Frequency estimation from crossings of an unknown level
(1980) In Biometrika 67(1). p.6572 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:
http://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
 Biometrika Trust
 external identifiers

 Scopus:0018825679
 ISSN
 00063444
 DOI
 10.1093/biomet/67.1.65
 language
 English
 LU publication?
 yes
 id
 444d9d1861bc4cac92746db2a7c78350 (old id 1273180)
 alternative location
 http://biomet.oxfordjournals.org/cgi/reprint/67/1/65
 date added to LUP
 20081209 14:36:47
 date last changed
 20161013 04:28:46
@misc{444d9d1861bc4cac92746db2a7c78350, 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 = {00063444}, keyword = {Central limit theorem,Gaussian process,Level crossing,Mean frequency,Spectral moment}, language = {eng}, number = {1}, pages = {6572}, publisher = {ARRAY(0x64c4e30)}, 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}, }