diff --git a/bootstrap/lecture/bootstrap-chapter.tex b/bootstrap/lecture/bootstrap-chapter.tex index 845b6b1..b61d395 100644 --- a/bootstrap/lecture/bootstrap-chapter.tex +++ b/bootstrap/lecture/bootstrap-chapter.tex @@ -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} diff --git a/bootstrap/lecture/bootstrap.tex b/bootstrap/lecture/bootstrap.tex index 667c833..20f01c2 100644 --- a/bootstrap/lecture/bootstrap.tex +++ b/bootstrap/lecture/bootstrap.tex @@ -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