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Variance of bootstrap sample of size n

  1. Dec 12, 2009 #1
    http://img138.imageshack.us/img138/6060/98259799.jpg [Broken]

    I have done part one and found that the bias is [tex]\frac{\theta}{n}[/tex]

    then i dont know how to proceed.

    in my notes, have the following result,

    http://img189.imageshack.us/img189/9699/resultc.jpg [Broken]

    i am thinking, this time i have to find the bias in [tex]\hat{\theta^*}[/tex]
    then, if i work through, i got it's unbiased...

    am i doing something wrong?

    I am confused with that, the result in my notes, is it for the mean of the sample?

    but here, we are aksed for the population variance?

    Thanks
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 31, 2009 #2

    EnumaElish

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    (ii) is asking about theta star HAT, not theta star BAR.
     
  4. Jan 2, 2010 #3
    i will look into it again
    sometimes, i really get confused what i am looking for
     
  5. Jan 4, 2010 #4
    I am now working on the bias is

    [tex]
    \bar{\theta}^{*} - \hat{\theta} = \frac{1}{n} \sum_{i=1}^n (y_i^* - \bar{y} )^2 - \frac{1}{n} \sum_{i=1}^n (y_i - \bar{y} )^2
    [/tex]
    after some munipulation , i got to

    [tex]

    \frac{1}{n} \sum_{i=1}^n \left( {y_i^*}^2 - y_i^2 -2\bar{y} (y_i^*+y_i) \right)

    [/tex]

    then i take expectation, i got stuck again...
     
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