Nonparametric Methods for Deconvolving Multiperiodic Functions

Abstract

Multiperiodic functions, or functions that can be represented as finite additive mixtures of periodic functions, arise in problems related to stellar radiation. There they represent the overall variation in radiation intensity with time. The individual periodic components generally correspond to different sources of radiation and have intrinsic physical meaning provided that they can be 'deconvolved' from the mixture. We suggest a combination of kernel and orthogonal series methods for performing the deconvolution, and we show how to estimate both the sequence of periods and the periodic functions themselves. We pay particular attention to the issue of identifiability, in a nonparametric sense, of the components. This aspect of the problem is shown to exhibit particularly unusual features, and to have connections to number theory. The matter of rates of convergence of estimators also has links there, although we show that the rate-of-convergence problem can be treated from a relatively conventional viewpoint by considering an appropriate prior distribution for the periods. Copyright 2003 Royal Statistical Society.

RobPer: AnRPackage to Calculate Periodograms for Light Curves Based on Robust Regression

“…The triangular shaped density offers an alternative periodic sampling design. Separately sampling observation cycle and phase was proposed by Hall and Yin (2003).…”

Improved nonparametric inference for multiple correlated periodic sequences

“…A number of nonparametric methods for period estimation in univariate time series have been proposed recently, including Hall et al. (), Hall and Yin (), Hall and Li (), Genton and Hall (), and Hall (). In these papers, to estimate the period of a periodic function, an appropriate random spacing of time points is needed in order to ensure consistency; in other words, unevenly spaced observations are needed.…”

Statistical Inference for Evolving Periodic Functions

“…However, we shall take a time domain approach, as in the work of Hall et al. (2000) and Hall and Yin (2003).…”

“…Evolving periods might also be tackled by using the notion of time-varying spectra; see, for example, Dahlhaus (1997) and Neumann and von Sachs (1997). However, we shall take a time domain approach, as in the work of Hall et al (2000) and Hall and Yin (2003). This paper is organized as follows.…”