Details of Grant 

EPSRC Reference:	GR/R52770/01
Title:	Hierarchical Functional Modelling
Principal Investigator:	Brown, Professor P
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Maths Statistics & Actuarial Sci
Organisation:	University of Kent
Scheme:	Standard Research (Pre-FEC)
Starts:	01 May 2001	Ends:	31 July 2001	Value (£):	6,450
EPSRC Research Topic Classifications:	Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
In our work together, we intend to develop Bayesian methods for nonparametrically modeling hierarchical functional data using wavelets. There is much statistical literature on the nonparametric estimation of single functions using various methods, including wavelet regression, but very little in the setting where replicated functions are observed within a hierarchical structure. Our primary aim is to extend the ideas of wavelet regression for a single function to this setting. The general approach involves transforming the data into the wavelet space using a discrete wavelet transform, using hierarchical modeling of the wavelet coefficients to filter out the noise from the functions and model their interrelationships within the hierarchy, then perform an inverse discrete wavelet transformation to arrive at mean function and covariance estimates in the data space. The orthogonality and whitening properties of the wavelet transform provide the key to realistic and flexible, yet parsimonious, modeling of the replicated functions in a nonparametric fashion. Besides developing a working method, we also intend to examine the performance of various wavelet shrinkage approaches, investigate the robustness of the method against violations of the Gaussian assumptions, extend the method to include other covariance structures, and streamline the computational procedure used to fit the models.
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Organisation Website:	http://www.kent.ac.uk