A Topical Dictionary of Statistics by Gary L. Tietjen

By Gary L. Tietjen

Statistics is the authorised physique of tools for summarizing or describing information and drawing conclusions from the precis measures. each person who has information to summarize hence wishes a few wisdom of facts. step one in gaining that wisdom is to grasp the pro jargon. This dictionary is geared to provide greater than the standard string of remoted and self reliant definitions: it offers additionally the context, functions, and comparable terminology. The meant viewers falls into 5 teams with really assorted wishes: (1) specialist statisticians who have to remember a definition, (2) scientists in disciplines except facts who want to know the suitable tools of summarizing info, (3) scholars of facts who have to develop their knowl­ fringe of their subject material and make consistent connection with it, (4) managers who can be studying statistical stories written by means of their staff, and (5) reporters who have to interpret govt or clinical reviews and transmit the knowledge to the public.

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Pitman estimators-The Pitman estimator for location is the one that has the uniformly smallest mean squared error within the class of location invariant estimators. The Pitman estimator for scale is the one with uniformly (e - 8)2/82. Those estimators have little smallest risk using the loss function practical importance. Many estimators can be classified as I of 3 basic types: An M-estimator (for maximum likelihood) for a location parameter A is a solution to the equation L\jJ(Xi - A) = 0 where Xi is the i-th data point and \jJ(x) is a defining equation.

The family of distributions is invariant under a group G of transformations if for every g in G and 0 in 8 there exists a unique 0' in 8 such that the distribution of g(X) is P(O') when the distribution of X is P(O). , L(O,a) = L(O' ,a'). The a' uniquely determined by g and a is denoted by g(a). Given the 0' and a' uniquely determined by an invariant decision problem, and a nonrandomized decision rule d(x), the decision rule is invariant if for every g in G and every x in the sample space, d[g(x)] = g[d(x)].

The asymptotically most efficient M-estimator uses \jJ(x) = - f (x)/ fix), where f(x) is the pdf and f (x) is the derivative of fix). 11r and \jJ(x) = 0 otherwise. The latter estimator has been widely used in outlier accommodation (as opposed to outlier detection). Estimation and Hypothesis Testing 35 An L-estimator (for linear combinations) is a weighted average of the order statistics of the sample. f(x» , and n+l n+l p is the cdf. In small samples the optimal weights are derived from the expected values and covariances of the order statistics.

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