Nonparametric methods for deconvolving multiperiodic functions
by
Peter Hall
Australian National University
Coauthors: Jiying Yin (Australian National University)

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.

Date received: March 3, 2002