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

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