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Math Help - Consistency using the median

  1. #1
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    Consistency using the median

    How can you use the sample median Y' to prove consistency?

    If 2n+1 random observations are drawn from a continuous and symmetric pdf with mean (mu) and if f_Y(mu;mu) does not equal 0, then the sample median Y'_(n+1), is unbiased for (mu) and Var( Y'_(n+1) ) = 1/8[ f_Y(mu;mu)^2 *n ]. Show that (mu) hat = Y'_(n+1) is consistent for (mu).
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  2. #2
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    Quote Originally Posted by lteece89 View Post
    How can you use the sample median Y' to prove consistency?

    If 2n+1 random observations are drawn from a continuous and symmetric pdf with mean (mu) and if f_Y(mu;mu) does not equal 0, then the sample median Y'_(n+1), is unbiased for (mu) and Var( Y'_(n+1) ) = 1/8[ f_Y(mu;mu)^2 *n ]. Show that (mu) hat = Y'_(n+1) is consistent for (mu).
    When the mean and variance exist it suffices to show that the mean converges to the thing you want and the variance goes to 0 (for all values of mu).
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