Search results
Results from the WOW.Com Content Network
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.
That is, for a non-linear function f and a mean-unbiased estimator U of a parameter p, the composite estimator f(U) need not be a mean-unbiased estimator of f(p). For example, the square root of the unbiased estimator of the population variance is not a mean-unbiased estimator of the population standard deviation : the square root of the ...
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 ...
That is why the sum of squares of the deviations from the sample mean is too small to give an unbiased estimate of the population variance when the average of those squares is found. The smaller the sample size, the larger is the difference between the sample variance and the population variance.
The sample mean ¯ (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator). The sample mean is a random variable, not a constant, since its calculated value will randomly differ depending on ...
The sample mean is a Fisher consistent and unbiased estimate of the population mean, but not all Fisher consistent estimates are unbiased. Suppose we observe a sample from a uniform distribution on (0,θ) and we wish to estimate θ. The sample maximum is Fisher consistent, but downwardly biased. Conversely, the sample variance is an unbiased ...
If the set is a sample from the whole population, then the unbiased sample variance can be calculated as 1017.538 that is the sum of the squared deviations about the mean of the sample, divided by 11 instead of 12. A function VAR.S in Microsoft Excel gives the unbiased sample variance while VAR.P is for population variance.
However, the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation. Further, for other distributions the sample mean and sample variance are not in general MVUEs – for a uniform distribution with unknown upper and lower bounds, the mid-range is the MVUE for the ...