diff --git a/memoire/chapitre4.tex b/memoire/chapitre4.tex index 8dba1fa..8ca051d 100644 --- a/memoire/chapitre4.tex +++ b/memoire/chapitre4.tex @@ -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 diff --git a/memoire/gabarit-maitrise.log b/memoire/gabarit-maitrise.log index 79d8a91..1028fec 100644 --- a/memoire/gabarit-maitrise.log +++ b/memoire/gabarit-maitrise.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.12.23) 25 JAN 2014 15:12 +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.30) 29 JAN 2014 21:07 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -2261,7 +2261,7 @@ re/texmf/fonts/type1/public/cm-super/sfrm1095.pfb> -Output written on gabarit-maitrise.pdf (155 pages, 1004092 bytes). +Output written on gabarit-maitrise.pdf (155 pages, 1004072 bytes). PDF statistics: 2851 PDF objects out of 2984 (max. 8388607) 2598 compressed objects within 26 object streams diff --git a/memoire/gabarit-maitrise.pdf b/memoire/gabarit-maitrise.pdf index 5fa7a2e..0b0f187 100644 Binary files a/memoire/gabarit-maitrise.pdf and b/memoire/gabarit-maitrise.pdf differ