Unbiased Estimate definition of Unbiased Estimate in the Free Online Encyclopedia.

unbiased estimate [¦ən′bī·əst ′es·tə·mət]

(statistics)

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, . . . . ,θ_s, then the functions θ_i^* (x₁, x₂, . . . , x_n) of the observational results x₁, x₂, . . . .x_n) are called unbiased estimates for the parameters θ_i, if for any admissible values of the parameters θ₁, θ₂, . . . , θ_s the mathematical expectation Eθ_i^* (x₁ , x₂, . . . , x_n) ═ θ_i. For example, if x₁, x₂, . . . , x_n 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 + . . . + x_n)/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

x_i1, x_i2, . . . , x_in (i ═ 1, 2, . . . , k)

with n observations in each, and let s_i² 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.

REFERENCES

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.

IU. V. PROKHOROV

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No references found	The authors conclude that the models provide reasonably accurate and unbiased estimates of annual [PM. Nationwide spatial modeling of [PM.sub.10] and [NO.sub.2] by Environmental Health Perspectives That is to say, we aim to find an unbiased estimate of the partial derivative of [y. The New Keynesian Phillips Curve and lagged inflation: a case of ... by Hall, Stephen G.; Hondroyiannis, George; Swamy, P.A.V.B.; Tavlas, G.S. / Southern Economic Journal ] is an N x N matrix that holds the unbiased estimate of the residual variance-covariance matrix, [[? On the use of multifactor models to evaluate mutual fund performance by Huij, Joop; Verbeek, Marno / Financial Management	Unamuno y Jugo, Miguel de Unamuno, Miguel de Unanimism Unanimity Principle in the United Nations unarmed unary unary operation unattached Unattainability unattended install unattended operation unattended time unavailable energy unavoidable unavoidable delay unavoidable set of configurations unavoidable-delay allowance unbalanced unbalanced cutter chain unbalanced hoisting unbalanced line unbalanced output unbalanced shothole unbalanced wire circuit unbeliever Unbiased Estimate unblanking pulse unbonded member unbonded posttensioning unbonded strain gage unbonded tendon unbounded manifold unbounded set of real numbers unbounded wave unbraced frame unbraced length unbreakable cipher unbridled unbroken unbundle unbundling unburnt brick UNC uncached speed uncage Uncas uncased uncatalog uncertainty Uncertainty Principle uncertainty relation	unbends unbeneficed Unbenevolence unbenevolent Unbenign unbent unbent Unbenumb UNBER Unbereaven Unbereft Unbeseem Unbeseeming Unbespeak Unbethink unbetraying Unbeware Unbewitch UNBF UNBI Unbias Unbias unbiased unbiased unbiased unbiased unbiased Unbiased Bit String Unbiased Converted Measurement Unbiased Converted Measurement Kalman Filter Unbiased Estimate Unbiased estimator Unbiased Estimators Unbiased Expectations Unbiased expectations hypothesis Unbiased Expectations Theory Unbiased Forward Rate Unbiased Forward Rate Hypothesis Unbiased Highly Accelerated Stress Test unbiased impulse Unbiased Mean-Squared Error Unbiased predictor Unbiased Random Walk Model unbiasedly unbiasedly unbiasedness unbiasedness unbiassed unbiassed unbid unbid unbidden unbidden Unbifurcated Unbifurcated Unbifurcated Unbifurcated Unbifurcated unbigoted unbigoted unbilled

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The authors conclude that the models provide reasonably accurate and unbiased estimates of annual [PM.

Nationwide spatial modeling of [PM.sub.10] and [NO.sub.2] by Environmental Health Perspectives

That is to say, we aim to find an unbiased estimate of the partial derivative of [y.

The New Keynesian Phillips Curve and lagged inflation: a case of ... by Hall, Stephen G.; Hondroyiannis, George; Swamy, P.A.V.B.; Tavlas, G.S. / Southern Economic Journal

] is an N x N matrix that holds the unbiased estimate of the residual variance-covariance matrix, [[?

On the use of multifactor models to evaluate mutual fund performance by Huij, Joop; Verbeek, Marno / Financial Management