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which is an unbiased estimator of the variance of the mean in terms of the observed sample variance and known quantities. If the autocorrelations are identically zero, this expression reduces to the well-known result for the variance of the mean for independent data. The effect of the expectation operator in these expressions is that the ...
The resulting estimator is unbiased and is called the (corrected) sample variance or unbiased sample variance. If the mean is determined in some other way than from the same samples used to estimate the variance, then this bias does not arise, and the variance can safely be estimated as that of the samples about the (independently known) mean.
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.
Firstly, while the sample variance (using Bessel's correction) is an unbiased estimator of the population variance, its square root, the sample standard deviation, is a biased estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality.
In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.
The variance of the sample ratio is approximately: ... of the x variates chosen in this fashion is an unbiased estimate of the ... commonly used to calculate ...
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
Additionally, unbiased estimators with smaller variances are preferred over larger variances because it will be closer to the "true" value of the parameter. The unbiased estimator with the smallest variance is known as the minimum-variance unbiased estimator (MVUE).