\ProvidesPackage{defsAndPackages}


\newcommand{\x}{\mathbf{x}}
\newcommand{\X}{\mathbb{X}}
\newcommand{\A}{\mathbb{A}}
\newcommand{\B}{\mathbb{B}}
\newcommand{\hbeta}{\hat{\beta}}
\newcommand{\MSE}{\textrm{MSE}} 
\newcommand{\AMSE}{\textrm{AMSE}} 
\newcommand{\hbetag}{\hbeta_{\textrm{good}}} 
\newcommand{\hbetar}[1]{\hat{\beta}_{\textrm{ridge},#1}}
\renewcommand{\v}{\mathbf{v}}
\renewcommand{\u}{\mathbf{u}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\V}{\mathbb{V}}
\newcommand{\R}{\mathbb{R}}

\newcommand{\data}{\mathcal{D}}
\newcommand{\F}{\mathcal{F}}

\renewcommand{\P}{\mathbb{P}}
\newcommand{\tr}{\textrm{trace}}
\newcommand{\rank}{\textrm{rank}}
\newcommand{\df}{\textrm{df}}
\newcommand{\train}{\hat{R}_{\textrm{train}}}
\newcommand{\opt}{\textrm{opt}}
\newcommand{\opthat}{\widehat{\textrm{opt}}}
\newcommand{\gichat}{\hat{R}_{\textrm{gic}}}
\newcommand{\gic}{R_{\textrm{gic}}}
\newcommand{\VV}{\mathcal{V}}
\newcommand{\CVV}{\textrm{CV}_{\VV}}
\newcommand{\CV}[1]{\textrm{CV}_{#1}}
\newcommand{\norm}[1]{\left|\left| #1 \right|\right|}

