A prescription for obtaining an estimate from a random sample of data. An estimator is a procedure, not a result, and therefore is a random variable and has a variance. For instance an estimator of the mean weight in adult men may consist of the prescription "Add up the weights of 100 men and divide by 100." The actual outcome (the estimate) will vary from sample to sample, but one answer will not be a random variable.

Least squares estimator, the prescription "Assign to the unknown parameter the value that minimises the mean of the squares of the residual errors".

Maximum likelihood estimator, the prescription "Assign to the unknown parameter that value that maximises the likelihood for the sample". For many problems this procedure is an optimal one.

(05 Mar 2000)

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