Unbiased Estimation of Standard Deviation

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.

Read more about Unbiased Estimation Of Standard DeviationBackground, Effect of Autocorrelation (serial Correlation), See Also, References

Other articles related to "unbiased, estimation":

Shayle R. Searle - Bibliography - Selected Journal Articles
... "Built-In Restrictions on Best Linear Unbiased Predictors (BLUP) of Random Effects in Mixed Models" ... "An overview of variance component estimation" ... Henderson, the Statistician and His Contributions to Variance Components Estimation" ...
Sample Maximum And Minimum - Applications - Estimation - Uniform Distribution
... 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 ...

Famous quotes containing the words standard, estimation and/or unbiased:

    Gentlemen, those confederate flags and our national standard are what has made this union great. In what other country could a man who fought against you be permitted to serve as judge over you, be permitted to run for reelection and bespeak your suffrage on Tuesday next at the poles.
    Laurence Stallings (1894–1968)

    No man ever stood lower in my estimation for having a patch in his clothes; yet I am sure that there is greater anxiety, commonly, to have fashionable, or at least clean and unpatched clothes, than to have a sound conscience.
    Henry David Thoreau (1817–1862)

    There is not a more disgusting spectacle under the sun than our subserviency to British criticism. It is disgusting, first, because it is truckling, servile, pusillanimous—secondly, because of its gross irrationality. We know the British to bear us little but ill will—we know that, in no case do they utter unbiased opinions of American books ... we know all this, and yet, day after day, submit our necks to the degrading yoke of the crudest opinion that emanates from the fatherland.
    Edgar Allan Poe (1809–1845)