分段检验理论研究及其应用

发布时间：2018-07-31 05:53

【摘要】：分段检验理论主要包括有序样本聚类与分段假设检验两部分.分段检验理论在企业营销效应,提升质量有效性等领域有着广泛的应用,准确评价相关措施或政策的有效性,对政策或措施的管理具有重要的意义,因而对分段检验理论及其应用的研究就显得尤为重要.在有序样本聚类方面,首先,提出利用组内离差平方和与组间离差平方和构建F统计量建立优化模型实现有序样本聚类,并将其应用于成都市和北京市环境空气指数历史数据分类.当样本容量较大时,基于F统计量的优化模型必须存储每一类的F值,最优分割法都必须存储每一类对应直径,使得计算效率差.而模拟退火算法具有良好的全局搜索能力,将模拟退火算法与最优分割法目标函数相结合可避免存储类的直径,提高算法计算效率,因此提出基于模拟退火算法的有序样本聚类.最后利用成都环境空气指数历史数据进行实证分析,取得较好的分类结果.在分段假设检验方面,根据样本是否存在相关性分为两类.当分段样本相互独立时,提出运用经典的假设检验理论进行均值与方差的参数检验,并将经典假设检验理论与基于F统计量的优化模型有序样本聚类结合评价成都市环境空气治理效应.当分段样本存在短期自相关时,结合平稳时间序列性质,对正态假设下均值与方差参数检验进行修正,并将分段检验中样本均值与样本方差的方差推广到伽马分布族.最后将分段检验理论与基于F统计量的优化模型有序样本聚类结合,实现北京市政府环境空气治理效应评价。
[Abstract]:The segmentation test theory mainly includes two parts: ordered sample clustering and segmental hypothesis test. Piecewise test theory has been widely used in the fields of enterprise marketing effect, improving quality and effectiveness. It is of great significance to accurately evaluate the effectiveness of relevant measures or policies for the management of policies or measures. Therefore, it is very important to study the theory of subsection test and its application. In the aspect of ordered sample clustering, first of all, an optimization model based on intra-group deviation square sum and inter-group deviation square sum is proposed to realize ordered sample clustering. It is applied to the classification of historical data of ambient air index in Chengdu and Beijing. When the sample size is large, the optimization model based on F statistics must store the F value of each class, and the optimal partition method must store the corresponding diameter of each class, which makes the calculation efficiency poor. The simulated annealing algorithm has a good global search ability. Combining the simulated annealing algorithm with the objective function of the optimal segmentation method can avoid the diameter of the storage class and improve the computational efficiency of the algorithm. Therefore, an ordered sample clustering based on simulated annealing algorithm is proposed. Finally, using the historical data of Chengdu Ambient Air Index, a good classification result is obtained. In segmented hypothesis testing, there are two categories according to the correlation of samples. When the piecewise samples are independent of each other, the classical hypothesis test theory is proposed to test the mean and variance parameters. The classical hypothesis test theory and the ordered sample clustering based on F statistics are combined to evaluate the effect of ambient air control in Chengdu. When there is a short-term autocorrelation in segmented samples, combining with the properties of stationary time series, the mean and variance parameter test under normal assumption is modified, and the variance of sample mean and sample variance is extended to the gamma distribution family. Finally, the piecewise test theory is combined with the ordered sample clustering of the optimization model based on F statistics to evaluate the environmental air control effect of Beijing government.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

【参考文献】