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Math Help - Limit distribution

  1. #1
    Member
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    Limit distribution

    Hello,

    I want to find the asymptotic distribution of \hat{\beta}. And this happens to be the sum of two normally distributed terms. i.e.

     \sqrt{n}(\hat{\beta} - \beta) = X-Y

    Where,

     X \longrightarrow N(0, \sigma^2 )

     Y \longrightarrow N(0, \omega^2 )

    __________________________________________________

    So is this correct:

     \sqrt{n}(\hat{\beta} - \beta) \longrightarrow N(0, \sigma^2 + \omega^2)

    ??

    Please help.
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  2. #2
    MHF Contributor matheagle's Avatar
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    All you seem to be doing is subtracting two normals.
    And you're assuming independence between X and Y.
    IF X=Y, then X-Y=0, which is not normal
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