$$
\newcommand{\esp}[1]{\mathbb{E}\left(#1\right)}
\newcommand{\var}[1]{\mbox{Var}\left(#1\right)}
\newcommand{\deriv}[1]{\dot{#1}(t)}
\newcommand{\prob}[1]{ \mathbb{P}\!(#1)}
\newcommand{\eqdef}{\mathop{=}\limits^{\mathrm{def}}}
\newcommand{\by}{\boldsymbol{y}}
\newcommand{\bc}{\boldsymbol{c}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\def\pmacro{\texttt{p}}
\def\like{{\cal L}}
\def\llike{{\cal LL}}
\def\logit{{\rm logit}}
\def\probit{{\rm probit}}
\def\one{{\rm 1\!I}}
\def\iid{\mathop{\sim}_{\rm i.i.d.}}
\def\simh0{\mathop{\sim}_{H_0}}
\def\df{\texttt{df}}
\def\res{e}
\def\xomega{x}
\newcommand{\argmin}[1]{{\rm arg}\min_{#1}}
\newcommand{\argmax}[1]{{\rm arg}\max_{#1}}
\newcommand{\Rset}{\mbox{$\mathbb{R}$}}
\def\param{\theta}
\def\setparam{\Theta}
\def\xnew{x_{\rm new}}
\def\fnew{f_{\rm new}}
\def\ynew{y_{\rm new}}
\def\nnew{n_{\rm new}}
\def\enew{e_{\rm new}}
\def\Xnew{X_{\rm new}}
\def\hfnew{\widehat{\fnew}}
\def\degree{m}
\def\nbeta{d}
\newcommand{\limite}[1]{\mathop{\longrightarrow}\limits_{#1}}
\def\ka{k{\scriptstyle a}}
\def\ska{k{\scriptscriptstyle a}}
\def\kel{k{\scriptstyle e}}
\def\skel{k{\scriptscriptstyle e}}
\def\cl{C{\small l}}
\def\Tlag{T\hspace{-0.1em}{\scriptstyle lag}}
\def\sTlag{T\hspace{-0.07em}{\scriptscriptstyle lag}}
\def\Tk{T\hspace{-0.1em}{\scriptstyle k0}}
\def\sTk{T\hspace{-0.07em}{\scriptscriptstyle k0}}
\def\thalf{t{\scriptstyle 1/2}}
\newcommand{\Dphi}[1]{\partial_\pphi #1}
\def\asigma{a}
\def\pphi{\psi}
\newcommand{\stheta}{{\theta^\star}}
\newcommand{\htheta}{{\widehat{\theta}}}
$$