Search results
Results from the WOW.Com Content Network
Then is called a pivotal quantity (or simply a pivot). Pivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels.
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 best unbiased estimator of that quantity. The Lehmann–Scheffé theorem is named after Erich Leo Lehmann and Henry Scheffé, given their two early papers. [2] [3]
A ancillary statistic is a specific case of a pivotal quantity that is computed only from the data and not from the parameters. They can be used to construct prediction intervals . They are also used in connection with Basu's theorem to prove independence between statistics.
Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on the population parameters, and thus it can be used regardless of what these ...
Such a pivotal quantity, depending only on observables, is called an ancillary statistic. [2] The usual method of constructing pivotal quantities is to take the difference of two variables that depend on location, so that location cancels out, and then take the ratio of two variables that depend on scale, so that scale cancels out.
Download as PDF; Printable version; ... the pivotal quantity (^ ... and other methods have been proposed for practical application. ...
Learn how to download and install or uninstall the Desktop Gold software and if your computer meets the system requirements.
In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate.