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complete

Did you mean: complete, Completeness, Complete (complexity), COMPLETE (abbreviation), Complete (News from Babel album), Complete (album), Complete metric space More...

 
Dictionary: com·plete   (kəm-plēt') pronunciation
 
adj., -plet·er, -plet·est.
  1. Having all necessary or normal parts, components, or steps; entire: a complete meal.
  2. Botany. Having all principal parts, namely, the sepals, petals, stamens, and pistil or pistils. Used of a flower.
  3. Having come to an end; concluded.
  4. Absolute; total: “In Cairo I have seen buildings which were falling down as they were being put up, buildings whose incompletion was complete” (William H. Gass).
    1. Skilled; accomplished: a complete musician.
    2. Thorough; consummate: a complete coward.
  5. Football. Caught in bounds by a receiver: a complete pass.
tr.v., -plet·ed, -plet·ing, -pletes.
  1. To bring to a finish or an end: She has completed her studies.
  2. To make whole, with all necessary elements or parts: A second child would complete their family.
  3. Football. To throw (a forward pass) so as to be caught by a receiver.

[Middle English complet, from Latin complētus, past participle of complēre, to fill out : com-, intensive pref.; see com– + plēre, to fill.]

completely com·plete'ly adv.
completeness com·plete'ness n.
completive com·ple'tive adj.

SYNONYMS  complete, close, end, finish, conclude, terminate. These verbs mean to bring or come to a natural or proper stopping point. Complete and finish suggest the final stage in an undertaking: “Nothing worth doing is completed in our lifetime” (Reinhold Niebuhr). “Give us the tools, and we will finish the job” (Winston S. Churchill). Close applies to the ending of something ongoing or continuing: The band closed the concert with an encore. End emphasizes finality: We ended the meal with fruit and cheese. Conclude is more formal than complete and close: The author concluded the article by restating the major points. Terminate suggests reaching an established limit: The playing of the national anthem terminated the station's broadcast for the night. It also indicates the dissolution of a formal arrangement: The firm terminated my contract yesterday.

USAGE NOTE   Complete is sometimes considered absolute like perfect or chief, which is not subject to comparison. Nonetheless, it can be qualified as more or less, for example. A majority of the Usage Panel accepts the example His book is the most complete treatment of the subject. See Usage Notes at absolute.


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Thesaurus: complete
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adjective

  1. Lacking nothing essential or normal: entire, full, intact, integral, perfect, whole. See part/whole.
  2. Including every constituent or individual: all, entire, gross, total, whole. See part/whole.
  3. Not shortened by omissions: unabbreviated, unabridged, uncensored, uncut, unexpurgated. See part/whole.
  4. Not more or less: entire, full, good, perfect, round, whole. See part/whole, precise/imprecise.
  5. Having reached completion: done, through. See part/whole.
  6. Covering all aspects with painstaking accuracy: all-out, exhaustive, full-dress, intensive, thorough, thoroughgoing, thoroughpaced. See big/small/amount, careful/careless.
  7. Completely such, without qualification or exception: absolute, all-out, arrant, consummate, crashing, damned, dead, downright, flat, out-and-out, outright, perfect, plain, pure, sheer, thorough, thoroughgoing, total, unbounded, unequivocal, unlimited, unmitigated, unqualified, unrelieved, unreserved, utter. Informal flat-out, positive. Chiefly British blooming. See big/small/amount, limited/unlimited.

verb

  1. To bring or come to a natural or proper end: close, conclude, consummate, end, finish, terminate, wind up, wrap up. See start/end.
  2. To supply what is lacking: complement, fill in (or out), round (off or out), supplement. See agree/disagree, part/whole.

 
Antonyms: complete
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adj

Definition: finished
Antonyms: imperfect, incomplete, unfinished

adj

Definition: total, not lacking
Antonyms: defective, deficient, imperfect, incomplete, lacking, missing, needy, short, wanting

v

Definition: carry out action
Antonyms: forget, give up, halt, ignore, neglect, stop


 
Veterinary Dictionary: complete
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Including all of the subdivisions of the whole.

 
Word Tutor: complete
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pronunciation

IN BRIEF: Possessing all necessary parts.

pronunciation The brain is not, and cannot be, the sole or complete organ of thought and feeling. — Antoinette Brown Blackwell, (1825-1921), American abolitionist, feminist, clergy.

 
Wikipedia: Completeness (statistics)
Top

In statistics, completeness is a property of a statistic for which the statistic optimally obtains information about the unknown parameters characterizing the distribution of the underlying data.

It is closely related to statistical sufficiency and often occurs in conjunction with it.

Contents

Mathematical definition

Suppose a random variable X (which may be a sequence (X1, ..., Xn) of scalar-valued random variables), has a probability distribution belonging to a known family of probability distributions Pθ parametrized by θ. Let s(X) be any statistic based on X.

Then s(X) is a complete statistic if and only if for every measurable function g,

E(g(s(X))) = 0 for all θ \Rightarrow Pθ(g(s(X)) = 0) = 1 for all θ

and is boundedly complete if the implication holds for all bounded g.

Completeness of the family

It is not guaranteed that for a particular family of probabilities, a complete sufficient statistic will always exist. The same is true for a minimal sufficient statistic (a case in which there is no minimal sufficient statistic was shown by Bahadur, 1957). However, under mild conditions, a minimal sufficient statistic does always exist. In particular, these conditions always hold if the random variables (associated with Pθ ) are all discrete or are all continuous.

If a complete sufficient statistic exists, it is typically, but not always, minimal sufficient. However, we have the following result: suppose T is a minimal sufficient statistic (and under the mild conditions mentioned above, such T can be found), and suppose U is a complete sufficient statistic. Then U is a minimal sufficient statistic (note: completeness does not necessarily imply sufficiency and sufficiency does not necessarily imply completeness). Taking this fact into account, the family Pθ of distributions is called complete if and only if its minimal sufficient statistic is complete.

Heuristic approach

A sufficient statistic retains at least enough information from the data to estimate θ. A complete statistic retains no irrelevant information in estimating θ (it is possible a complete statistic may retain no information). If the intersection of these two groups exists, it will contain complete sufficient statistics. In other words, it contains efficient statistics that retain as much information as possible from the data and will retain no irrelevant information.

Examples

Sum of normals

Suppose (X1, X2) are independent, identically distributed random variables, normally distributed with expectation θ and variance 1. The sum

s((X_1, X_2)) = X_1 + X_2\,\!

is a complete statistic for θ.

To show this one demonstrates that there is no non-zero function g such that the expectation of

g(s(X_1, X_2)) = g(X_1+X_2)\,\!

remains zero regardless of the value of θ.

That fact may be seen as follows. The probability distribution of X1 + X2 is normal with expectation 2θ and variance 2. Its probability density function in x is therefore proportional to

\exp\left(-(x-2\theta)^2/4\right).

The expectation of g above would therefore be a constant times

\int_{-\infty}^\infty g(x)\exp\left(-(x-2\theta)^2/4\right)\,dx.

A bit of algebra reduces this to

k(\theta) \int_{-\infty}^\infty h(x)e^{x\theta}\,dx\,\!

where k(θ) is nowhere zero and

h(x)=g(x)e^{-x^2/4}.\,\!

As a function of θ this is a two-sided Laplace transform of h(X), and cannot be identically zero unless h(x) is zero almost everywhere. The exponential is not zero, so this can only happen if g(x) is zero almost everywhere.

Counterexample 1

Again suppose (X1, X2) are independent, identically distributed random variables, normally distributed with expectation θ and variance 1.

Then

g((X_1,\ X_2)) = X_1 - X_2\,\!

is an unbiased estimator of zero. Therefore the pair (X1, X2) itself is not a complete statistic (though it is a sufficient statistic in a sample of size 2).

Counterexample 2

Let U follow Uniform[−½, ½]. Let X = U + θ, so that the distribution of X is parametrized by the mean θ = E(X).

Then if g(x) = sin(2πx), then E(g(X)) = 0 irrespective of θ. Therefore X itself is not a complete statistic for θ.

Utility

Lehmann–Scheffé theorem

The major importance of completeness is in the application of the Lehmann–Scheffé theorem, which states that a statistic that is unbiased, complete and sufficient for some parameter θ is the best unbiased estimator for θ, i.e., the one that has a smaller expected loss for any convex loss function (in typical practice, a smaller mean squared error) among any estimators with the same expected value.

See also minimum-variance unbiased estimator.

Basu's theorem

Completeness is also a prerequisite for the applicability of Basu's theorem: A statistic which is both complete and sufficient is independent of any ancillary statistic (one independent of the parameters θ).


 
Translations: Complete
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Dansk (Danish)
adj. - komplet, færdig, fuldendt
v. tr. - fuldføre, opfylde, udfylde, berigtige, fylde (år)

idioms:

  • complete with    med tilhørende

Nederlands (Dutch)
compleet, voltallig, voltooien, afwikkelen, invullen (formulier)

Français (French)
adj. - complet, achevé, total, parfait (gentleman, sportif)
v. tr. - arranger, être complété, terminer, achever, compléter, remplir (questionnaire)

idioms:

  • complete with    compléter par, mettre une touche finale

Deutsch (German)
v. - vervollständigen, komplettieren, beenden, abschließen
adj. - vollständig, komplett, völlig

idioms:

  • complete with    komplett mit

Ελληνική (Greek)
v. - συμπληρώνω, αποπερατώνω, ολοκληρώνω
adj. - πλήρης, ακέραιος, τέλειος, ολοκληρωμένος, (καθομ.) βέρος, γνήσιος, τέλειος, σκέτος

idioms:

  • complete with    περιλαμβάνων και, χωρίς να του λείπει

Italiano (Italian)
completare, compiere, finire, terminare, ultimare, riempire, essere portato a fine, essere finito, essere terminato, completo, intero

idioms:

  • complete with    adempiere a

Português (Portuguese)
v. - concluir, inteirar, completar
adj. - completo, concluído, perfeito

idioms:

  • complete with    preencher com

Русский (Russian)
заканчивать, выполнять, закончиться

idioms:

  • complete with    снабдить

Español (Spanish)
adj. - completo, acabado, terminado, perfecto, consumado, total
v. tr. - terminar, completar, concluir, acabar, llenar

idioms:

  • complete with    lleno de, con ... y todo

Svenska (Swedish)
v. - avsluta, komplettera
adj. - komplett, uttömmande

中文(简体)(Chinese (Simplified))
完整的, 完成的, 全部的, 结束的, 使齐全, 完成, 使完整, 结束

idioms:

  • complete with    连同, 具有

中文(繁體)(Chinese (Traditional))
adj. - 完整的, 完成的, 全部的, 結束的
v. tr. - 使齊全, 完成, 使完整, 結束

idioms:

  • complete with    連同, 具有

한국어 (Korean)
adj. - 완전한, 철저한
v. tr. - 완성하다, 전부 갖추다, 성공하다

idioms:

  • complete with    ~로 채우다

日本語 (Japanese)
adj. - 全部の, 完備した, 完全な, 完了した, 完成した
v. - 完成する, 終える, 完全なものにする

idioms:

  • complete with    完備した

العربيه (Arabic)
‏(فعل) كمل, أكمل, أتم, أنهى, أنجز, فرغ من (صفه) تام, كامل‏

עברית (Hebrew)
adj. - ‮שלם, מושלם, מוחלט, גמור‬
v. tr. - ‮סיים, השלים‬


 
Best of the Web: complete
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Some good "complete" pages on the web:


American Sign Language
commtechlab.msu.edu
 

Math
mathworld.wolfram.com
 
 
 

Did you mean: complete, Completeness, Complete (complexity), COMPLETE (abbreviation), Complete (News from Babel album), Complete (album), Complete metric space More...

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