mnb96
Feb16-11, 11:30 AM
Hi,
let's suppose we are given N statistically independent samples x_1,\ldots,x_n from a certain distribution f_X(x;\theta) depending on a parameter \theta.
We are also given an estimator for \theta defined as follows:
\hat{\theta}}(N) = \min\{ x_i \\ : \\ i=1..N \}
How am I supposed to compute E\{ \hat{\theta}(N) \}?
I tried to apply the definition of mean-value as follows, but I can't go any further:
\int_{\mathbb{R}}\ldots\int_{\mathbb{R}} \min\{ x_1,\ldots,x_N \} \\ f_X(x_1)\ldots f_X(x_N)dx_1\ldots dx_N
Any idea?
let's suppose we are given N statistically independent samples x_1,\ldots,x_n from a certain distribution f_X(x;\theta) depending on a parameter \theta.
We are also given an estimator for \theta defined as follows:
\hat{\theta}}(N) = \min\{ x_i \\ : \\ i=1..N \}
How am I supposed to compute E\{ \hat{\theta}(N) \}?
I tried to apply the definition of mean-value as follows, but I can't go any further:
\int_{\mathbb{R}}\ldots\int_{\mathbb{R}} \min\{ x_1,\ldots,x_N \} \\ f_X(x_1)\ldots f_X(x_N)dx_1\ldots dx_N
Any idea?