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The theory of median-unbiased estimators was revived by George W. Brown in 1947: [8]. An estimate of a one-dimensional parameter θ will be said to be median-unbiased, if, for fixed θ, the median of the distribution of the estimate is at the value θ; i.e., the estimate underestimates just as often as it overestimates.
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.
Although an unbiased estimator is theoretically preferable to a biased estimator, in practice, biased estimators with small biases are frequently used. A biased estimator may be more useful for several reasons. First, an unbiased estimator may not exist without further assumptions. Second, sometimes an unbiased estimator is hard to compute.
An alternative estimator of the population excess kurtosis, which is unbiased in random samples of a normal distribution, is defined as follows: [3] = = [(+) ()] () () = () [(+) ()] = () [(+) +] = (+) () = (¯) (= (¯)) () = (+) () = (¯) () where k 4 is the unique symmetric unbiased estimator of the fourth cumulant, k 2 is the unbiased ...
For example, a single observation is itself an unbiased estimate of the mean and a pair of observations can be used to derive an unbiased estimate of the variance. The U-statistic based on this estimator is defined as the average (across all combinatorial selections of the given size from the full set of observations) of the basic estimator ...
False priors are initial beliefs and knowledge which interfere with the unbiased evaluation of factual evidence and lead to incorrect conclusions. Biases based on false priors include: Agent detection bias, the inclination to presume the purposeful intervention of a sentient or intelligent agent.
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In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. [1] The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the data only through a complete , sufficient statistic is the unique ...