1 I don't see where the bootstrap comes in
2 I guess M is the largest order stat.
3 Is n=25 or do you want this for any sample size?
I'm having some problems understanding this question related to the bootstrap method:
Generate a sample from from the uniform distrubition on
We pretend not to know of (which is in fact 10) and try two estimators for this parameter:
To choose between and we are interested in the MSE and . We can estimate these by inserting an estimator in the expressions of their expectation value and variance. Determine a based on the data to do this and compare the answers.
I found the expectation value of both and , but I have no idea what is meant by inserting an estimator , and how to determine this from a given 25 draws from the distribution. Could someone help me by explaining this?
The question is under the header parametric bootstrap, because the next question is estimating the MSE by drawing from . That question is easy I think.
M is indeed the largest order stat, and an explanation for n=25 or really any any would be great. I just don't understand the part where I decide an estimator from the data and fill it in in the expectation and variance of and .
Err, well I though I had the expectation and variance right, but I don't think I got em. Could someone help me with these for both T_1[/tex] and ?
The expectation of both would be simply but how do I get the variance? o_O
Well, the question is about n = 25, but for general n I need to know the variance.
Is this correct?
The M is the maximum out of the n variables. For the uniform distribution on The epectation value for this is and the variance is
For the uniform distribution with instead of 1, I guess this translates to the expectation value times theta, although I don't know what to do with the variance.
The propability function of M is the beta distribution with paramters a and 1 I think.
What remains even more vague to me is how I deduce an estimator from a dataset with 25 X's, and how I should fill that in in the expectations and variances...
The bootstrap comes in in the next question: determine the MSE of and by use of parametric bootstrap. First determine an estimator of and then simulate and