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There seems to be confusion. In standard books "completeness" is defined for families of distributions. The concept of "complete sufficient statistic" is only ever considered in the context where the statistic is already known or assumed to be sufficient. E.g. texts say "If a sufficent statistic
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We have one example showing that a statistic is sufficient and complete, and two examples showing that a statistic is sufficient but not complete. If the statement that "completeness does not entail sufficiency" is true, then we still need one more example to show a statistic is complete but not
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But, if you look at the subsection "Completeness of the family" you will see that it is the family of distributions that is said to be complete, not a "statistic". Thus your suggested title would be more restrictive than necessary. As to "more descriptive", both are equally descriptive, but of
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This redirect page should probably be removed. Better, someone should convert it into an actual article on the complete class theorem. At the very least, the redirect page should point to a "to be done" article on the complete class theorem, not to the "Completeness (statistics)" page.
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The rename is good and this above argument is not right! The definition of a complete statistic should be state it is complete for a specific family. rather than just for all theta. I mean it should be for all theta in Theta. The big Theta is the specified family.
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If X1 and X2 are two independent random variables with
Bernoulli(theta) distribution. Isn't X1 complete and not sufficient? A similar example is to take a sample from Normal(theta,1) and choose as your statistic the mean of a sub-sample.
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And if the discussion is to include things like ancillary statistics, it would be good to have definitions of what sufficiency and completeness means where the nuisance parameters are shown explicitly.
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page 30. I have found no reference for "complete statistic" (none in article either) although one might suppose that this is a statistic whose family of distributions is complete.
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It should suffice to present examples from standard books, e.g. Bickel Doksum or
Lehmann, without inventing new examples. Using standard examples will save everybody time.
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that points to this page (I cannot figure out how to produce the redirect page directly, so click on the "redirected from" line at the top of the page).
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completeness does not necessarily imply sufficiency and sufficiency does not necessarily imply completeness). Taking this fact into account, the family
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What does
Lehmann say, Melcombe? Of course, Lehmann's TSP is the canonical reference. Your quote displays already some inadequacies of Cox and Hinkley.
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Consider any family P and the statistic T(X) = 5 (i.e. your statistic always estimates 5, no matter what data is given). Then E(g(T)) = 0 for all
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sufficient. I feel that the statement is not true, but I am not able to prove it. Can someone please prove it is either way (true or not true).
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If a complete sufficient statistic exists, then it need not be minimal sufficient. However, we have the following result: suppose
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909:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
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is an unbiased estimator of zero (Observe that it's distribution does not depend on the parameter. This means that it is an
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references this page, as does the decision theory page, but the references and discussion on this page give no help.
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This example will show that the statistic (X1,X2) is sufficient but not complete for the model. Again suppose (
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It seems that this material would be better suited to an article comparing and contrasting the two concepts.
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But this "Completeness (statistics)" page is completely unrelated to the complete class theorem in
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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This example shows that the statistic X is sufficient but not complete for the model. Let
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is a minimal sufficient statistic (and under the mild conditions mentioned above, such
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A sufficient statistic retains at least enough information from the data to estimate
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Also, it seems to me that the article suffered from an over-emphasis on sufficiency.
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Last edited at 01:40, 16 April 2008 (UTC). Substituted at 19:53, 1 May 2016 (UTC)
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Needs examples of statistics that are complete but not sufficient and vice versa.
776:(satisfies certain conditions) then it is called complete" e.g Cox & Hinkley
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This example is to show a statistic is complete but not sufficient. ....
440:. A complete statistic retains no irrelevant information in estimating
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Distraction about sufficiency: Needs work before being reinserted
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what is the example for? I put it there, why remove it??
617:) is a sufficient statistic when the sample size is 2).
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567:{\displaystyle g((X_{1},\ X_{2}))=X_{1}-X_{2}\,\!}
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905:, and are posted here for posterity. Following
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899:The comment(s) below were originally left at
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184:This article is within the scope of
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38:It is of interest to the following
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350:implies that p(g = 0) = 1 for all
262:? I think it is more descriptive.—
254:In line with the recently renamed
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198:and see a list of open tasks.
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280:Melcombe
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