Research On Outlier Detection Methods For Functional Data

In recent years,with the continuous progress of data acquisition technology,functional data has increasingly appeared in various disciplines.Functional data analysis has also become a hot research direction of statistics,in which the detection of outliers in functional data is an important issue.The existence of outliers will have a negative impact on the modeling and analysis of functional data,so the detection and processing of outliers have important research value.Given that the data depth can be used to identify outliers,and there are obvious differences between derivative curves of shape outlier curves,this thesis proposes an improved outlier detection algorithm based on the depth of functional data,which processes the derivative curves corresponding to the original data in two ways,so as to better capture the information of curve shape changes,thus effectively improving the positive rate of outlier detection compared with the original algorithm.This thesis provides the theoretical basis and visualization results of the proposed method.Finally,numerous numerical simulations and actual data analysis show that the proposed algorithm is an excellent and effective outlier detection algorithm for functional data.