Discrete functional data analysis

Abstract

In this paper, we try to extend the framework of Functional Data Analysis (FDA). FDA is an exciting theme that continues development in data analysis. We can sometimes find out valuable information through FDA. Most methods on FDA assume that the functions that represent data are differentiable. But we discuss the use of discrete functions for FDA. Discrete functions are indifferentiable of course, but we can use differences of the functions. At first, we construct a new definition of first order and high order differences for discrete functional data analysis. Then we propose a method to look at the structures that the discrete functional data have by utilizing the proposed high order differences.