NDLI: Similarity law in spectral estimation of a time series. IV

Content Provider	Springer Nature Link
Author	Terebizh, V. Yu
Copyright Year	1998
Abstract	A continuation of V. Yu. Terebizh, Astrofizika,40, 139, 273, 413 (1997). An explicit representation is found for the Fisher matrix for spectral density, enabling one to calculate the lower limit of the variance of an arbitrary unbiased density estimate. Basic equations describing smoothed density estimates are given for comparison with exact results. By numerical modeling based on the example of an AR-1 process, it is shown that the relative accuracy q of estimation of density is some universal function of the parameter w = (F -1)/N, where F is the number of parameters underlying the estimate and N is the length of the time series. The relationship q = θ(w), a similarity law, explains why a number of density estimates proposed earlier (Schuster’s periodogram, in particular) proved to be statistically inconsistent. It is just these estimates that presume an extremely detailed model of spectral density. The need for the complexity of the model to be consistent with the observational data follows from the limitation of information about the spectrum of the random process included in a sample of readings from a series of fixed volume.
Starting Page	73
Ending Page	79
Page Count	7
File Format	PDF
ISSN	05717256
Journal	Astrophysics
Volume Number	41
Issue Number	1
e-ISSN	15738191
Language	English
Publisher	Springer Netherlands
Publisher Date	1998-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Astronomy, Astrophysics and Cosmology Astrophysics Extraterrestrial Physics, Space Sciences Astronomy
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics

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