correction test Wald chapitre 4

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François Pelletier 2014-01-29 21:09:15 -05:00
parent 99ebb83662
commit 7889eeb181
3 changed files with 6 additions and 6 deletions

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@ -870,15 +870,15 @@ que la somme de deux variables aléatoires normales l'est aussi:
\begin{align}
\label{eq:moyennevariancesomme}
E\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &=
E\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] -
E\left[\sqrt{T}\left(\tilde\theta - \theta_0\right) \right]\nonumber\\
E\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] +
E\left[\sqrt{T}\left(\theta_0 - \tilde\theta\right) \right]\nonumber\\
&= 0 - 0 \nonumber\\
&= 0 \\
V\left[\sqrt{T}\left(\hat\theta - \tilde\theta\right) \right] &=
V\left[\sqrt{T}\left(\hat\theta - \theta_0\right) \right] +
V\left[\sqrt{T}\left(\theta_0 - \tilde\theta\right) \right]\nonumber\\
&= \left(I+(P-I)\right)\mathcal{J}_0^{-1}\nonumber\\
&= P\mathcal{J}_0^{-1}.
&= T\left(I+(P-I)\right)\mathcal{J}_0^{-1}\nonumber\\
&= TP\mathcal{J}_0^{-1}.
\end{align}
On définit la statistique $\chi^{WALD,1}$, qui a asymptotiquement une

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