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[bootstrap] updated text and exercises

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Jan Benda
2019-12-03 08:57:40 +01:00
parent bfad4ac339
commit 006fa998cc
11 changed files with 72 additions and 69 deletions
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bootstrap/lecture/bootstrap.tex
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@@ -84,9 +84,11 @@ standard errors and confidence intervals).
Bootstrapping methods create bootstrapped samples from a SRS by
resampling. The bootstrapped samples are used to estimate the sampling
distribution of a statistical measure. The bootstrapped samples have
the same size as the original sample and are created by randomly drawing with
replacement. That is, each value of the original sample can occur
once, multiple time, or not at all in a bootstrapped sample.
the same size as the original sample and are created by randomly
drawing with replacement. That is, each value of the original sample
can occur once, multiple time, or not at all in a bootstrapped
sample. This can be implemented by generating random indices into the
data set using the \code{randi()} function.
\section{Bootstrap of the standard error}
@@ -165,13 +167,13 @@ data points $(x_i, y_i)$. By calculating the correlation coefficient
we can quantify how strongly $y$ depends on $x$. The correlation
coefficient alone, however, does not tell whether the correlation is
significantly different from a random correlation. The null hypothesis
for such a situation would be that $y$ does not depend on $x$. In
for such a situation is that $y$ does not depend on $x$. In
order to perform a permutation test, we need to destroy the
correlation by permuting the $(x_i, y_i)$ pairs, i.e. we rearrange the
$x_i$ and $y_i$ values in a random fashion. Generating many sets of
random pairs and computing the resulting correlation coefficients,
random pairs and computing the resulting correlation coefficients
yields a distribution of correlation coefficients that result
randomnly from uncorrelated data. By comparing the actually measured
randomly from uncorrelated data. By comparing the actually measured
correlation coefficient with this distribution we can directly assess
the significance of the correlation
(figure\,\ref{permutecorrelationfig}).
@@ -183,10 +185,10 @@ Estimate the statistical significance of a correlation coefficient.
and calculate the respective $y$-values according to $y_i =0.2 \cdot x_i + u_i$
where $u_i$ is a random number drawn from a normal distribution.
\item Calculate the correlation coefficient.
\item Generate the distribution according to the null hypothesis by
generating uncorrelated pairs. For this permute $x$- and $y$-values
\matlabfun{randperm()} 1000 times and calculate for each
permutation the correlation coefficient.
\item Generate the distribution of the null hypothesis by generating
uncorrelated pairs. For this permute $x$- and $y$-values
\matlabfun{randperm()} 1000 times and calculate for each permutation
the correlation coefficient.
\item Read out the 95\,\% percentile from the resulting distribution
of the null hypothesis and compare it with the correlation
coefficient computed from the original data.