Unbiased estimation of standard deviation information
Procedure to estimate standard deviation from a sample
In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value. Except in some important situations, outlined later, the task has little relevance to applications of statistics since its need is avoided by standard procedures, such as the use of significance tests and confidence intervals, or by using Bayesian analysis.
However, for statistical theory, it provides an exemplar problem in the context of estimation theory which is both simple to state and for which results cannot be obtained in closed form. It also provides an example where imposing the requirement for unbiased estimation might be seen as just adding inconvenience, with no real benefit.
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theory, unbiasedestimationof a standarddeviation is the calculation from a statistical sample of an estimated value of the standarddeviation (a measure...
equation of the correction factor for small samples of n < 20. See unbiasedestimationofstandarddeviation for further discussion. The standard error on...
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U-statistic U test Umbrella sampling Unbiased estimator – see bias (statistics) Unbiasedestimationofstandarddeviation Uncertainty Uncertainty coefficient...
Agresti A. 1990. The Concise Encyclopedia of Statistics. Springer: Dodge, Y. 2008. Best Linear UnbiasedEstimation and Prediction. New York: John Wiley &...
an unbiased estimate of the population standarddeviation (σ): see Unbiasedestimationofstandarddeviation.) It is possible to make statistical inferences...
variance + square of bias. In particular, for an unbiased estimator, the variance equals the mean squared error. The standarddeviationof an estimator θ...
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the correction, the corrected sample variance is unbiased, while the corrected sample standarddeviation is still biased, but less so, and both are still...
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