renamed package (naming conflict with bioconductor)

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%%
%% This is file `jss.cls'
\def\fileversion{3.2}
\def\filename{jss}
\def\filedate{2020/12/09}
%%
%% Package `jss' to use with LaTeX2e for JSS publications (http://www.jstatsoft.org/)
%% License: GPL-2 | GPL-3
%% Copyright: (C) Achim Zeileis
%% Please report errors to Achim.Zeileis@R-project.org
%%
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{jss}[\filedate\space\fileversion\space jss class by Achim Zeileis]
%% options
\newif\if@article
\newif\if@codesnippet
\newif\if@bookreview
\newif\if@softwarereview
\newif\if@review
\newif\if@shortnames
\newif\if@nojss
\newif\if@notitle
\newif\if@noheadings
\newif\if@nofooter
\@articletrue
\@codesnippetfalse
\@bookreviewfalse
\@softwarereviewfalse
\@reviewfalse
\@shortnamesfalse
\@nojssfalse
\@notitlefalse
\@noheadingsfalse
\@nofooterfalse
\DeclareOption{article}{\@articletrue%
\@codesnippetfalse \@bookreviewfalse \@softwarereviewfalse}
\DeclareOption{codesnippet}{\@articlefalse%
\@codesnippettrue \@bookreviewfalse \@softwarereviewfalse}
\DeclareOption{bookreview}{\@articlefalse%
\@codesnippetfalse \@bookreviewtrue \@softwarereviewfalse}
\DeclareOption{softwarereview}{\@articlefalse%
\@codesnippetfalse \@bookreviewfalse \@softwarereviewtrue}
\DeclareOption{shortnames}{\@shortnamestrue}
\DeclareOption{nojss}{\@nojsstrue}
\DeclareOption{notitle}{\@notitletrue}
\DeclareOption{noheadings}{\@noheadingstrue}
\DeclareOption{nofooter}{\@nofootertrue}
\ProcessOptions
\LoadClass[11pt,a4paper,twoside]{article}
%% required packages
\RequirePackage{graphicx,color,ae,fancyvrb}
\RequirePackage[T1]{fontenc}
\IfFileExists{upquote.sty}{\RequirePackage{upquote}}{}
\IfFileExists{lmodern.sty}{\RequirePackage{lmodern}}{}
%% bibliography
\if@shortnames
\usepackage[authoryear,round]{natbib}
\else
\usepackage[authoryear,round,longnamesfirst]{natbib}
\fi
\bibpunct{(}{)}{;}{a}{}{,}
\bibliographystyle{jss}
%% page layout
\topmargin 0pt
\textheight 46\baselineskip
\advance\textheight by \topskip
\oddsidemargin 0.1in
\evensidemargin 0.15in
\marginparwidth 1in
\oddsidemargin 0.125in
\evensidemargin 0.125in
\marginparwidth 0.75in
\textwidth 6.125in
%% paragraphs
\setlength{\parskip}{0.7ex plus0.1ex minus0.1ex}
\setlength{\parindent}{0em}
%% for all publications
\newcommand{\Address}[1]{\def\@Address{#1}}
\newcommand{\Plaintitle}[1]{\def\@Plaintitle{#1}}
\newcommand{\Shorttitle}[1]{\def\@Shorttitle{#1}}
\newcommand{\Plainauthor}[1]{\def\@Plainauthor{#1}}
\newcommand{\Volume}[1]{\def\@Volume{#1}}
\newcommand{\Year}[1]{\def\@Year{#1}}
\newcommand{\Month}[1]{\def\@Month{#1}}
\newcommand{\Issue}[1]{\def\@Issue{#1}}
\newcommand{\Submitdate}[1]{\def\@Submitdate{#1}}
%% for articles and code snippets
\newcommand{\Acceptdate}[1]{\def\@Acceptdate{#1}}
\newcommand{\Abstract}[1]{\def\@Abstract{#1}}
\newcommand{\Keywords}[1]{\def\@Keywords{#1}}
\newcommand{\Plainkeywords}[1]{\def\@Plainkeywords{#1}}
%% for book and software reviews
\newcommand{\Reviewer}[1]{\def\@Reviewer{#1}}
\newcommand{\Booktitle}[1]{\def\@Booktitle{#1}}
\newcommand{\Bookauthor}[1]{\def\@Bookauthor{#1}}
\newcommand{\Publisher}[1]{\def\@Publisher{#1}}
\newcommand{\Pubaddress}[1]{\def\@Pubaddress{#1}}
\newcommand{\Pubyear}[1]{\def\@Pubyear{#1}}
\newcommand{\ISBN}[1]{\def\@ISBN{#1}}
\newcommand{\Pages}[1]{\def\@Pages{#1}}
\newcommand{\Price}[1]{\def\@Price{#1}}
\newcommand{\Plainreviewer}[1]{\def\@Plainreviewer{#1}}
\newcommand{\Softwaretitle}[1]{\def\@Softwaretitle{#1}}
\newcommand{\URL}[1]{\def\@URL{#1}}
\newcommand{\DOI}[1]{\def\@DOI{#1}}
%% for internal use
\newcommand{\Seriesname}[1]{\def\@Seriesname{#1}}
\newcommand{\Hypersubject}[1]{\def\@Hypersubject{#1}}
\newcommand{\Hyperauthor}[1]{\def\@Hyperauthor{#1}}
\newcommand{\Footername}[1]{\def\@Footername{#1}}
\newcommand{\Firstdate}[1]{\def\@Firstdate{#1}}
\newcommand{\Seconddate}[1]{\def\@Seconddate{#1}}
\newcommand{\Reviewauthor}[1]{\def\@Reviewauthor{#1}}
%% defaults
\author{Firstname Lastname\\Affiliation}
\title{Title}
\Abstract{---!!!---an abstract is required---!!!---}
\Plainauthor{\@author}
\Volume{VV}
\Year{YYYY}
\Month{MMMMMM}
\Issue{II}
\Submitdate{yyyy-mm-dd}
\Acceptdate{yyyy-mm-dd}
\Address{
Firstname Lastname\\
Affiliation\\
Address, Country\\
E-mail: \email{name@address}\\
URL: \url{http://link/to/webpage/}
}
\Reviewer{Firstname Lastname\\Affiliation}
\Plainreviewer{Firstname Lastname}
\Booktitle{Book Title}
\Bookauthor{Book Author}
\Publisher{Publisher}
\Pubaddress{Publisher's Address}
\Pubyear{YYY}
\ISBN{x-xxxxx-xxx-x}
\Pages{xv + 123}
\Price{USD 69.95 (P)}
\URL{http://link/to/webpage/}
\DOI{10.18637/jss.v000.i00}
\if@article
\Seriesname{Issue}
\Hypersubject{Journal of Statistical Software}
\Plaintitle{\@title}
\Shorttitle{\@title}
\Plainkeywords{\@Keywords}
\fi
\if@codesnippet
\Seriesname{Code Snippet}
\Hypersubject{Journal of Statistical Software -- Code Snippets}
\Plaintitle{\@title}
\Shorttitle{\@title}
\Plainkeywords{\@Keywords}
\fi
\if@bookreview
\Seriesname{Book Review}
\Hypersubject{Journal of Statistical Software -- Book Reviews}
\Plaintitle{\@Booktitle}
\Shorttitle{\@Booktitle}
\Reviewauthor{\@Bookauthor\\
\@Publisher, \@Pubaddress, \@Pubyear.\\
ISBN~\@ISBN. \@Pages~pp. \@Price.\\
\url{\@URL}}
\Plainkeywords{}
\@reviewtrue
\fi
\if@softwarereview
\Seriesname{Software Review}
\Hypersubject{Journal of Statistical Software -- Software Reviews}
\Plaintitle{\@Softwaretitle}
\Shorttitle{\@Softwaretitle}
\Booktitle{\@Softwaretitle}
\Reviewauthor{\@Publisher, \@Pubaddress. \@Price.\\
\url{\@URL}}
\Plainkeywords{}
\@reviewtrue
\fi
\if@review
\Hyperauthor{\@Plainreviewer}
\Keywords{}
\Footername{Reviewer}
\Firstdate{\textit{Published:} \@Submitdate}
\Seconddate{}
\else
\Hyperauthor{\@Plainauthor}
\Keywords{---!!!---at least one keyword is required---!!!---}
\Footername{Affiliation}
\Firstdate{\textit{Submitted:} \@Submitdate}
\Seconddate{\textit{Accepted:} \@Acceptdate}
\fi
%% Sweave(-like)
\DefineVerbatimEnvironment{Sinput}{Verbatim}{fontshape=sl}
\DefineVerbatimEnvironment{Soutput}{Verbatim}{}
\DefineVerbatimEnvironment{Scode}{Verbatim}{fontshape=sl}
\newenvironment{Schunk}{}{}
\DefineVerbatimEnvironment{Code}{Verbatim}{}
\DefineVerbatimEnvironment{CodeInput}{Verbatim}{fontshape=sl}
\DefineVerbatimEnvironment{CodeOutput}{Verbatim}{}
\newenvironment{CodeChunk}{}{}
\setkeys{Gin}{width=0.8\textwidth}
%% footer
\newlength{\footerskip}
\setlength{\footerskip}{2.5\baselineskip plus 2ex minus 0.5ex}
\newcommand{\makefooter}{%
\vspace{\footerskip}
\if@nojss
\begin{samepage}
\textbf{\large \@Footername: \nopagebreak}\\[.3\baselineskip] \nopagebreak
\@Address \nopagebreak
\end{samepage}
\else
\begin{samepage}
\textbf{\large \@Footername: \nopagebreak}\\[.3\baselineskip] \nopagebreak
\@Address \nopagebreak
\vfill
\hrule \nopagebreak
\vspace{.1\baselineskip}
{\fontfamily{pzc} \fontsize{13}{15} \selectfont Journal of Statistical Software}
\hfill
\url{http://www.jstatsoft.org/}\\ \nopagebreak
published by the Foundation for Open Access Statistics
\hfill
\url{http://www.foastat.org/}\\[.3\baselineskip] \nopagebreak
{\@Month{} \@Year, Volume~\@Volume, \@Seriesname~\@Issue}
\hfill
\@Firstdate\\ \nopagebreak
{\href{https://doi.org/\@DOI}{\tt doi:\@DOI}}
\hfill
\@Seconddate \nopagebreak
\vspace{.3\baselineskip}
\hrule
\end{samepage}
\fi
}
\if@nofooter
%% \AtEndDocument{\makefooter}
\else
\AtEndDocument{\makefooter}
\fi
%% required packages
\RequirePackage{hyperref}
%% new \maketitle
\def\@myoddhead{
{\color{white} JSS}\\[-1.42cm]
\hspace{-2em} \includegraphics[height=23mm,keepaspectratio]{jsslogo} \hfill
\parbox[b][23mm]{118mm}{\hrule height 3pt
\center{
{\fontfamily{pzc} \fontsize{28}{32} \selectfont Journal of Statistical Software}
\vfill
{\it \small \@Month{} \@Year, Volume~\@Volume, \@Seriesname~\@Issue.%
\hfill \href{https://doi.org/\@DOI}{doi:\,\@DOI}}}\\[0.1cm]
\hrule height 3pt}}
\if@review
\renewcommand{\maketitle}{
\if@nojss
%% \@oddhead{\@myoddhead}\\[3\baselineskip]
\else
\@oddhead{\@myoddhead}\\[3\baselineskip]
\fi
{\large
\noindent
Reviewer: \@Reviewer
\vspace{\baselineskip}
\hrule
\vspace{\baselineskip}
\textbf{\@Booktitle}
\begin{quotation} \noindent
\@Reviewauthor
\end{quotation}
\vspace{0.7\baselineskip}
\hrule
\vspace{1.3\baselineskip}
}
\thispagestyle{empty}
\if@nojss
\markboth{\centerline{\@Shorttitle}}{\centerline{\@Hyperauthor}}
\else
\markboth{\centerline{\@Shorttitle}}{\centerline{\@Hypersubject}}
\fi
\pagestyle{myheadings}
}
\else
\def\maketitle{
\if@nojss
%% \@oddhead{\@myoddhead} \par
\else
\@oddhead{\@myoddhead} \par
\fi
\begingroup
\def\thefootnote{\fnsymbol{footnote}}
\def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}}
\long\def\@makefntext##1{\parindent 1em\noindent
\hbox to1.8em{\hss $\m@th ^{\@thefnmark}$}##1}
\@maketitle \@thanks
\endgroup
\setcounter{footnote}{0}
\if@noheadings
%% \markboth{\centerline{\@Shorttitle}}{\centerline{\@Hypersubject}}
\else
\thispagestyle{empty}
\if@nojss
\markboth{\centerline{\@Shorttitle}}{\centerline{\@Hyperauthor}}
\else
\markboth{\centerline{\@Shorttitle}}{\centerline{\@Hypersubject}}
\fi
\pagestyle{myheadings}
\fi
\let\maketitle\relax \let\@maketitle\relax
\gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax
}
\def\@maketitle{\vbox{\hsize\textwidth \linewidth\hsize
\if@nojss
%% \vskip 1in
\else
\vskip 1in
\fi
{\centering
{\LARGE\bf \@title\par}
\vskip 0.2in plus 1fil minus 0.1in
{
\def\and{\unskip\enspace{\rm and}\enspace}%
\def\And{\end{tabular}\hss \egroup \hskip 1in plus 2fil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\large\bf\rule{\z@}{24pt}\ignorespaces}%
\def\AND{\end{tabular}\hss\egroup \hfil\hfil\egroup
\vskip 0.1in plus 1fil minus 0.05in
\hbox to \linewidth\bgroup\rule{\z@}{10pt} \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\large\bf\rule{\z@}{24pt}\ignorespaces}
\hbox to \linewidth\bgroup\rule{\z@}{10pt} \hfil\hfil
\hbox to 0pt\bgroup\hss \begin{tabular}[t]{c}\large\bf\rule{\z@}{24pt}\@author
\end{tabular}\hss\egroup
\hfil\hfil\egroup}
\vskip 0.3in minus 0.1in
\hrule
\begin{abstract}
\@Abstract
\end{abstract}}
\textit{Keywords}:~\@Keywords.
\vskip 0.1in minus 0.05in
\hrule
\vskip 0.2in minus 0.1in
}}
\fi
%% sections, subsections, and subsubsections
\newlength{\preXLskip}
\newlength{\preLskip}
\newlength{\preMskip}
\newlength{\preSskip}
\newlength{\postMskip}
\newlength{\postSskip}
\setlength{\preXLskip}{1.8\baselineskip plus 0.5ex minus 0ex}
\setlength{\preLskip}{1.5\baselineskip plus 0.3ex minus 0ex}
\setlength{\preMskip}{1\baselineskip plus 0.2ex minus 0ex}
\setlength{\preSskip}{.8\baselineskip plus 0.2ex minus 0ex}
\setlength{\postMskip}{.5\baselineskip plus 0ex minus 0.1ex}
\setlength{\postSskip}{.3\baselineskip plus 0ex minus 0.1ex}
\newcommand{\jsssec}[2][default]{\vskip \preXLskip%
\pdfbookmark[1]{#1}{Section.\thesection.#1}%
\refstepcounter{section}%
\centerline{\textbf{\Large \thesection. #2}} \nopagebreak
\vskip \postMskip \nopagebreak}
\newcommand{\jsssecnn}[1]{\vskip \preXLskip%
\centerline{\textbf{\Large #1}} \nopagebreak
\vskip \postMskip \nopagebreak}
\newcommand{\jsssubsec}[2][default]{\vskip \preMskip%
\pdfbookmark[2]{#1}{Subsection.\thesubsection.#1}%
\refstepcounter{subsection}%
\textbf{\large \thesubsection. #2} \nopagebreak
\vskip \postSskip \nopagebreak}
\newcommand{\jsssubsecnn}[1]{\vskip \preMskip%
\textbf{\large #1} \nopagebreak
\vskip \postSskip \nopagebreak}
\newcommand{\jsssubsubsec}[2][default]{\vskip \preSskip%
\pdfbookmark[3]{#1}{Subsubsection.\thesubsubsection.#1}%
\refstepcounter{subsubsection}%
{\large \textit{#2}} \nopagebreak
\vskip \postSskip \nopagebreak}
\newcommand{\jsssubsubsecnn}[1]{\vskip \preSskip%
{\textit{\large #1}} \nopagebreak
\vskip \postSskip \nopagebreak}
\newcommand{\jsssimplesec}[2][default]{\vskip \preLskip%
%% \pdfbookmark[1]{#1}{Section.\thesection.#1}%
\refstepcounter{section}%
\textbf{\large #1} \nopagebreak
\vskip \postSskip \nopagebreak}
\newcommand{\jsssimplesecnn}[1]{\vskip \preLskip%
\textbf{\large #1} \nopagebreak
\vskip \postSskip \nopagebreak}
\if@review
\renewcommand{\section}{\secdef \jsssimplesec \jsssimplesecnn}
\renewcommand{\subsection}{\secdef \jsssimplesec \jsssimplesecnn}
\renewcommand{\subsubsection}{\secdef \jsssimplesec \jsssimplesecnn}
\else
\renewcommand{\section}{\secdef \jsssec \jsssecnn}
\renewcommand{\subsection}{\secdef \jsssubsec \jsssubsecnn}
\renewcommand{\subsubsection}{\secdef \jsssubsubsec \jsssubsubsecnn}
\fi
%% colors
\definecolor{Red}{rgb}{0.5,0,0}
\definecolor{Blue}{rgb}{0,0,0.5}
\if@review
\hypersetup{%
hyperindex = {true},
colorlinks = {true},
linktocpage = {true},
plainpages = {false},
linkcolor = {Blue},
citecolor = {Blue},
urlcolor = {Red},
pdfstartview = {Fit},
pdfpagemode = {None},
pdfview = {XYZ null null null}
}
\else
\hypersetup{%
hyperindex = {true},
colorlinks = {true},
linktocpage = {true},
plainpages = {false},
linkcolor = {Blue},
citecolor = {Blue},
urlcolor = {Red},
pdfstartview = {Fit},
pdfpagemode = {UseOutlines},
pdfview = {XYZ null null null}
}
\fi
\if@nojss
\AtBeginDocument{
\hypersetup{%
pdfauthor = {\@Hyperauthor},
pdftitle = {\@Plaintitle},
pdfkeywords = {\@Plainkeywords}
}
}
\else
\AtBeginDocument{
\hypersetup{%
pdfauthor = {\@Hyperauthor},
pdftitle = {\@Plaintitle},
pdfsubject = {\@Hypersubject},
pdfkeywords = {\@Plainkeywords}
}
}
\fi
\if@notitle
%% \AtBeginDocument{\maketitle}
\else
\@ifundefined{AddToHook}{\AtBeginDocument{\maketitle}}{\AddToHook{begindocument}[maketitle]{\maketitle}}
\fi
%% commands
\newcommand\code{\bgroup\@makeother\_\@makeother\~\@makeother\$\@codex}
\def\@codex#1{{\normalfont\ttfamily\hyphenchar\font=-1 #1}\egroup}
%%\let\code=\texttt
\let\proglang=\textsf
\newcommand{\pkg}[1]{{\fontseries{m}\fontseries{b}\selectfont #1}}
\newcommand{\email}[1]{\href{mailto:#1}{\normalfont\texttt{#1}}}
\ifx\csname urlstyle\endcsname\relax
\newcommand\@doi[1]{doi:\discretionary{}{}{}#1}\else
\newcommand\@doi{doi:\discretionary{}{}{}\begingroup
\urlstyle{tt}\Url}\fi
\newcommand{\doi}[1]{\href{https://doi.org/#1}{\normalfont\texttt{\@doi{#1}}}}
\newcommand{\E}{\mathsf{E}}
\newcommand{\VAR}{\mathsf{VAR}}
\newcommand{\COV}{\mathsf{COV}}
\newcommand{\Prob}{\mathsf{P}}
\endinput
%%
%% End of file `jss.cls'.

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\documentclass[article]{jss}
\usepackage{thumbpdf, lmodern} % recommended by `JSS`
\usepackage{amsmath, amssymb, amstext}
% Configure `Sweave`
% Prevent `Sweave` to include its styles (line as is, already in `JSS` styles)
%% need no \usepackage{Sweave.sty}
%\SweaveUTF8
<<echo = FALSE>>=
options(prompt = "R> ", continue = "+ ", width = 70, useFancyQuotes = FALSE)
set.seed(1729) # taxicab number
@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Typesetting %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \newcommand{\class}[1]{`\code{#1}'}
% \newcommand{\fct}[1]{\code{#1()}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Operators %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\t}[1]{{#1}^{T}}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\E}{\operatorname{\mathbb{E}}}
\newcommand{\var}{\operatorname{Var}}
% \newcommand{\sd}{\operatorname{sd}}
% \newcommand{\independent}{\operatorname{\bot\!\!\!\bot}}
% \newcommand{\stiefel}[2]{\operatorname{St_{#2}}(\mathbb{R}^{#1})}
% \newcommand{\grassmann}[2]{\operatorname{Gr_{#2}}(\mathbb{R}^{#1})}
% \newcommand{\orthogonalGroup}[1]{\operatorname{O}(#1)}
% \newcommand{\argmin}{\operatorname*{arg\,min}}
% \newcommand{\argmax}{\operatorname*{arg\,max}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Meta Information %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\author{Daniel Kapla\\TU Wien
\And Lukas Fertl\\TU Wien
\And Efstathia Bura\\TU Wien}
\Plainauthor{Daniel Kapla, Lukas Fertl, Efstathia Bura}
%% - \title{} in title case
%% - \Plaintitle{} without LaTeX markup (if any)
%% - \Shorttitle{} with LaTeX markup (if any), used as running title
\title{Conditional Variance Estimation With the \pkg{CVE} Package in \proglang{R}}
\Plaintitle{Conditional Variance Estimation With the CVE Package in R}
\Shorttitle{The \pkg{CVE} Package}
\Abstract{
Conditional variance estimation (CVE) is a novel sufficient dimension
reduction (SDR) method for regressions satisfying $\E(Y | X) = \E(Y | \t{B} X)$,
where $\t{B}X$ is a lower dimensional projection of the predictors. CVE,
similarly to its main competitor, the mean average variance estimation (MAVE),
is not based on inverse regression, and does not require the restrictive
linearity and constant variance conditions of moment based SDR methods. CVE
is data-driven and applies to additive error regressions with continuous
predictors and link function. Let $Y$ be a real univariate response and $X$
a real $p$-dimensional covariate vector. We assume that the dependence of
$Y$ and $X$ is modelled by
\begin{displaymath}
Y = g(\t{B}X) + \epsilon
\end{displaymath}
where $X$ is independent of $\epsilon$ with positive definite variance-covariance
matrix $\var(X) = \Sigma_X$. $\epsilon$ is a mean zero random variable with
finite $\var(\epsilon) = \E(\epsilon^2)$, $g$ is an unknown, continuous
non-constant function, and $B = (b_1 , ..., b_k)$ is a real $p \times k$
matrix of rank $k \leq p$. Without loss of generality $B$ is assumed to be
orthonormal.
}
%% - \Keywords{} with LaTeX markup, at least one required
%% - \Plainkeywords{} without LaTeX markup (if necessary)
%% - Should be comma-separated and in sentence case.
\Keywords{Dimension reduction, \proglang{R}}
\Plainkeywords{Dimension reduction, R}
%% - \Address{} of at least one author
%% - May contain multiple affiliations for each author
%% (in extra lines, separated by \emph{and}\\).
%% - May contain multiple authors for the same affiliation
%% (in the same first line, separated by comma).
\Address{
Daniel Kapla\\
Technische Universit\"at Wien\\
Institute of Statistics and Mathematical Methods in Economics\\
Faculty of Mathematics and Geoinformation\\
TU Wien, Vienna, Austria\\
E-mail: \email{daniel.kapla@tuwien.ac.at}\\
URL: \url{https://kapla.at}\\
\\
Lukas Fertl\\
Technische Universit\"at Wien\\
Institute of Statistics and Mathematical Methods in Economics\\
Faculty of Mathematics and Geoinformation\\
TU Wien, Vienna, Austria\\
E-mail: \email{lukas.fertl@tuwien.ac.at}\\
\\
Efstathia Bura\\
Technische Universit\"at Wien\\
Institute of Statistics and Mathematical Methods in Economics\\
Faculty of Mathematics and Geoinformation\\
TU Wien, Vienna, Austria
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\section[Introduction: Sufficient dimension reduction in R]{Introduction: Sufficient dimension reduction in \proglang{R}}\label{sec:intro}
A bit of text
<<>>=
library(CVE)
dataset <- function(n, p = 20, p.mix = 0.5, lambda = 1, sd = 0.5) {
B <- rep(1 / sqrt(p), p)
# B <- c(rep(1 / sqrt(p), p / 2), rep(-1 / sqrt(p), p / 2))
X <- matrix(rnorm(n * p), n, p)
X <- X + lambda * (2 * rbinom(n, 1, p.mix) - 1)
Y <- abs(X %*% B) + rnorm(n, 0, sd)
list(B = B, X = X, Y = Y)
}
ds <- dataset(100)
ds.test <- dataset(100)
@
Then we apply both methods, the \code{CVE} and the \code{MAVE} methods
<<>>=
fit.cve <- with(ds, cve(Y ~ X, k = 1))
fit.mave <- with(ds, MAVE::mave(Y ~ X, max.dim = 1, method = "meanMAVE"))
@
Get the estimated reduction matrices
<<>>=
B.cve <- coef(fit.cve, 1)
B.mave <- coef(fit.mave, 1)
@
and compute the prediction errors
<<>>=
Y.hat.cve <- with(ds.test, predict(fit.cve, X, 1))
Y.hat.mave <- with(ds.test, predict(fit.mave, X, 1))
# MSE - cve
mean((ds.test$Y - Y.hat.cve)^2)
# MSE - mave
mean((ds.test$Y - Y.hat.mave)^2)
@
and another bit of text
\newpage % required! Fixes vertical spacing problems with code chunks (last page)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Bibliography %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% - References need to be provided in a .bib BibTeX database.
%% - All references should be made with \cite, \citet, \citep, \citealp etc.
%% - `JSS` - specific markup (\proglang, \pkg, \code) should be used in the .bib.
%% - Titles in the .bib should be in title case.
%% - DOIs should be included where available.
\bibliography{refs}
\end{document}

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@Manual{R,
title = {\proglang{R}: {A} Language and Environment for Statistical Computing},
author = {{\proglang{R} Core Team}},
organization = {\proglang{R} Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2020},
url = {https://www.R-project.org/},
}
@Manual{pkg:MAVE,
title = {\pkg{MAVE}: Methods for Dimension Reduction},
author = {Hang Weiqiang and Xia Yingcun},
year = {2019},
note = {\proglang{R} package version 1.3.10},
url = {https://CRAN.R-project.org/package=MAVE}
}
@Book{pkg:MASS,
title = {Modern Applied Statistics with S},
author = {W. N. Venables and B. D. Ripley},
publisher = {Springer},
edition = {Fourth},
address = {New York},
year = {2002},
note = {ISBN 0-387-95457-0},
url = {http://www.stats.ox.ac.uk/pub/MASS4/}
}
@Manual{pkg:mda,
title = {\pkg{mda}: Mixture and Flexible Discriminant Analysis},
author = {S original by Trevor Hastie & Robert Tibshirani. Original R port by Friedrich Leisch and Kurt Hornik and Brian D. Ripley.},
year = {2017},
note = {\proglang{R} package version 0.4-10},
url = {https://CRAN.R-project.org/package=mda}
}