Research on small sample probability relational degree model

小样本概率关联度模型研究

¹ China Huayin Ordnance Test Center, Huayin 714200, China
² Xi'an Modern Control Technology Research Institute, Xi'an 710065, China
³ School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received: 21 December 2021

Abstract

针对小样本条件下多元时间序列之间的关联分析问题, 提出了一种小样本概率关联度模型。使用样本函数或样本统计量代替样本构造累积经验分布函数并计算概率关联系数。当比较序列样本容量n < 5, 使用样本顺序统计量的经验分布函数计算概率关联系数; 当比较序列样本容量n≥5, 使用Bootstrap方法重抽样扩充样本后再构造经验分布函数计算概率关联系数, 改进了概率关联度模型中关联系数的计算方法, 解决了小样本条件下这一类多元数据关联分析问题。证明了小样本概率关联度模型满足的基本性质, 给出了小样本概率关联分析的基本步骤, 仿真案例和实际应用验证了文中模型的正确性和有效性。

摘要

The probability degree model is suitable for correlation analysis between multivariate time series, but its application effect is poor under the small sample condition. An improved probability degree model for small sample problem is proposed in this paper. Firstly, by using sample function or sample statistics instead of samples to construct cumulative empirical distribution function and calculate probability correlation coefficient, the framework of probability correlation degree model is developed and expanded. Secondly, the calculation method of correlation coefficient in the original model of probability correlation degree is improved. For the problem of sample size n < 5, the empirical distribution function of sample order statistics is used to calculate the probability correlation coefficient; For the problem of comparison sequence sample size n≥5, the Bootstrap method is used to resample to construct the empirical distribution function to calculate the probability correlation coefficient. Thus, the problem of dynamic multivariate data association analysis under the condition of small samples is solved. It is proved that the small sample probability correlation degree model satisfies the correlation theorem and its basic properties. The basic steps of small sample probabilistic correlation analysis are given. At last simulation cases and practical application verify the rationality and effectiveness of the model and method.