Difference between revisions of "Efficient estimator"
From Encyclopedia of Mathematics
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(I deleted the sentence "An unbiased statistical estimator whose variance is the lower bound in the Rao–Cramér inequality." because an efficient estimator does not have to be unbiased.) |
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| − | + | An efficient estimator is a [[Sufficient statistic|sufficient statistic]] for the parameter to be estimated. If an efficient estimator exists, then it can be obtained by the maximum-likelihood method. Owing to the fact that in many cases the lower bound in the Rao–Cramér inequality cannot be attained, in mathematical statistics an efficient estimator is frequently defined as one having minimal variance in the class of all unbiased estimators (cf. [[Unbiased estimator|Unbiased estimator]]) of the parameter in question. | |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> C.R. Rao, "Linear statistical inference and its applications" , Wiley (1965)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> C.R. Rao, "Linear statistical inference and its applications" , Wiley (1965)</TD></TR></table> | ||
Revision as of 13:36, 24 October 2012
An efficient estimator is a sufficient statistic for the parameter to be estimated. If an efficient estimator exists, then it can be obtained by the maximum-likelihood method. Owing to the fact that in many cases the lower bound in the Rao–Cramér inequality cannot be attained, in mathematical statistics an efficient estimator is frequently defined as one having minimal variance in the class of all unbiased estimators (cf. Unbiased estimator) of the parameter in question.
References
| [1] | H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946) |
| [2] | I.A. Ibragimov, R.Z. [R.Z. Khas'minskii] Has'minskii, "Statistical estimation: asymptotic theory" , Springer (1981) (Translated from Russian) |
| [3] | C.R. Rao, "Linear statistical inference and its applications" , Wiley (1965) |
How to Cite This Entry:
Efficient estimator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Efficient_estimator&oldid=13642
Efficient estimator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Efficient_estimator&oldid=13642
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article