Unbiased Estimate

unbiased estimate

[¦ən′bī·əst ′es·tə·mət]
An estimate for a parameter θ whose expected value is θ.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Unbiased Estimate


an estimate of a parameter of a probability distribution that is based on observed values and is free of systematic errors. More precisely, if the distribution to be estimated depends on the parameters θ1, θ2, . . . . ,θs, then the functions θi* (x1, x2, . . . , xn) of the observational results x1, x2, . . . .xn) are called unbiased estimates for the parameters θi, if for any admissible values of the parameters θ1, θ2, . . . , θs the mathematical expectation Eθi* (x1 , x2, . . . , xn) ═ θi. For example, if x1, x2, . . . , xn are the results of n independent observations of a random variable having a normal distribution

with unknowns a (mathematical expectation) and σ2 (variance), then the arithmetic mean

(1) x̄ ═ (x1 + x2 + . . . + xn)/n

is an unbiased estimate for a. The quantity

which is often used as an estimate for the variance, is not an unbiased estimate. An unbiased estimate for σ2 is

while an unbiased estimate for the standard deviation σ has the more complicated form

The estimate (1) for the mathematical expectation and the estimate (2) for the variance are unbiased estimates in the more general case of distributions that differ from a normal distribution; the estimate (3) for the standard deviation in general (for distributions other than normal) may be biased.

The use of unbiased estimates is necessary in estimating an unknown parameter by means of a large number of series of observations, each of which consists of a small number of observations. For example, let there be k sequences

xi1, xi2, . . . , xin (i ═ 1, 2, . . . , k)

with n observations in each, and let si2 be the unbiased estimate [defined as in (2)] for σ2 computed from the i th sequence of observations. Then, for large k, from the law of large numbers we have

even when n is small. Unbiased estimates play an important role in the statistical control of mass production.


Cramer, H. Mathematicheskie melody statistiki. Moscow, 1948. (Translated from English.)
Kolmogorov, A. N. “Nesmeshchennye otsenki.” Izv. AN SSSR. Seriia matematicheskaia, 1950, no. 4.
Gnedenko, B. V., lu. K. Beliaev, and A. D. Solov’ev. Matematicheskie melody ν teorii nadezhnosti. Moscow, 1965.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
In their study, the bias introduced by matching occurs when assumptions of difference-in-differences hold and researchers could derive an unbiased estimate using standard methods.
"We are confident that the number--2,975--is the most accurate and unbiased estimate of excess mortality to date," the statement read.
'We are confident that the number-2,975-is the most accurate and unbiased estimate of excess mortality to date.'
An appraisal is carried out by a qualified, independent professional who gives an unbiased estimate of the true or fair market value of a property.
Indeed, guidelines published by CADTH and similar HTA agencies internationally indicate that a life-time horizon is required to construct an unbiased estimate of the long-term incremental costs and effects of technologies such as RARP.
Random surveys are designed to provide an unbiased estimate of the mean, whereas fixed-station surveys, in general, provide a biased estimate; however, the magnitude of that bias could be anywhere from negligible to substantial.
2014) to generate an unbiased estimate of tertiary sex-ratio and production using band recoveries and wings collected from hunter-harvested birds.
Then the unbiased estimate of the system state (1) in the batch form is determined by the expression (2), where
(2011) presented an unbiased estimate of DoFs of PLS with m latent components, T = ([t.sub.1], [t.sub.2], ..., [t.sub.m]), which is given by
[14] not only gave the unbiased estimate of the degrees of freedom of Lasso model, but also proved the following consistency of the estimate.
It should be noted that [[??].sub.k + 1|k] is the unbiased estimate of [Z.sub.k + 1] because E([[??].sub.k|k]) = -E([Z.sub.k]) and E([[??].sub.k]) = E([F.sub.k]); then, E([Z.sub.k + 1]) = E([[??].sub.k + 1|k]) can be obtained from (4).
For example, in Figure 1e, adjusting for C (0) is sufficient to control confounding and to provide an unbiased estimate of the causal effect.