# how to compute Wald Statistic for $\beta_2=0$ and $\beta_2-\beta_1=0$

$\sqrt{T}(\hat{b}-b)\sim N(0,E)$, where $E$ is the matrix $\begin{pmatrix}1&0.5\\0.5&3\end{pmatrix}$ and $b= (b1, b2)$.

Q: what is the distribution of AX?

Q2: what is the asymptotic distribution of $b1+b2$ and $b1-b2$?

Q3: what is the Wald Statistic with hypothesis that $b1-b2=0$ and $b2=0$?

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. –  Brett Frankel Jan 31 '13 at 22:37
This is a better fit for Cross-Validated. It will probably get a better answer there. –  robjohn Feb 1 '13 at 6:24