[bootstrap] split exercises

bootstrap/exercises/Makefile

@@ -1,4 +1,3 @@
-TEXFILES=resampling-1.tex
+TEXFILES=$(wildcard resampling-?.tex)
-# resampling2.tex
 
 include ../../exercises.mk

bootstrap/exercises/resampling-1.tex

@@ -18,69 +18,6 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \question \qt{Read chapter 7 of the script on ``resampling methods''!}\vspace{-3ex}
 
-\question \qt{Bootstrap the standard error of the mean}
-We want to compute the standard error of the mean of a data set by
-means of the bootstrap method and compare the result with the formula
-``standard deviation divided by the square-root of $n$''.
-\begin{parts}
-  \part Download the file \code{thymusglandweights.dat} from Ilias.
-  This is a data set of the weights of the thymus glands of 14-day old chicken embryos
-  measured in milligram.
-  \part Load the data into Matlab (\code{load} function).
-  \part Compute histogram, mean, and standard error of the mean of the first 80 data points.
-  \part Compute the standard error of the mean of the first 80 data
-  points by bootstrapping the data 500 times. Write a function that
-  bootstraps the standard error of the mean of a given data set. The
-  function should also return a vector with the bootstrapped means.
-  \part Compute the 95\,\% confidence interval for the mean from the
-  bootstrap distribution (\code{quantile()} function) --- the
-  interval that contains the true mean with 95\,\% probability.
-  \part Use the whole data set and the bootstrap method for computing
-  the dependence of the standard error of the mean from the sample
-  size $n$.
-  \part Compare your result with the formula for the standard error
-  $\sigma/\sqrt{n}$.
-\end{parts}
-\begin{solution}
-  \lstinputlisting{bootstrapmean.m}
-  \lstinputlisting{bootstraptymus.m}
-  \includegraphics[width=0.5\textwidth]{bootstraptymus-datahist}
-  \includegraphics[width=0.5\textwidth]{bootstraptymus-meanhist}
-  \includegraphics[width=0.5\textwidth]{bootstraptymus-samples}
-\end{solution}
-
-
-\question \qt{Student t-distribution}
-The distribution of Student's t, $t=\bar x/(\sigma_x/\sqrt{n})$, the
-estimated mean $\bar x$ of a data set of size $n$ divided by the
-estimated standard error of the mean $\sigma_x/\sqrt{n}$, where
-$\sigma_x$ is the estimated standard deviation, is not a normal
-distribution but a Student-t distribution.  We want to compute the
-Student-t distribution and compare it with the normal distribution.
-\begin{parts}
-\part Generate 100000 normally distributed random numbers.
-\part Draw from these data 1000 samples of size $n=3$, 5, 10, and
-50. For each sample size $n$ ...
-\part ... compute the mean $\bar x$ of the samples and plot the
-probability density of these means.
-\part ... compare the resulting probability densities with corresponding
-normal distributions.
-\part ... compute Student's $t=\bar x/(\sigma_x/\sqrt{n})$ and compare its
-distribution with the normal distribution with standard deviation of
-one. Is $t$ normally distributed? Under which conditions is $t$
-normally distributed?
-\end{parts}
-\newsolutionpage
-\begin{solution}
-  \lstinputlisting{tdistribution.m}
-  \includegraphics[width=1\textwidth]{tdistribution-n03}\\
-  \includegraphics[width=1\textwidth]{tdistribution-n05}\\
-  \includegraphics[width=1\textwidth]{tdistribution-n10}\\
-  \includegraphics[width=1\textwidth]{tdistribution-n50}
-\end{solution}
-
-
-\continue
 \question \qt{Permutation test of correlations} \label{correlationtest}
 We want to compute the significance of a correlation by means of a permutation test.
 \begin{parts}
@@ -109,6 +46,7 @@ y = randn(n, 1) + a*x;
   \includegraphics[width=1\textwidth]{correlationsignificance}
 \end{solution}
 
+\newsolutionpage
 \question \qt{Bootstrap the correlation coefficient} 
 The permutation test generates the distribution of the null hypothesis
 of uncorrelated data and we check whether the correlation coefficient
@@ -137,7 +75,7 @@ We take the same data set that we have generated in exercise
 \end{solution}
 
 
-\continuepage 
+\continue 
 \question \qt{Permutation test of difference of means}
 We want to test whether two data sets come from distributions that
 differ in their mean by means of a permutation test.

bootstrap/exercises/resampling-2.tex

@@ -0,0 +1,84 @@
+\documentclass[12pt,a4paper,pdftex]{exam}
+
+\newcommand{\exercisetopic}{Resampling}
+\newcommand{\exercisenum}{X2}
+\newcommand{\exercisedate}{December 14th, 2020}
+
+\input{../../exercisesheader}
+
+\firstpagefooter{Prof. Dr. Jan Benda}{}{jan.benda@uni-tuebingen.de}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+
+\input{../../exercisestitle}
+
+\begin{questions}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\question \qt{Read chapter 7 of the script on ``resampling methods''!}\vspace{-3ex}
+
+\question \qt{Bootstrap the standard error of the mean}
+We want to compute the standard error of the mean of a data set by
+means of the bootstrap method and compare the result with the formula
+``standard deviation divided by the square-root of $n$''.
+\begin{parts}
+  \part Download the file \code{thymusglandweights.dat} from Ilias.
+  This is a data set of the weights of the thymus glands of 14-day old chicken embryos
+  measured in milligram.
+  \part Load the data into Matlab (\code{load} function).
+  \part Compute histogram, mean, and standard error of the mean of the first 80 data points.
+  \part Compute the standard error of the mean of the first 80 data
+  points by bootstrapping the data 500 times. Write a function that
+  bootstraps the standard error of the mean of a given data set. The
+  function should also return a vector with the bootstrapped means.
+  \part Compute the 95\,\% confidence interval for the mean from the
+  bootstrap distribution (\code{quantile()} function) --- the
+  interval that contains the true mean with 95\,\% probability.
+  \part Use the whole data set and the bootstrap method for computing
+  the dependence of the standard error of the mean from the sample
+  size $n$.
+  \part Compare your result with the formula for the standard error
+  $\sigma/\sqrt{n}$.
+\end{parts}
+\begin{solution}
+  \lstinputlisting{bootstrapmean.m}
+  \lstinputlisting{bootstraptymus.m}
+  \includegraphics[width=0.5\textwidth]{bootstraptymus-datahist}
+  \includegraphics[width=0.5\textwidth]{bootstraptymus-meanhist}
+  \includegraphics[width=0.5\textwidth]{bootstraptymus-samples}
+\end{solution}
+
+
+\question \qt{Student t-distribution}
+The distribution of Student's t, $t=\bar x/(\sigma_x/\sqrt{n})$, the
+estimated mean $\bar x$ of a data set of size $n$ divided by the
+estimated standard error of the mean $\sigma_x/\sqrt{n}$, where
+$\sigma_x$ is the estimated standard deviation, is not a normal
+distribution but a Student-t distribution.  We want to compute the
+Student-t distribution and compare it with the normal distribution.
+\begin{parts}
+\part Generate 100000 normally distributed random numbers.
+\part Draw from these data 1000 samples of size $n=3$, 5, 10, and
+50. For each sample size $n$ ...
+\part ... compute the mean $\bar x$ of the samples and plot the
+probability density of these means.
+\part ... compare the resulting probability densities with corresponding
+normal distributions.
+\part ... compute Student's $t=\bar x/(\sigma_x/\sqrt{n})$ and compare its
+distribution with the normal distribution with standard deviation of
+one. Is $t$ normally distributed? Under which conditions is $t$
+normally distributed?
+\end{parts}
+\newsolutionpage
+\begin{solution}
+  \lstinputlisting{tdistribution.m}
+  \includegraphics[width=1\textwidth]{tdistribution-n03}\\
+  \includegraphics[width=1\textwidth]{tdistribution-n05}\\
+  \includegraphics[width=1\textwidth]{tdistribution-n10}\\
+  \includegraphics[width=1\textwidth]{tdistribution-n50}
+\end{solution}
+
+\end{questions}
+
+\end{document}