A data-adaptive method for outlier detection from functional data

Abstract

Outliers present in a data set can severely impact the statistical analysis and lead to erroneous conclusions. Hence, outlier identification is an important task before analysis of data is undertaken. Outliers being different from the rest of the observations in a data set may contain valuable information which can be obtained by carefully examining the identified outliers. While several methods of outlier identification exists for univariate and multivariate data, not that many methods exist for functional data. In sequential identification of outliers from a set of functional data, the corresponding estimation of covariance operator is affected by the outliers that are still present in the data. This leads to degradation in performance of these methods when the proportion of outliers in the data set increases. In this paper we propose a new outlier detection algorithm that uses an adaptive and data driven approach of dimension selection. The proposed method is seen to have better efficiency in an extensive simulation exercise in comparison to the existing method. Three illustrations with real life environmental data sets are also reported.