Outlier Detection In Functional Data

Nowadays,functional data analysis has been attracted wide attention.Although the existence of outliers in data will adversely affect the results of data analysis,it provides important information for researchers.So the outlier detection is very important.The traditional outlier detection method is no longer suitable for outlier detection of functional data.Therefor this paper will provide a new method of outlier detection for functional data.It includes two steps,firstly make the establishment of distance statistics according to the expectation of weighted residuals and combine the Least Trimmed Squares while excluding outliers in data sets.Then find a clean subset.Secondly get the robust estimation of parameters from clean subsets and construct the threshold rules for detecting outliers according to the asymptotic distribution of distance statistics.The distance statistics presented in this paper have asymptotic distribution which can control the false alarm rate effectively in the process of outlier detection.The numerical simulation results show that the proposed method can detect outliers effectively.