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Encyclopedia of Measurement and Statistics

Neil J. Salkind & Kristin Rasmussen

Pub. date: 2007 | DOI: http://dx.doi.org/10.4135/9781412952644

Print ISBN: 9781412916110 | Online ISBN: 9781412952644

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Encyclopedia Entry

Unbiased Estimator

Javier Rojo

Let the data be represented by X 1 , X 2 ,…, X n , a collection of random variables, whose behavior can be modeled by a probability distribution F θ , where θ represents a parameter to be estimated from the data. Here, θ may be a k -dimensional vector. For example, F θ may be the family of normal distributions with θ representing the mean of the X i s, or θ may be a two-dimensional vector, θ = (μ, σ 2 ), representing the mean and variance of the X i s. Let δ( X 1 ,…, X n ) be a function of the data. That is, δ( X 1 ,…, X n ) is an estimator. The estimator δ( X 1 ,…, X n ) is ...

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