Unbiased Estimate

unbiased estimate

[¦ən′bī·əst ′es·tə·mət]
An estimate for a parameter θ whose expected value is θ.

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.


References in periodicals archive ?
For example, in Figure 1e, adjusting for C (0) is sufficient to control confounding and to provide an unbiased estimate of the causal effect.
Finally, a consistent and unbiased estimate of the quantity of money demand is a useful indicator of GDP.
For each parameter 0, by its unbiased estimate, we mean a function [?
Finally, Theobald and Richardson use this SWIT to discuss the assumptions necessary for common estimation methods to produce an unbiased estimate of the treatment effect of a non-randomized educational intervention.
I was particularly interested in getting an unbiased estimate of the turnout.
In (1) when = 0 and = 1 the consumption growth as per national accounts is unbiased estimate of the same in survey data where residual is assumed to have zero mean.
We performed descriptive statistical analysis and exact conditional logistic regression to compute the most likely estimate or, when small cell sizes required, the median unbiased estimate of matched odds ratios (mORs) with 95% confidence intervals (CIs).
If selection is used to find the final model, even if the selection occurs in test sets, a separate data set is needed to obtain an unbiased estimate of fit or of effect.
Under inverse sampling (4) if 'n' is the sample size, at which the mth case appears, an unbiased estimate of P is given by,
5], the average of all monitoring data available at a regular interval should be an unbiased estimate of true [PM.
An unbiased estimate of future cash flows, using assumptions a "market place participant" would make.
TABLE 2 Evaluation of Simplified Damage Assessment Methods Simplified Method Feature FL MN NJ WA Simple to use yes yes yes yes Legal recognition yes no no yes Transparent no potentially potentially no Reflect variation in scope yes yes yes yes Net present value calculated appropriately no no partly no Unbiased estimate of public use and nonuse values no no no no Reflect socioeconomic characteristics no no somewhat somewhat Simplified Method Benefit NOAA Feature CA Transfer Type A Simple to use yes no yes Legal recognition no yes yes Transparent yes potentially yes Reflect variation in scope yes potentially yes Net present value calculated appropriately yes potentially yes Unbiased estimate of public use and nonuse values no yes no Reflect socioeconomic characteristics no yes no