Wavelet Methods for Sparse Functional Data

Due to advanced modern technology for continuously measuring and recording data at multiple discrete locations and times, functional data are ubiquitous such as weather data and stock market data. Such kind of data usually has smoothness characteristics in the form of functions with complex structures and can be analyzed through many different techniques developed in functional data analysis. Currently, functional data analysis has received a lot of attention in recent years due to their tremendous applications in many areas. In this project, we shall explore the wavelet-based approach for efficiently estimating the means and covariance of sparse functional data. In particular, through extensive numerical simulations, we want to figure out what are the main properties (such as short support, orders of vanishing moments, and time-frequency localization) of wavelet frames that determine their performance for the sparse functional data analysis. The findings from this project will set the stage for further future investigation on functional data analysis using wavelets and wavelet frames on bounded intervals with various desired properties. This project also provides a collaboration opportunity for researchers from both Canada and France.

Faculty Supervisor:

Bin Han

Student:

Partner:

Université de Bretagne Occidentale

Discipline:

Mathematics

Sector:

Information and Communications Technology

University:

University of Alberta

Program: