A term used in mathematical statistics as a name for functions of the results of observations.
Let a random variable take values in the sample space . Any -measurable mapping from onto a measurable space is then called a statistic, and the probability distribution of the statistic is defined by the formula
1) Let be independent identically-distributed random variables which have a variance. The statistics
are then unbiased estimators for the mathematical expectation and the variance , respectively.
constructed from the observations , are statistics.
called the periodogram, is an asymptotically-unbiased estimator for , given certain specific conditions of regularity on , i.e.
In the theory of estimation and statistical hypotheses testing, great importance is attached to the concept of a sufficient statistic, which brings about a reduction of data without any loss of information on the (parametric) family of distributions under consideration.
|||E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1988)|
|||V.G. Voinov, M.S. Nikulin, "Unbiased estimates and their applications" , Moscow (1989) (In Russian)|
Statistics. M.S. Nikulin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Statistics&oldid=14854