Local Rank Based Outlier Detection In Functional Data With Applications To PM_2.5 Levels

The presence of outliers of functional data have serious adverse effects on analysis and modeling. In this paper, we propose a local rank based outlier detection method in functional data which can effectively identify shape and magnitude outliers. Traditional outlier detection methods cannot identify the two types of outliers correctly since most of them are based on functional principal component or functional data depth. So this article puts forward the concept of local rank to measure the relative position of the sample curves. A weighted average and weighted standard deviation of local rank can be calculated to measure the position and shape of a curve. Then we simulate date with outliers to comparing this method to other outliers detection methods such as functional boxplot, HDR boxplot, functional bagplot and outliergram. In the last part of this article, we analysis China’s PM2.5 data, our results show that the local rank based method can identify shape and magnitude outliers simultaneity.