In statistics, a k-statistic is a statistic constructed from a sample to estimate a cumulant of the underlying population distribution. For a sample of independent and identically distributed random variables, the rth k-statistic is the unique symmetric unbiased estimator of the rth cumulant and has minimum variance among unbiased estimators.
The first k-statistic is the sample mean, which estimates the first cumulant. The second k-statistic is the usual unbiased sample variance, which estimates the second cumulant. Higher-order k-statistics provide corresponding unbiased estimators of higher-order cumulants.
History K-statistics were developed by Ronald Fisher in his work on the moments and product moments of sampling distributions.
Applications Multivariate k-statistics can be used to estimate joint cumulants. In signal processing, they have been applied to the unbiased estimation of polyspectra (higher-order spectra), including the bispectrum and trispectrum.
See also
Cumulant Estimator Minimum-variance unbiased estimator Method of moments (statistics) Polykay
References
External links
k-Statistic at Wolfram MathWorld kStatistics package for R