Consistent estimator: Difference between revisions

Revision as of 14:38, 23 September 2014

Revision as of 17:49, 12 February 2015

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In practice one constructs an estimator as a function of an available sample of [[sample size|size]] ''n'', and then imagines being able to keep collecting data and expanding the sample ''ad infinitum''. In this way one would obtain a sequence of estimates indexed by ''n'', and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value ''θ''₀, it is called a consistent estimator; otherwise the estimator is said to be '''inconsistent'''.

Consistency as defined here is sometimes referred to as ''weak consistency''. When we replace convergence in probability with [[almost sure convergence]], then the estimator is said to be ''strongly consistent''. Consistency is related to [[bias of an estimator|bias]] in that consistent estimators are convergent and ''asymptotically'' unbiased (hence converge to the correct value), though individual estimators in a consistent sequence may be biased, so long as the bias converges to zero; see [[#Bias versus consistency|bias versus consistency]].

== Definition ==