Let X1,X2,,Xn be samples (with observations Xi=xi) from a distributionPlanetmathPlanetmath with probability density function f(Xθ), where θ is a real-valued unknown parameter ( in f. Consider θ as a random variableMathworldPlanetmath and let τ(θ) be its realization.

An estimatorMathworldPlanetmath for θ is a statisticMathworldMathworldPlanetmath ηθ=ηθ(X1,X2,,Xn) that is used to, loosely speaking, estimate τ(θ). Any value ηθ(X1=x1,X2=x2,,Xn=xn) of ηθ is called an estimate of τ(θ).

Example. Let X1,X2,,Xn be iid from a normal distributionMathworldPlanetmath N(μ,σ2). Here the two parameters are the mean μ and the varianceMathworldPlanetmath σ2. The sample mean X¯ is an estimator of μ, while the sample variance s2 is an estimator of σ2. In addition, sample median, sample mode, sample trimmed mean are all estimators of μ. The statistic defined by


where m is a sample median, is another estimator of σ2.

Title estimator
Canonical name Estimator
Date of creation 2013-03-22 14:52:22
Last modified on 2013-03-22 14:52:22
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 62A01
Defines estimate