重尾序列均值变点检测

Heavy-tailed sequences has been apllied in many scientific fields, such as finances, communications, signal processing. However, the financial market will be affected by some emergency, to establish a precise model, one would have to detect and estimate the location of the time, or a faulty model will lead to a wrong estimate of the financial risk, and bring about some unnecessary loss.This is the problem of change point.. In this project, We shall study the detecttion of the change point in the mean of heavytailed sequences. (1)Since the Bootstrap procedures are often applied in the inference for heavytailed sequences, we shall apllied the procedures in the detection of the mean change in heavytailed sequences, moreover, we shall study the validity of the procedures in change point problems and gave some principle of the selection of the size of the subsamples.(2)For the detection of the multiple mean changes in the heavytailed sequences, we shall propose some statistic and estimate the locations of the changes

重尾序列近年来被广泛应用到金融、通讯、信号处理等领域的统计建模之中。金融市场通常会受到一些突发事件的影响，使得金融数据发的生成过程发生突变，因此对该数据建模时，必须对突变时刻及跃度进行检验与估计，否则所建立的不准确模型，将导致对投资风险的错误估计，从而产生不必要的损失。这个问题即为重尾序列的变点问题。. 本项目主要研究重尾序列的均值变点检测问题,研究内容包括: (1)针对研究重尾序列统计推断问题中常用的Bootstrap抽样方法，研究将Bootstrap抽样应用于重尾序列变点检测问题上的合理性，并研究Bootstrap子样本容量的选取标准。(2)针对重尾序列均值多变点的检测问题，构造合理的统计量，并得到每个变点位置的估计。

重尾序列近年来被广泛应用到金融、通讯、信号处理等领域的统计建模之中。金融市场通常会受到一些突发事件的影响，使得金融数据发的生成过程发生突变，因此对该数据建模时，必须对突变时刻及跃度进行检验与估计，否则所建立的不准确模型，将导致对投资风险的错误估计，从而产生不必要的损失。这个问题即为重尾序列的变点问题。. 本项目主要研究重尾序列的均值变点检测问题,研究内容包括: (1)针对重尾序列均值变点，基于t统计量构造CUSUM统计量，应用bootstrap方法，计算此时统计量的临界值进行检验，并证明其合理性，模拟结果表明，t统计量构造的CUSUM统计量具有更高的经验势。(2针对重尾序列均值的多变点问题，基于拟极大似然函数，应用符号统计量构造多变点检验统计量，模拟结果表明，符号统计量在多变点场合，对重尾序列稳健。并得到每个变点位置的估计。

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