Frequency Estimation Using Unequally-Spaced Astronomical Data.

Details Frequency Estimation Using Unequally-Spaced Astronomical Data. Frequency Estimation Using Unequally-Spaced Astronomical Data.

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........20r&link_type=abstract

Thesis (PH.D.)--UNIVERSITY OF CALIFORNIA, BERKELEY, 1994.Source: Dissertation Abstracts International, Volume: 56-05, Section: B

Astronomy and Astrophysics

Astronomy

28

Scientific paper

This thesis studies estimation of the frequency of a periodic function of time, when the function is observed with noise at a collection of unequally-spaced times. This research was motivated by the detection and classification of variable stars in astronomy. Most of the statistical literature on frequency estimation assumes equally-spaced times, but observation times in astronomy are often unequally -spaced with a sampling distribution that contains periodic effects due to being able to collect data only at certain times of day. In Chapter 1 we describe the database of variable stars collected by the MACHO collaboration and present examples which illustrate the common types of variable stars and the nature of the estimation problem. In Chapter 2 we provide background material and give models for the periodic function and sampling times. We derive the asymptotic behavior of frequency estimates based on periodogram and least-squares estimation methods for sinusoidal periodic curves and sample times that are randomly distributed about equally-spaced values, and evaluate these estimators using a simulation study. We also discuss bounds on the variance of frequency estimates for general periodic functions under two sampling models. In Chapter 3 we outline various methods for estimating frequency in practice, apply these methods to some example data, and compare their precision through the use of a simulation study.

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