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Bayesian Statistics

  1. Mar 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Let [itex]Y_n[/itex] be the nth order statistic of a random sample of size n from a distribution with pdf [itex]f(x|\theta) = 1/\theta[/itex], [itex]0<x<\theta[/itex], zero elsewhere. Take the loss function to be [itex]L[\theta, \delta(y)] = [\theta - \delta(y_n)]^2[/itex]. Let [itex]\theta[/itex] be an observed value of the random variable [itex]\Theta[/itex], which ahs the prior pdf [itex]h(\theta) = \beta\alpha^{\beta}/\theta^{\beta+1}[/itex], [itex]\alpha < \theta < \infty[/itex], zero elsewhere, with [itex]\alpha > 0[/itex], [itex]\beta > 0[/itex]. Find hte Bayes solution [itex]\delta(y_n)[/itex] for a point estimate of [itex]\theta[/itex].

    2. Relevant equations



    3. The attempt at a solution

    I'm a little confused with finding the likelihood function. Since they are telling us that [itex]Y_n[/itex] is the nth statistic...does that mean that we only have one function in the likelihood function?

    Thanks in advance
     
  2. jcsd
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