Editing Point estimation (section)

=== Biasedness ===
“[[Bias of an estimator|Bias]]” is defined as the difference between the expected value of the estimator and the true value of the population parameter being estimated. It can also be described that the closer the [[expected value]] of a parameter is to the measured parameter, the lesser the bias. When the estimated number and the true value is equal, the estimator is considered unbiased. This is called an ''unbiased estimator.'' The estimator will become a ''best unbiased estimator'' if it has minimum [[variance]]. However, a biased estimator with a small variance may be more useful than an unbiased estimator with a large variance.<ref name=":0">{{Cite book|title=A Modern Introduction to Probability and Statistics|publisher=F.M. Dekking, C. Kraaikamp, H.P. Lopuhaa, L.E. Meester|year=2005|language=English}}</ref> Most importantly, we prefer point estimators that have the smallest [[Mean squared error|mean square errors.]]

If we let T = h(X<sub>1</sub>,X<sub>2</sub>, . . . , X<sub>n</sub>) be an estimator based on a random sample X<sub>1</sub>,X<sub>2</sub>, . . . , X<sub>n</sub>, the estimator T is called an unbiased estimator for the parameter θ if E[T] = θ, irrespective of the value of θ.<ref name=":0"/> For example, from the same random sample we have E(x̄) = μ (mean) and E(s<sup>2</sup>) = σ<sup>2</sup> (variance), then x̄ and s<sup>2</sup> would be unbiased estimators for μ and σ<sup>2</sup>. The difference E[T ] − θ is called the bias of T ; if this difference is nonzero, then T is called biased.