mean squared error

**brod04** · March 27th 2009, 10:21 AM

Suppuse X is uniformly distributed on ( 0, theta). suppose we estimate theta with the maximum value from a random sample of size n. Compute the mean squared error for the estimator.

**matheagle** · March 27th 2009, 03:34 PM

You need the density of the largest order stat from a $U(0,\theta)$ .

The orginal density is ${1\over \theta}$ on $(0,\theta)$ .

F(x) is ${x\over \theta}$ on $(0,\theta)$ .

And the density of $F_{(n)}(x)=n(F(x))^{n-1}f(x)$ on $(0,\theta)$ .

From that you can answer all your questions.

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