance and economy.
【学位授予单位】：北京工商大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：C829.2

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