Commit a2e8ddea by Eric Coissac

Lastest changes

parent fd173c3b
......@@ -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
......
No preview for this file type
......@@ -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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