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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1273180
- author
- Jack, Cuzick
and Lindgren, Georg
LU
- organization
- publishing date
- 1980
- 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
- Oxford University Press
- 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
- 2016-04-04 09:20:34
- date last changed
- 2021-01-03 06:20:05
@article{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}},
keywords = {{Central limit theorem; Gaussian process; Level crossing; Mean frequency; Spectral moment}},
language = {{eng}},
number = {{1}},
pages = {{65--72}},
publisher = {{Oxford University Press}},
series = {{Biometrika}},
title = {{Frequency estimation from crossings of an unknown level}},
url = {{http://dx.doi.org/10.1093/biomet/67.1.65}},
doi = {{10.1093/biomet/67.1.65}},
volume = {{67}},
year = {{1980}},
}