基于筛选排序算法的多均值变点估计

Multiple Mean Change-points Estimation Based on Screening and Ranking Algorithm

多均值变点估计问题是目前统计界的一个热点问题。文献中已有多种算法处理该问题,其中筛选排序算法(Screening and Ranking algorithm,SaRa)由于具有快速检测和高精度的特点而被广泛关注。值得注意的是,该算法在筛选步骤的阈值选取倾向于保守,其主要原因是SaRa算法中方差参数采用了分段方法进行估计。本文的主要目的是改进多均值变点估计的SaRa算法。首先,运用局部多项式结合交叉验证方法给出了误差标准差的一个全局估计,并将其应用于初筛变点步骤中。然后,通过对候选变点的局部诊断函数值进行排序,进而结合MBIC准则得到了最终的变点估计。数值模拟结果显示了本文所提出的改进的SaRa算法在变点的数目及位置的估计准确率均高于现有的方法。最后,将该方法应用于深圳市车流量实际数据,通过分析该区域的工作日及非工作日变点分布特点,可为交管部门和出行人群提供参考建议。

The multiple change-points estimation problem is a hot issue in current statistics,and there are many algorithms in the literature.Among them,Screening and Ranking algorithm(SaRa)has attracted wide attention due to its fast detection and high precision characteristics.However,this algorithm tends to be conservative in the threshold selection of the screening procedure.The reason is that the variance in SaRa is separately estimated in each segment process.The main purpose of this paper is to improve SaRa.Firstly,a global estimate of the variance is calculated through local polynomial approximation with the bandwith selected by the cross validation method.The initial change-points are obtained from screening based on the improved threshold.Then,to order those points in terms of the local diagnostic function values,the number of final change-points is determined by maximizing the MBIC.Numerical results show that the proposed algorithm has high accuracies in the estimation of the number and locations of change points in comparison to existing methods.Finally,this method is applied to the actual traffic flow data of Shenzhen city.The distribution characteristics of change points on working days and non-working days in this area are analyzed,which can provide some guidance for traffic control departments and travelers.