In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional techniques of lower-order statistics, which use constant, linear, and quadratic terms (zeroth, first, and second powers). The third and higher moments, as used in the skewness and kurtosis, are examples of HOS, whereas the first and second moments, as used in the arithmetic mean (first), and variance (second) are examples of low-order statistics. HOS are particularly used in the estimation of shape parameters, such as skewness and kurtosis, as when measuring the deviation of a distribution from the normal distribution.
In statistical theory, one long-established approach to higher-order statistics, for univariate and multivariate distributions is through the use of cumulants and joint cumulants.[1] In time series analysis, the extension of these is to higher order spectra, for example the bispectrum and trispectrum.
An alternative to the use of HOS and higher moments is to instead use L-moments, which are linear statistics (linear combinations of order statistics), and thus more robust than HOS.
Referencesedit
^Kendall, MG., Stuart, A. (1969) The Advanced Theory of Statistics, Volume 1: Distribution Theory, 3rd Edition, Griffin. ISBN0-85264-141-9 (Chapter 3)
higher, order, statistics, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, . This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Higher order statistics news newspapers books scholar JSTOR July 2022 Learn how and when to remove this message In statistics the term higher order statistics HOS refers to functions which use the third or higher power of a sample as opposed to more conventional techniques of lower order statistics which use constant linear and quadratic terms zeroth first and second powers The third and higher moments as used in the skewness and kurtosis are examples of HOS whereas the first and second moments as used in the arithmetic mean first and variance second are examples of low order statistics HOS are particularly used in the estimation of shape parameters such as skewness and kurtosis as when measuring the deviation of a distribution from the normal distribution In statistical theory one long established approach to higher order statistics for univariate and multivariate distributions is through the use of cumulants and joint cumulants 1 In time series analysis the extension of these is to higher order spectra for example the bispectrum and trispectrum An alternative to the use of HOS and higher moments is to instead use L moments which are linear statistics linear combinations of order statistics and thus more robust than HOS References edit Kendall MG Stuart A 1969 The Advanced Theory of Statistics Volume 1 Distribution Theory 3rd Edition Griffin ISBN 0 85264 141 9 Chapter 3 External links edithttp www maths leeds ac uk Applied news dir issue2 hos intro html https web archive org web 20061125033107 http lpce cnrs orleans fr ddwit lalonde lalonde presentations horbury2 pdf http www ics uci edu welling publications papers RobCum aistats pdf nbsp This statistics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Higher order statistics amp oldid 1097738241, wikipedia, wiki, book, books, library,
