中文题名: | Wild Binary Segmentation算法理论及其模拟应用 |
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保密级别: | 公开 |
论文语种: | 中文 |
学科代码: | 071201 |
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学生类型: | 学士 |
学位: | 理学学士 |
学位年度: | 2018 |
学校: | 北京师范大学 |
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第一导师姓名: | |
第一导师单位: | |
提交日期: | 2018-05-24 |
答辩日期: | 2018-05-16 |
中文关键词: | 变点问题 ; 二进制分割算法 ; Wild Binary Segmentation算法 ; 似然比统计量 ; CUSUM统计量 |
中文摘要: |
现如今,变点问题一直是统计学中一类热门的课题. 统计学家几十年来都对于变点问题中变点的搜寻非常感兴趣. 变点问题也在经济、金融、地球物理等领域得到广泛应用.
引言部分,主要对变点问题及其两种研究方法进行了简要的描述.
第一部分中,对变点问题进行了简单的概念描述,提出主要有两类变点问题.
第二部分中,对研究变点问题的常见方法二进制分割算法进行了介绍. 该算法主要运用两种统计量:似然比统计量和CUSUM(累积和)统计量. 通过进一步研究发现这种算法存在一定问题.
第三部分中,由于二进制分割算法的问题,引出了一种新的研究方法——Wild Binary Segmentation算法. 这一算法可进行多个变点的搜寻,也解决了二进制分割算法产生的问题.
第四部分中,将这一算法进行模拟应用,应用于指数序列下的变点问题. 发现利用CUSUM统计量得到的结果并不符合设定的模型,故建议利用似然比统计量进行模拟.
第五部分中,对上述研究进行了总结,并列举了不足.
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外文摘要: |
Nowadays, the change point problem has been a hot topic on statistics. Statisticians have been interested in change point detection problems for many decades. Change point problems are widely used in several fields such as economics, finance and geophysics.
In the introduction part, it introduces the change point problem and its research methods briefly.
In the first part, it describes the concept of the change point problem and states that there are two major types of this problem. In the second part, it simply introduces one of the methods that research on this problem, Standard Binary Segmentation. This method uses two types of statistics, likelihood ratio statistic and CUSUM statistic. However, there are some problems on this method. In the third part, because of the problems indicated in the second part, it puts forward a new method to solve the change point detection problem. WBS algorithm can be used for multiple change point detection problems and it greatly solves the problems caused by BS algorithm. In the fourth part, WBS algorithm is used for simulation, especially the change point detection for the exponential distribution. It doesn’t perform well because it computes CUSUM statistic. Therefore, it suggests the likelihood ratio statistic to simulate. In the fifth part, it concludes the results of this research and points out some weaknesses to improve.
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参考文献总数: | 13 |
馆藏号: | 本071201/18028 |
开放日期: | 2019-07-09 |