$\newcommand{\mat}[1]{ { \boldsymbol{ \mathrm{#1} } } } \newcommand{\vect}[1]{ { \boldsymbol{ \mathrm{#1} } } } \newcommand{\rmat}[1]{ { \boldsymbol{#1} } } \newcommand{\rvect}[1]{ { \boldsymbol{#1} } } \newcommand{\information}{\boldsymbol{\mathcal{I}}} \newcommand{\transpose}{\mathrm{T}} \newcommand{\independent}{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}} \newcommand{\indep}{\independent} \newcommand{\nindep}{\not \independent} \newcommand{\ex}{{\mathbb{E}}} \newcommand{\var}{{\mathbb{Var}}} \newcommand{\cov}{{\mathbb{Cov}}} \newcommand{\corr}{{\mathbb{Corr}}} \newcommand{\prob}{{\mathbb{P}}} \newcommand{\bias}{{\text{bias}}} \newcommand{\p}{{\mathbb{P}}}$