Recent Advances in Robust Functional Data Analysis

• Activity Number: 383
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nedret Billor*+
• Companies: Auburn University
• Keywords: Outliers ; Functional Data ; Robust ; Principal Component

Abstract

In the last fifteen years, a substantial amount of attention has been drawn to the field of functional data analysis (FDA). While the study of the probabilistic tools for infinite dimensional variables started in the beginning of the 20th century, the development of statistical models and methods for functional data has only really been developed in the last two decades since many scientific fields involving applied statistics have started measuring and recording massive continuous data due to rapid technological advancements. The statistical methodologies for FDA have been developed under one of the most important assumptions: homogeneity of data (i.e. free of outliers). However, in practice, this is almost never true. Existence of genuine outliers is common across the entire spectrum of functional data analysis and functional data modeling applications, such as: fMRI and NIR spectral data. Identification of such functional curves is very crucial in this field. In addition, developing robust FDA techniques in the presence of outliers is also necessary to obtain correct statistical conclusions. In last five years, there has been an increasing trend on research activity around r