# Point estimator

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A statistical estimator whose values are points in the set of values of the quantity to be estimated.

Suppose that in the realization of the random vector , taking values in a sample space , , the unknown parameter (or some function ) is to be estimated. Then any statistic producing a mapping of the set into (or into the set of values of ) is called a point estimator of (or of the function to be estimated). Important characteristics of a point estimator are its mathematical expectation and the covariance matrix The vector is called the error vector of the point estimator . If is the zero vector for all , then one says that is an unbiased estimator of or that is free of systematic errors; otherwise, is said to be biased, and the vector is called the bias or systematic error of the point estimator. The quality of a point estimator can be defined by means of the risk function (cf. Risk of a statistical procedure).

How to Cite This Entry:
Point estimator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Point_estimator&oldid=16171
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article