Consistent estimator: Difference between revisions

Revision as of 17:12, 9 March 2019

Revision as of 07:41, 8 April 2019

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=== Unbiased but not consistent ===

An estimator can be [[biased estimator|unbiased]] but not consistent. For example, for an [[iid]] sample {''x''{{su|b=1}},..., ''x{{su|b=n}}''} one can use ''T{{su|b=n}}''(''X'') = ''x''{{su|b=1n}} as the estimator of the mean E[''x'']. Note that here the sampling distribution of ''T{{su|b=n}}'' is the same as the underlying distribution (for any ''n,'' as it ignores all points but the firstlast), so E[''T{{su|b=n}}''(''X'')] = E[''x''] and it is unbiased, but it does not converge to any value.

However, if a sequence of estimators is unbiased ''and'' converges to a value, then it is consistent, as it must converge to the correct value.