By Gary L. Tietjen
Statistics is the accredited physique of tools for summarizing or describing facts and drawing conclusions from the precis measures. all people who has info to summarize hence wishes a few wisdom of records. 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 similar terminology. The meant viewers falls into 5 teams with relatively diverse wishes: (1) specialist statisticians who have to bear in mind a definition, (2) scientists in disciplines except statistics who want to know the appropriate tools of summarizing information, (3) scholars of information who have to increase their knowl fringe of their subject material and make consistent connection with it, (4) managers who might be examining statistical reviews written by means of their staff, and (5) newshounds who have to interpret executive or clinical experiences and transmit the knowledge to the public.
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Extra info for A Topical Dictionary of Statistics
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. An R-estimator (for ranks) is a solution of 'i, sgn(Xj - A) r [R(IX j - AI)/ (n+ 1)] = 0, where r(u) = 1(112 + ul2), R(u) is the rank of u, and sgn is the signum function.
Under the null hypothesis Ho : (J"=(J"o, V has a chi-square distribution with (n - 1) degrees of freedom. Using a level of significance of a, reject the null hypothesis in favor of the hypothesis (J" > (J"o if V exceeds the 1 - a percentile of the chi-square distribution. (6) To test whether the standard deviations of 2 normal populations are equal, calculate V = S;/S~, where S; is the largest variance, and reject the null hypothesis that (J"x = (J"y in favor of (J"x > (J"y if V exceeds the I - a percentile of the F-distribution with (nx - I) and (ny - 1) degrees of freedom.
An estimator is minimax if its maximum risk over all 8 is less than or equal to the maximum risk of any other estimator. The Bayes risk of an estimator is the average (expected value) of the risk, the averaging being taken over the parameter space with respect to the prior distribution of 8. For a given loss function and prior density, the Bayes estimator of 8 is the estimator with smallest Bayes risk. Bayesian methods provide a formal way of combining some notions about the uncertainties in the parameters (through the prior) with the data to obtain better information about the parameters (expressed through the posteriors).