modified reg analysis

doc/src/Regression/Regression.do.txt

@@ -1605,53 +1605,16 @@ o It is relatively simple to apply the bootstrap to complex data-collection plan
 
 
 
-\textcite{efron_jackknife_1987} 
-explains that resampling methods
-'scramble' the observations which describe the parameter
-$\vec{\theta}$ in some way. The purpose of scrambling the data is to
-obtain useful estimates of the probability distribution of the
-estimator $\widehat{\vec{\theta}}$. This is often done if deriving the
-distribution of $\widehat{\vec{\theta}}$ by analytical means is
-impossible or inconvenient. The significance of this is reflected in
-that Efron's original paper has more than 16 000 citations by early
-spring 2018. Although these citations have come from all the sciences,
-a lot of work has been done by statisticians and mathematicians. On
-'Web of Science', a search for the topic \textit{bootstrap} returns
-nearly 6 500 papers in journals on statistics and probability theory
-alone. A similar search on 'Scopus' returns more than 7 000 papers in
-the field of mathematics. In addition, there has been a renaissance in
-the study of resampling methods in the 21st century, with more than 6
-000 papers in just 18 years in mathematics. Part of the reason is
-that, even though the ideas which will be presented here seem innocent
-and simple, the required mathematics is deep. In fact, there exists
-conjectures too deep for present mathematics
-\parencite{efron_jackknife_1987}. This will become apparent to us
-because often we will only give intuitive explanations for why the
-methods are valid. We could have done substantially more with measure
-theory in place, but this is not economical in light of the present
-results. However, using our introduction to real analysis, it is
-possible to state and understand a few results in some detail. See for
-example theorem \ref{thm:independent_strap_frechet}.\\ \\ Two famous
-resampling methods are \textit{the independent bootstrap} and
-\textit{the jackknife}. It would make most sense to start by
-discussing the independent bootstrap, because the jackknife method
-follows by making a linearization of the parameters of interest
-\parencite{efron_jackknife_1987,efron_bootstrap_1979}. As such, the
-jackknife is a special case of the independent bootstrap
-\parencite{efron_jackknife_1987}. Still, the jackknife was made
+Two famous
+resampling methods are \textit{the independent bootstrap} and \textit{the jackknife}. 
+
+The jackknife is a special case of the independent bootstrap. Still, the jackknife was made
 popular prior to the independent bootstrap. And as the popularity of
-the independent bootstrap soared, new variants, such as \textit{the
-  dependent bootstrap}\footnote{We will only consider non-parametric
-  bootstrap, but there exists a popular variant called parametric
-  bootstrap, which assumes knowledge of the probability distribution
-  of the observations} or stationary bootstrap were introduced, see
-for example \textcite{politis_stationary_1994} or
-\textcite{politis_automatic_2006}. There also exists textbooks on the
-subject. The mathematical complexity of the latter variants is also
-greater, and consequently it is pedagogical to introduce the methods
-in this order.\\ \\ The Jackknife and independent bootstrap work for
-independent, identically distributed random variables
-\parencite{efron_jackknife_1987}. If these conditions are not
+the independent bootstrap soared, new variants, such as _the dependent bootstrap_.
+
+The Jackknife and independent bootstrap work for
+independent, identically distributed random variables.
+If these conditions are not
 satisfied, the methods will fail. This is important for the results of
 the thesis, because here the variables are dependent, and we will need
 the dependent bootstrap. Yet, it should be said that if the data are