Maximum spacing estimation: Difference between revisions

Revision as of 16:07, 16 July 2014

Revision as of 09:31, 17 July 2014

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\hat{a} = \frac{nx_{(1)} - x_{(n)}}{n-1},\ \ \hat{b} = \frac{nx_{(n)}-x_{(1)}}{n-1}.

</math>

These are known to be the [[uniformly minimum variance unbiased]] (UMVU) estimators for the continuous uniform distribution .<ref name="CA83">{{harvtxt|Cheng|Amin|1983}}</ref>. In comparison, the maximum likelihood estimates for this problem <math alt="ML estimate of a is the smallest of x’s">\scriptstyle\hat{a}=x_{(1)}</math> and <math alt="ML estimate of b is the largest of x’s">\scriptstyle\hat{b}=x_{(n)}</math> are biased and have higher [[mean-squared error]].

==Properties==