Hello,

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

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

Where,

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

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

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So is this correct:

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

??

Please help.