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[bootstrap] notes on how to extend the permutation tests

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Jan Benda 2020-12-08 11:48:07 +01:00
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commit 0380b7a96f
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7
bootstrap/lecture/bootstrap-chapter.tex
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@ -17,10 +17,15 @@
\include{bootstrap}
\section{TODO}
This chapter easily covers two lectures:
\begin{itemize}
\item 1. Bootstrapping with a proper introduction of of confidence intervals
\item 2. Permutation test with a proper introduction of statistical tests (dsitribution of nullhypothesis, significance, power, etc.)
\item 2. Permutation test with a proper introduction of statistical tests (distribution of nullhypothesis, significance, power, etc.)
\end{itemize}
Add jacknife methods to bootstrapping
Add permutation test for significant different means of two distributions.
\end{document}

19
bootstrap/lecture/bootstrap.tex
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@ -1,8 +1,12 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Bootstrap methods}
\chapter{Resampling methods}
\label{bootstrapchapter}
\exercisechapter{Bootstrap methods}
\exercisechapter{Resampling methods}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Bootstrapping}
Bootstrapping methods are applied to create distributions of
statistical measures via resampling of a sample. Bootstrapping offers several
@ -94,7 +98,8 @@ sample. This can be implemented by generating random indices into the
data set using the \code{randi()} function.
\section{Bootstrap of the standard error}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Bootstrap of the standard error}
Bootstrapping can be nicely illustrated at the example of the
\enterm{standard error} of the mean (\determ{Standardfehler}). The
@ -138,7 +143,9 @@ distribution is the standard error of the mean.
\end{exercise}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Permutation tests}
Statistical tests ask for the probability of a measured value to
originate from a null hypothesis. Is this probability smaller than the
desired \entermde{Signifikanz}{significance level}, the
@ -166,6 +173,12 @@ while we conserve all other statistical properties of the data.
statistically significant.}
\end{figure}
%\subsection{Significance of a difference in the mean}
%See \url{https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests.}
\subsection{Significance of correlations}
A good example for the application of a
\entermde{Permutationstest}{permutaion test} is the statistical
assessment of \entermde[correlation]{Korrelation}{correlations}. Given