# Nonparametric methods for deconvolving multiperiodic functions

#### by Professor Peter Hall

Institution: Australian National University (ANU), Canberra
Date: Wed 15th September 2004
Time: 11:00 AM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: Abstract: Time series describing the intensity of radiation from stars
can be used to classify the stars into types, particularly if the
radiation is periodic or can be expressed as the convolution of a small
number of periodic functions. Signals of the latter type are conveniently
referred to as multiperiodic functions.'' Classification can involve accessing the individual periodic components, which generally correspond to different sources of radiation and have intrinsic physical meaning. Therefore they need to be deconvolved'' from the mixture. We shall
discuss a combination of kernel and orthogonal series methods for performing the deconvolution, and show how to estimate both the sequence of periods and the periodic functions themselves. Particular attention will be paid to the issue of identifiability, in a nonparametric sense, of
the components. This aspect of the problem exhibits unusual features, and has connections to number theory, as too do convergence rates of estimators.