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Frequency estimation from crossings of an unknown level

Jack, Cuzick and Lindgren, Georg LU (1980) In Biometrika 67(1). p.65-72
Abstract
By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and variance of the estimator, and conditions for its asymptotic normality. Numerical examples show that the estimator behaves reasonably for levels within one standard deviation from the process mean.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Central limit theorem, Gaussian process, Level crossing, Mean frequency, Spectral moment
in
Biometrika
volume
67
issue
1
pages
65 - 72
publisher
Biometrika Trust
external identifiers
  • Scopus:0018825679
ISSN
0006-3444
DOI
10.1093/biomet/67.1.65
language
English
LU publication?
yes
id
444d9d18-61bc-4cac-9274-6db2a7c78350 (old id 1273180)
alternative location
http://biomet.oxfordjournals.org/cgi/reprint/67/1/65
date added to LUP
2008-12-09 14:36:47
date last changed
2016-10-13 04:28:46
@misc{444d9d18-61bc-4cac-9274-6db2a7c78350,
  abstract     = {By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and variance of the estimator, and conditions for its asymptotic normality. Numerical examples show that the estimator behaves reasonably for levels within one standard deviation from the process mean.},
  author       = {Jack, Cuzick and Lindgren, Georg},
  issn         = {0006-3444},
  keyword      = {Central limit theorem,Gaussian process,Level crossing,Mean frequency,Spectral moment},
  language     = {eng},
  number       = {1},
  pages        = {65--72},
  publisher    = {ARRAY(0x8622bb0)},
  series       = {Biometrika},
  title        = {Frequency estimation from crossings of an unknown level},
  url          = {http://dx.doi.org/10.1093/biomet/67.1.65},
  volume       = {67},
  year         = {1980},
}