Unbiased Estimation Of Standard Deviation
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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... are sufficient and complete statistics for the unknown endpoints thus an unbiased estimator derived from these will be UMVU estimator ... for the population maximum, but the unbiased estimator (where m is the sample maximum and k is the sample size) is the UMVU estimator see German tank ... If both endpoints are unknown, then the mid-range is an unbiased (and hence UMVU) estimator of the midpoint of the interval (here equivalently the population ...
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