# Bayesian Statistics

1. Mar 28, 2013

### Artusartos

1. The problem statement, all variables and given/known data

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

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 $Y_n$ is the nth statistic...does that mean that we only have one function in the likelihood function?