Search results
Results From The WOW.Com Content Network
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.
The bias of an estimator is the difference between an estimator's expected value and the true value of the parameter being estimated. 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.
Bias is a property of the estimator, not of the estimate. Often, people refer to a "biased estimate" or an "unbiased estimate", but they really are talking about an "estimate from a biased estimator", or an "estimate from an unbiased estimator". Also, people often confuse the "error" of a single estimate with the "bias" of an estimator.
Efficient estimators are always minimum variance unbiased estimators. However the converse is false: There exist point-estimation problems for which the minimum-variance mean-unbiased estimator is inefficient. [6] Historically, finite-sample efficiency was an early optimality criterion. However this criterion has some limitations:
Two or more statistical models may be compared using their MSEs—as a measure of how well they explain a given set of observations: An unbiased estimator (estimated from a statistical model) with the smallest variance among all unbiased estimators is the best unbiased estimator or MVUE (Minimum-Variance Unbiased Estimator).
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.
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.
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to the concept of an ancillary statistic . While an ancillary statistic contains no information about the model parameters, a complete statistic contains only information about the parameters, and ...