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单词 estimator
释义

estimator


es·ti·mate

E0221400 (ĕs′tə-māt′)tr.v. es·ti·mat·ed, es·ti·mat·ing, es·ti·mates 1. To calculate approximately (the amount, extent, magnitude, position, or value of something).2. To form an opinion about; evaluate: "While an author is yet living we estimate his powers by his worst performance" (Samuel Johnson).n. (-mĭt)1. a. A tentative evaluation or rough calculation, as of worth, quantity, or size: an estimate of the damage caused by the storm.b. A statement of the approximate cost of work to be done, such as a building project or car repairs.2. A judgment based on one's impressions; an opinion: I have a high estimate of his character.
[Latin aestimāre, aestimāt-.]
es′ti·ma′tive adj.es′ti·ma′tor n.Synonyms: estimate, appraise, assess, evaluate, rate1
These verbs have to do with the consideration of judgment in ascertaining value or weighing the relative merits of something: estimated the street value of the drugs to be $500,000; appraised the diamond ring; assessing real estate for investors; evaluated a student's thesis for content and organization; rated the restaurant higher than any other in the city.

estimator

(ˈɛstɪˌmeɪtə) n1. a person or thing that estimates2. (Statistics) statistics a derived random variable that generates estimates of a parameter of a given distribution, such as ̄X, the mean of a number of identically distributed random variables Xi. If ̄X is unbiased, ̄x, the observed value should be close to E(Xi). See also sampling statistic
Thesaurus
Noun1.estimator - an expert at calculation (or at operating calculating machines)estimator - an expert at calculation (or at operating calculating machines)calculator, figurer, reckoner, computerexpert - a person with special knowledge or ability who performs skillfullyadder - a person who adds numbersnumber cruncher - someone able to perform complex and lengthy calculationsactuary, statistician - someone versed in the collection and interpretation of numerical data (especially someone who uses statistics to calculate insurance premiums)subtracter - a person who subtracts numbers
Translations
IdiomsSeeestimate

Estimator


estimator

[′es·tə‚mād·ər] (statistics) A random variable or a function of it used to estimate population parameters.

Estimator

 

in statistics, a function of the results of observations that is used to estimate an unknown parameter of the probability distribution of random variables that are under study. In English, a distinction is sometimes, but not always, made between the terms “estimator” and “estimate”: an estimate is the numerical value of the estimator for a particular sample.

Suppose, for example, that X1, . . . , Xn are independent random variables having the same normal distribution with the unknown mean a. Possible point estimators of a are the arithmetic mean of the observation results

and the sample median μ = μ(X1,..., Xn).

In choosing an estimator of a parameter θ, it is natural to select a function θ*(X1, . . . , Xn) of the observation results X1, . . . , Xn that is in some sense close to the true value of the parameter. By adopting some measure of the closeness of an estimator to the parameter being estimated, different estimators can be compared with respect to quality. A commonly used measure of closeness is the magnitude of the mean squared error

Eθ(θ* – θ)2 = Dθθ* + (θ - Eθθ*)2

which is expressed here in terms of the mathematical expectation Eθθ* and variance Dθθ* of the estimator.

The estimator θ* is said to be unbiased if Eθθ* = θ. In the class of all unbiased estimators, the best estimators from the standpoint of mean squared error are those that have for a given n the minimum possible variance for all θ. The estimator X̄ defined above for the parameter a of a normal distribution is the best unbiased estimator, since the variance of any other unbiased estimator a* of a satisfies the inequality Daa* DaX̄ = σ2/n, where σ2 is the variance of the normal distribution. If a minimum-variance unbiased estimator exists, an unbiased best estimator can also be found in the class of functions that depend only on a sufficient statistic.

In constructing estimators for large n, it is natural to assume that as n → ∞, the probability of deviations of θ* from the true value of θ that exceed some given number will be close to θ. Estimators with this property are said to be consistent. Unbiased estimators whose variance approaches θ as n→ ∞ are consistent. Because the rate at which the limit is approached plays an important role here, an asymptotic comparison of two estimators is made by considering the ratio of their asymptotic variances. In the example given above, the arithmetic mean X̄ is the best, and consequently the asymptotically best, estimator for the parameter a, whereas the sample median μ, although an unbiased estimator, is not asymptotically best, since

Nonetheless, the use of μ sometimes has advantages. If, for example, the true distribution is not exactly normal, the variance of X̄ may increase sharply while the variance of μ remains almost the same—that is, μ has the property known as robustness.

A widely used general method of obtaining estimators is the method of moments. In this technique, a certain number of sample moments are equated to the corresponding moments of the theoretical distribution, which are functions of the unknown parameters, and the equations obtained are solved for these parameters. The method of moments is convenient to use, but the estimators produced by it are not in general asymptotically best estimators. From the theoretical point of view, the maximum likelihood method is more important. It yields estimators that, under certain general conditions, are asymptotically best. The method of least squares is a special case of the maximum likelihood method.

An important supplement to the use of estimators is provided by the estimation of confidence intervals.

REFERENCES

Kendall, M., and A. Stuart. Statisticheskie vyvody i sviazi. Moscow, 1973. (Translated from English.)
Cramér, H. Matematicheskie metody statistiki, 2nd ed. Moscow, 1975. (Translated from English.)

A. V. PROKHOROV

estimator

A person who, by experience and training, is capable of estimating the probable cost of a building or portion thereof.

estimator


estimate

 [es´tĭ-ma] 1. a rough calculation or one based on incomplete data.2. a statistic used to characterize the value of a population parameter. Called also estimator.3. (es´tĭ-māt) to produce or use such a calculation or statistic.

es·ti·ma·tor

(es'tĭ-mā'tŏr), A prescription for obtaining an estimate from a random sample of data. An estimator is a procedure, not a result, and therefore is a random variable and has a variance. For instance, an estimator of the mean weight in adult men may consist of the prescription "Add up the weights of 100 men and divide by 100." The actual outcome (the estimate) will vary from sample to sample, but one answer will not be a random variable.

es·ti·ma·tor

(es'tĭ-mā'tŏr) A prescription for obtaining an estimate from a random sample of data.

Patient discussion about estimator

Q. Hi friends, I like to estimate my body fat based on my height and weight. Hi friends, I like to estimate my body fat based on my height and weight. When I enquired about this I heard about BMI. Though I understood little about it I want to know more about what is BMI and why is it useful?A. the BMI is not a very good method...it only helps if you are an average person. you can gain weight if you start training and still get in shape and loose fat. but it is our only cheap method...there are gyms that hold a way of measuring body fat- maybe try going to one of those?

More discussions about estimator

estimator


Related to estimator: Unbiased estimator
  • noun

Synonyms for estimator

noun an expert at calculation (or at operating calculating machines)

Synonyms

  • calculator
  • figurer
  • reckoner
  • computer

Related Words

  • expert
  • adder
  • number cruncher
  • actuary
  • statistician
  • subtracter
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