Properties of Maximum-Likelihood Estimators

List the properties of Maximum-Likelihood Estimators

Properties of Maximum-Likelihood Estimators

Maximum-likelihood estimators have the following general properties:

• Maximum-likelihood estimators are consistent; as the sample size increases, the estimator converges in probability to its true value

• They are asymptotically unbiased, although they may be biased in small samples.

• They are asymptotically efficient—no asymptotically unbiased estimator has a smaller asymptotic variance.

• They are asymptotically normally distributed. As the sample size increases, the distribution of the estimator is normal. No other estimator will have a smaller standard error.         

• If there is a sufficient statistic for a parameter, then the maximum-likelihood estimator of the parameter is a function of a sufficient statistic.
• A sufficient statistic is a statistic that exhausts all of the information in the sample about the parameter of interest.

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properties of maximum likelihood estimators

ML estimators are consistence