\documentclass[a4paper, 11pt]{article}

%%% packages

%\usepackage{german}
%\usepackage[german]{babel}
\usepackage[latin1]{inputenc}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{verbatim}
\usepackage{epsfig}
\usepackage{fleqn}
\usepackage{color}
%\usepackage{titlesec}
%\usepackage{titletoc}
\usepackage[colorlinks=true, linkcolor=blue, anchorcolor=blue,
											citecolor=blue, filecolor=blue, menucolor=blue, pagecolor=blue,
											urlcolor=blue, plainpages=false, pdfpagelabels]{hyperref}
										
%\usepackage{mathrsfs}
%\usepackage{eufrak}
%\usepackage[mathcal]{euscript}
\usepackage{graphicx}
%\usepackage{multicol}
\usepackage{amsbsy}
\usepackage{amscd}
\usepackage{bm}
%\usepackage[ruled]{algorithm2e}
%\usepackage[nonamebreak,square,numbers]{natbib}
\usepackage{natbib}
%\usepackage{tikz}
%\citestyle{authoryear,aysep={},yysep={;},numbers}

%%% page layout

%\parindent0pt
%\parskip1.2ex
%\oddsidemargin0.5cm
%\evensidemargin+20pt
%\addtolength{\evensidemargin}{-2cm}
%\addtolength{\marginparwidth}{3cm}
%\addtolength{\marginparsep}{3cm}
%\addtolength{\oddsidemargin}{-2cm}
%\topmargin-1.8cm
%\textheight22cm
%\textwidth15.5cm
%\headsep0.5cm
%\setlength{\footskip}{0.5cm}
%\linespread
%\usepackage{E:/R_Installation/share/texmf/Sweave}
%\pagestyle{headings}

\parindent0pt
\parskip1ex
\oddsidemargin-0.6cm
\evensidemargin-0.6cm
\topmargin-1.5cm
\textheight24cm
\textwidth15.1cm
\headsep0.5cm
\footskip1cm
%\usepackage{E:/R_Installation/share/texmf/Sweave}
\pagestyle{plain}


%%% Operators

\newcommand{\R}{{\mathbb R}}
\newcommand{\N}{{\mathbb N}}
\newcommand{\C}{{\mathbb C}}
\newcommand{\K}{{\mathbb K}}
\newcommand{\Z}{{\mathbb Z}}
\DeclareMathOperator*{\var}{var}
\DeclareMathOperator*{\cov}{cov}
\DeclareMathOperator*{\cor}{cor}
\DeclareMathOperator*{\tr}{tr}
\DeclareMathOperator*{\diag}{diag}
\DeclareMathOperator*{\E}{E}
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
\DeclareMathOperator*{\p}{P}
\providecommand{\wt}[1]{\widetilde{#1}}
\providecommand{\wh}[1]{\widehat{#1}}

\providecommand{\ov}[1]{\overline{#1}}
\providecommand{\norm}[1]{\left \lVert#1 \right \rVert}
\newcommand{\scp}[2]{\left\langle#1, #2\right\rangle}
%\newcommand{\op}[2]{\textbf#1\left[#2 \right]}
\providecommand{\M}[1]{\mathbf#1}
%\providecommand{\B}[1]{\bm#1}
\providecommand{\mc}[1]{\mathcal#1}
%\providecommand{\ms}[1]{\mathscr#1}
\providecommand{\T}{\top}
\newcommand{\sign}{\operatorname{sign}}
%\newcommand{\argmin}{\operatorname{argmin}}
%\newcommand{\argmax}{\operatorname{argmax}}
\newcommand{\logit}{\operatorname{logit}}
\newcommand{\corr}{\mathrel{\widehat{=}}}
\newcommand{\lin}{\text{lin} \; }
\newcommand{\dev}[2]{\Big\lvert _{{#1}={#2}}}
\newcommand{\devs}[1]{\Big\lvert _{{#1}}}
\newcommand{\bou}[2]{\Big\lvert _{{#1}}^{#2}}
\newcommand{\indep}{\rotatebox[origin=c]{90}{$\models$}}

\newcommand{\func}[5]{%
	\begin{tabular}[t]{lrcl}
	$#1$~: & $#2$ & $\rightarrow$ & $#3$\\
	& $#4$ & $\mapsto$ & $#5$
	\end{tabular}}
\newcommand{\blanco}[1]{  }

\newcommand{\deriv}[3]{%
\ifthenelse{#1 = 1}{\frac{d\,#2}{d\,#3}}{\frac{d^{{#1}} #2}{d{#3}^{{#1}}}}
} 


\newcommand{\partials}[3]{%
\ifthenelse{#1 = 1}{\frac{\partial\,#2}{\partial\,#3}}{\frac{\partial^{#1}
    #2}{\partial#3^{#1}}}
} 

\def\su{\sum_{i=1}^n}
%\def\lap{\Delta}
%\def\etall{\mbox{{\it et al., }}}
%\def\etal{\mbox{{\it et al. }}}
%\def\theequation{\arabic{equation}}
\def\sdef{\stackrel{\text{def}}{\Leftrightarrow}}
\def \coloneq{\mathrel{\mathop:}=}
\def \invcoloneq{=\mathrel{\mathop:}}
%\def\ch{\varphi}  
\def \ninf{n \; \rightarrow \; \infty}   
%\numberwithin{equation}{section} 


\newtheorem{theo}{Theorem}
\newtheorem{propo}{Theorem}
\newtheorem{definitio}{Theorem}
\newtheorem{definitioA}{Theorem}
\newtheorem{theoA}{Theorem}


\newtheorem{theorem}[theo]{Theorem}
  \newtheorem{defn}[definitio]{Definition}
  \newtheorem{defnA}[definitioA]{Definition A.}
  \newtheorem{theoremA}[theoA]{Theorem A.}
  \newtheorem{prop}[propo]{Proposition}
  

\newenvironment{bew}{\begin{proof}[Proof]}{\end{proof}}
\newenvironment{sketch}{\begin{proof}[Sketch of proof]}{\end{proof}}

%% some common estimators for the sparsity section


%\def\ols{\wh{\bm{\beta}}^{\text{ols}}}
%\def\ridge{\wh{\bm{\beta}}^{\text{ridge}}}  
%\def\lasso{\wh{\bm{\beta}}^{\text{lasso}}}

%\newcommand{\est}[1]{%
%\wh{\bm{\beta}}^{\text{#1}}
%} 

%\newcommand{\estj}[2]{%
%\wh{\beta}_{{#2}}^{\text{{#1}}}
%} 

%\newcommand{\xj}[1]{%
%\bm{x}_{\bullet #1}
%} 

\newcommand{\conv}[1]{%
\stackrel{\text{{#1}}}{\rightarrow}
} 

%%% algorithmic section

%\newcommand{\mycite}[1]{\citeauthor{#1} (\citeyear{#1}, \citep{#1})}

\newcommand{\ik}{^{(k)}}
\newcommand{\LL}{\bm{\Lambda}}
\newcommand{\La}{\bm{L}}
\newcommand{\Si}{\bm{\Sigma}}
\newcommand{\bk}{\bm{\beta}\ik}
\newcommand{\mk}{\bm{\mu}\ik}
\newcommand{\nk}{n\ik}
\newcommand{\bhk}{\wh{\bm{\beta}}\ik}
\newcommand{\mhk}{\wh{\bm{\mu}}\ik}
\newcommand{\Sih}{\wh{\Si}}
\newcommand{\X}{\bm{X}}
\newcommand{\Xt}{\bm{X}^{\T}}


%\newcommand{\gr}[1]{%
%-\nabla \ell(#1) 
%} 

%\newcommand{\he}[1]{%
%\bm{F}(#1) 
%} 

%\newcommand{\lpen}[1]{%
%\ell_{\text{pen}}({#1})
%} 

\def \betak{\wh{\bm{\beta}}^{(k)}}
\def \ass{\leftarrow}

%\usepackage{fancyhdr}
%\pagestyle{fancy}
% with this we ensure that the chapter and section
% headings are in lowercase.
%\renewcommand{\chaptermark}[1]{%
%\leftmark{\thechapter\ #1}}
%\renewcommand{\sectionmark}[1]{%
%\leftmark{\thechapter\ #1}}
%\renewcommand{\sectionmark}[1]{%
%\markright{\thesection\ #1}}
%\fancyhf{} % delete current header and footer
%\fancyhead[LE,RO]{\bfseries\thepage}
%\fancyhead[LO]{\bfseries\leftmark}
%\fancyhead[RE]{\bfseries\rightmark}
%\fancyhead[RE]{\bfseries\leftmark}
%\renewcommand{\headrulewidth}{0.5pt}
%\renewcommand{\footrulewidth}{0pt}
%\addtolength{\headheight}{0.5pt} % space for the rule
%\fancypagestyle{plain}{%
%\fancyhead{} % get rid of headers on plain pages
%\renewcommand{\headrulewidth}{0pt} % and the line
%}

%\titleformat{\chapter}[display]{\Large\filcenter\sffamily}
%{\titlerule[1pt]%
%\vspace{1pt}%
%\titlerule
%\vspace{1pc}%
%\titlerule
%\textbf{\sffamily \LARGE{\chaptertitlename} \thechapter}}
%{1pc}
%{\titlerule
%\vspace{1pc}%
%\bfseries\LARGE}

%\titlespacing{\chapter}{0pt}{*0.2}{*4}

%\titleformat{\section}
%{\titlerule
%\vspace{1ex}
%\large \bfseries
%}{\thesection.}{0.5em}{}















