Outlier And Change-Point Detection Methods For Distributional Data With Applications

With the development of functional data analysis,distributional data analysis,involving statistical analysis and modeling for probability density functions by viewing them as random objects,are receiving increased research interests,and has also been applied in many fields such as engineering,finance,medicine.In structural health monitoring,distributional regression(a representative research topic in distributional data analysis)has been successfully applied in data reconstruction,complex correlation analysis,etc.Moreover,a class of recently developed structural condition diagnostic methods that based on the change of distributional information of structural responses is also closely related to distributional data analysis.Outlier and change-point detections are important research topics in statistics,which also has broad application prospects in engineering;however,related studies for distributional data are still quite rare.To fill this gap,this study focuses on developing statistical methods for distributional outlier and change-point detections in the framework of functional data analysis as well as their applications in structural health monitoring and robust distributional regression.The main contents are as follows:(1)This study proposes various functional outlier detection methods for detecting density-valued outliers.Firstly,the functional directional outlyingness(FDO)method(originally developed for ordinary functional data)is modified to suit for density-valued data,simulation studies are conducted for effectiveness validation and performance evaluation.Then,a more effective multiple transformation-based approach is proposed for density-valued outlier detection,along with a general transformation framework that suits to both distributional data and ordinary functional data.Using synthetic data,the effectiveness of the proposed method will be validated and its performance will be compared with the FDO-based method.Finally,a multiple detection method will also be proposed for accounting for the uncertainties induced by detection parameters as well as for fusing different detection methods,whose effectiveness will be validated through application to real strain data.(2)This study proposes a functional change-point detection method for density-valued time series.Firstly,a structural break model for the mean function of the density-valued time series is presented based on the Bayes space theory;then,related hypothesis testing method for distributional change-point detection is presented based on the isometric isomorphic transformation and functional change-point detection theory in the transformed space.Simulation studies are conducted for effectiveness validation,as well as comparing its performance with an alternative strategy that treats density functions as ordinary functional data.Moreover,extensive simulation studies will be conducted for evaluating the robustness performance of the proposed method in the presents of distributional outliers,related strategy will also be proposed for addressing such outlier-induced issues based on the proposed distributional outlier detection methods.(3)Representative applications of the proposed methods are also investigated.For engineering application,the proposed distributional change-point detection method is applied to detect and locate the structural break of the distributional data corresponding to the ratios of the cable force monitoring data of a long-span cable-stayed bridge,under the background of condition diagnosis for the cables based on the change of the distributional information of structural responses.For statistical application,a robust distributional regression model will be presented based on the proposed distributional outlier detection methods.