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Commit b376f608 by Eric Coissac
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New version with most of the mat-meth

parent ca0e354e
Showing with 64 additions and 105 deletions
manuscript/.gitignore
......@@ -2,3 +2,5 @@ main.synctex.gz
main-concordance.tex
main.blg
main.log
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SimulationRls.R
manuscript/cache/__packages
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manuscript/main.aux 0 → 100644
\relax
\citation{Ramsay:84:00}
\citation{Smilde:09:00}
\citation{Escoufier:73:00}
\citation{Szekely:07:00}
\citation{SzeKely:13:00}
\citation{Lingoes:74:00}
\citation{Gower:71:00}
\citation{Peres-Neto:01:00}
\citation{Bravais:44:00}
\newcplabel{^_1}{1}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\newlabel{eq:CovLs}{{1}{1}}
\newlabel{eq:Rls}{{2}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Approach}{1}}
\citation{Robert:76:00}
\citation{El-Ghaziri:15:00,Mayer:11:00,Smilde:09:00}
\citation{Szekely:07:00}
\citation{SzeKely:13:00}
\citation{Jackson:95:00}
\citation{Peres-Neto:01:00}
\citation{Dixon:03:00}
\citation{Dray:07:00}
\newlabel{eq:SVD}{{3}{2}}
\newlabel{eq:CovLsSVD}{{4}{2}}
\newlabel{eq:ICovLs}{{5}{2}}
\newlabel{eq:IRLs}{{6}{2}}
\newlabel{eq:IRls.partial}{{7}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Methods}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{3.1}}Monte-Carlo estimation of $\overline {\rcovls (\mathbf {X},\mathbf {Y})}$}{2}}
\newlabel{eq:RCovLsMC}{{8}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{3.2}}Simulating data for testing sensibility to overfitting}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{3.3}}Empirical assessment of the coefficient of determination}{2}}
\citation{CSoRgo:96:00}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Theoritical distribution of the shared variation between the four matrices $\mathbf {A},\tmspace +\thinmuskip {.1667em}\mathbf {B},\tmspace +\thinmuskip {.1667em}\mathbf {C},\tmspace +\thinmuskip {.1667em}\mathbf {D}$, expressed in permille.}}{3}}
\newlabel{fig:nested_shared_variation}{{1}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{3.4}}Testing significance of $\irls (\mathbf {X},\mathbf {Y})$}{3}}
\newlabel{eq:pvalue}{{9}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A) Sensibility to overfitting for various correraltion coefficients. (A) Both simulated data sets are matrices of size $(n \times p)$ with $p > 1$. B) Correlated data sets are vectors ($p=1$) with a various number of individuals $n$ (vector length). A \& B) 100 simulations are run for each combination of parameters}}{3}}
\newlabel{fig:h0_overfit}{{2}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Results}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{4.1}}Relative sensibility of $IRLs(X,Y)$ to overfitting}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{4.2}}Evaluating the shared variation}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Shared variation ($R^2$) between two matrices is mesured with both the corrected ($\irls $) and the original ($\rls $) versions of the procrustean correlation coefficient. A gradiant of $R^2$ is simulated for two population sizes ($n \in \{10,24\}$) and two numbers of descriptive variables ($p \in \{10,100\}$). The black dashed line corresponds to a perfect match where measured $R^2$ equals the simulated one.}}{4}}
\newlabel{fig:shared_variation}{{3}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Estimation error on the partial determination coefficient. Error is defined as the absolute value of the difference between the expected and the estimated partial $R^2$ using the corrected $\irls _{partial}$ and not corrected $\rls _{partial}$ procruste correlation coefficient.}}{4}}
\newlabel{fig:nested_shared}{{4}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces $P_{values}$ of the Cramer-Von Mises test of conformity of the distribution of $P_{values}$ correlation test to $\mathcal {U}(0,1)$ under the null hypothesis.}}{4}}
\newlabel{tab:alpha_pvalue}{{1}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{4.3}}$p_{value}$ distribution under null hyothesis}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {{4.4}}Power of the test based on randomisation}{4}}
\bibstyle{natbib}
\bibdata{Document}
\global\@namedef{@lastpage@}{5}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Power estimation of the procruste tests for two low level of shared variations $5\%$ and $10\%$.}}{5}}
\newlabel{tab:power}{{2}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Discussion}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A}Notations}{5}}
manuscript/main.bbl
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\end{thebibliography}
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