By Gary L. Tietjen

ISBN-10: 1461291682

ISBN-13: 9781461291688

ISBN-10: 1461319676

ISBN-13: 9781461319672

Statistics is the authorized physique of equipment for summarizing or describing info and drawing conclusions from the precis measures. each person who has information to summarize therefore wishes a few wisdom of facts. step one in gaining that wisdom is to grasp the pro jargon. This dictionary is geared to supply greater than the standard string of remoted and self sustaining definitions: it presents additionally the context, purposes, and similar terminology. The meant viewers falls into 5 teams with fairly various wishes: (1) expert statisticians who have to bear in mind a definition, (2) scientists in disciplines except facts who want to know the appropriate tools of summarizing info, (3) scholars of records who have to increase their knowl fringe of their material and make consistent connection with it, (4) managers who may be studying statistical stories written via their staff, and (5) newshounds who have to interpret executive or clinical stories and transmit the knowledge to the public.

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Another measure of relative efficiency, called Bahadur efficiency, is more involved than we have space for discussing here. A sequence of estimators is defined to be mean squared error consistent (12 if the limit of E(a n - 8)2 is zero for all 8 as n ~ 00. That implies that both the bias and the variance of e approach zero as n gets large. Mean squared error consistency implies simple consistency. An estimator that is best asymptotically normal (BAN) is one that is consistent and efficient. One further desirable property of estimators is that of invariance.

If the distribution does not depend on e, the sample contains no additional information about e. A statistic can be tested for sufficiency in various ways. For some problems no single sufficient exists. There is always a set of statistics that is jointly sufficient. The set of statistics SI' S2' ... , Sk is said to be jointly sufficient if and only if the conditional distributionofX" X2 , • • • ,XngivenS, = Sl" •. ,Sk = skdoesnotdepend Estlmation and Hypothesis Testlng 31 on 6. A set of jointly sufficient statistics is minimal sufficient if it is a function of every other set of sufficient statistics.

C. A book with valuable information on less-standard techniques is Hahn, G. , and Shapiro, S. S. 1967. · The 2 classics in mathematical statistics are Mood, A. , Graybill, F. , and Boes, D. C. 1974. Introduction to the Theory of Statistics. 3rd ed. New York: McGraw-Hill, and Hogg, R. , and Craig, A. T. 1978. Introduction to Estimatlon and Hypothesis Testing 45 Mathematical Statistics, 4th ed. New York: MacMillan. , and Tiao, G. 1973. : Addison-Wesley. The very important topic of nonparametric statistics is well covered in Conover, W.

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