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Maximum Likelihood Estimator

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Let Y1<Y2<...<Yn be the order statistics of a random sample from a distribution with pdf [tex]f(x; \theta) = 1[/tex], [tex]\theta - 0.5 < x < \theta + 0.5[/tex]. Show that every statistic u(X1,X2,...,Xn) such that [tex]Y_n - 0.5<u(X_1,X_2,...,X_n)<Y_1 + 0.5[/tex] is a mle of theta. In particular [tex](4Y_1 + 2Y_n + 1)/6, (Y_1 + Y_n)/2, (2Y_1 + 4Y_n - 1)/6[/tex] are three such statistics.

    2. Relevant equations

    3. The attempt at a solution

    I don't even know how to start this problem. Can someone please point me in the right direction?
  2. jcsd
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