# Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]

having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).

Demonstrate that the mle theta;hat is a sufficient statistic for theta;.

Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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#### Solution Summary

This solution shows step-by-step calculations and brief explanations to determine the sufficient statistic for theta, ancillary statistics for the distribution and the equivalency of mle of theta.

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