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 ... ... @@ -191,7 +191,7 @@ For every values of $p$ and $q$ including $1$, $\overline{\rcovls(\X,\Y)}$ can b \label{eq:RCovLsMC} \end{equation} Even when $\X=\Y$ to estimate $\varls(\X)$, $\overline{\rcovls(\X,\Y)}$ is estimated with two independent sets of random matrix $RX$ and $RY$, both having the same structure than $\X$. Even when $\X=\Y$ to estimate $\ivarls(\X)$, $\overline{\rcovls(\X,\X)}$ is estimated with two independent sets of random matrix $RX$ and $RY$, both having the same structure than $\X$. \subsubsection*{Empirical assessment of $\overline{\rcovls(\X,\Y)}$} ... ... @@ -937,6 +937,10 @@ print(tab, }{\ } % <- we can add a footnote in the last curly braces \end{table} Two main parameters can influencate the Monte Carlo estimation of $\overline{\rcovls(\X,\Y)}$ : the distribution used to generate the random matrices and $k$ the number of random matrix pair. The normal and the exponential distributions are very different. The first one is symetric where the second is not with a high probability for small values and a long tail of large ones. Despite the use of these contrasted distributions, estimates of $\overline{\rcovls(\X,\Y)}$ and of $\sigma_{\overline{\rcovls(\X,\Y)}}$ are similare (Table~\ref{tab:mrcovls}). \subsection{Relative sensibility of $IRLs(X,Y)$ to overfitting} \begin{figure}[!tpb]%figure1 ... ...
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 ... ... @@ -215,7 +215,7 @@ For every values of $p$ and $q$ including $1$, $\overline{\rcovls(\X,\Y)}$ can b \label{eq:RCovLsMC} \end{equation} Even when $\X=\Y$ to estimate $\varls(\X)$, $\overline{\rcovls(\X,\Y)}$ is estimated with two independent sets of random matrix $RX$ and $RY$, both having the same structure than $\X$. Even when $\X=\Y$ to estimate $\ivarls(\X)$, $\overline{\rcovls(\X,\X)}$ is estimated with two independent sets of random matrix $RX$ and $RY$, both having the same structure than $\X$. \subsubsection*{Empirical assessment of $\overline{\rcovls(\X,\Y)}$} ... ... @@ -335,7 +335,7 @@ To evaluate relative power of the three considered tests, pairs of to random mat \begin{table}[!t] \processtable{Estimation of $\overline{\rcovls(\X,\Y)}$ according to the number of random matrices (k) aligned.\label{tab:mrcovls}}{ % latex table generated in R 3.5.2 by xtable 1.8-4 package % Tue Jun 25 08:35:32 2019 % Tue Jun 25 09:08:19 2019 \begin{tabular}{rrrrrrr} \hline & & \multicolumn{2}{c}{normal} & & \multicolumn{2}{c}{exponential}\\ \cline{3-4} \cline{6-7}p & k &\multicolumn{1}{c}{mean} & \multicolumn{1}{c}{sd} & \multicolumn{1}{c}{ } &\multicolumn{1}{c}{mean} & \multicolumn{1}{c}{sd}\\\hline\multirow{3}{*}{10} & 10 & 0.5746 & $1.3687 \times 10^{-2}$ & & 0.5705 & $1.1714 \times 10^{-2}$ \\ ... ... @@ -356,6 +356,10 @@ To evaluate relative power of the three considered tests, pairs of to random mat }{\ } % <- we can add a footnote in the last curly braces \end{table} Two main parameters can influencate the Monte Carlo estimation of $\overline{\rcovls(\X,\Y)}$ : the distribution used to generate the random matrices and $k$ the number of random matrix pair. The normal and the exponential distributions are very different. The first one is symetric where the second is not with a high probability for small values and a long tail of large ones. Despite the use of these contrasted distributions, estimates of $\overline{\rcovls(\X,\Y)}$ and of $\sigma_{\overline{\rcovls(\X,\Y)}}$ are similare (Table~\ref{tab:mrcovls}). \subsection{Relative sensibility of $IRLs(X,Y)$ to overfitting} \begin{figure}[!tpb]%figure1 ... ... @@ -423,7 +427,7 @@ whatever the $p$ tested (Table~\ref{tab:alpha_pvalue}). This ensure that the pro of the distribution of $P_{values}$ correlation test to $\mathcal{U}(0,1)$ under the null hypothesis.\label{tab:alpha_pvalue}} { % latex table generated in R 3.5.2 by xtable 1.8-4 package % Tue Jun 25 08:35:36 2019 % Tue Jun 25 09:08:22 2019 \begin{tabular*}{0.98\linewidth}{@{\extracolsep{\fill}}crrr} \hline & \multicolumn{3}{c}{Cramer-Von Mises p.value} \\ ... ... @@ -445,7 +449,7 @@ Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is \begin{table}[!t] \processtable{Power estimation of the procruste tests for two low level of shared variations $5\%$ and $10\%$.\label{tab:power}} { % latex table generated in R 3.5.2 by xtable 1.8-4 package % Tue Jun 25 08:35:36 2019 % Tue Jun 25 09:08:22 2019 \begin{tabular}{lcrrrrrrrrr} \hline & $R^2$ & \multicolumn{4}{c}{5\%} & &\multicolumn{4}{c}{10\%} \\ ... ...
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