\makeatletter
\usepackage{amsmath}    % need for subequations
\usepackage{amssymb}

% some traditional definitions that can be blamed on craig barratt
\newcommand{\BEAS}{\begin{eqnarray*}}
\newcommand{\EEAS}{\end{eqnarray*}}
\newcommand{\BEA}{\begin{eqnarray}}
\newcommand{\EEA}{\end{eqnarray}}
\newcommand{\BEQ}{\begin{equation}}
\newcommand{\EEQ}{\end{equation}}
\newcommand{\BIT}{\begin{itemize}}
\newcommand{\EIT}{\end{itemize}}
\newcommand{\BNUM}{\begin{enumerate}}
\newcommand{\ENUM}{\end{enumerate}}


% my definitions

\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\begm}[1]{\begin{equation}\label{#1}}
\newcommand{\begeq}[1]{\begin{eqnarray}\label{#1}}
%\def\argmin{\arg\!\!\min}
\def\rP{{\mathbb P}}
\def\rA{{\mathbb A}}
\def\rB{{\mathbb B}}
\def\rR{{\mathbb R}}
\def\rN{{\mathbb N}}
\def\rQ{{\mathbb Q}}
\def\rE{{\mathbb E}}
\def\rI{{\mathbb I}}
\def\rZ{{\mathbb Z}}
\def\rC{{\mathbb C}}
\def\rX{{\mathbb X}}
\def\rY{{\mathbb Y}}
\def\rU{{\mathbb U}}
\def\rL{{\mathbb L}}
\def\rVar{\mbox{\rm Var}}
\def\sign{\mbox{\rm sign}}
\def\rCov{\mbox{\rm Cov}}
\def\c{$\bullet\bullet$}
\def\weak{\Rightarrow}
\def\Pconv{\stackrel{p}{\longrightarrow}}
\def\Lconv{\stackrel{L_1}{\longrightarrow}}
\newcommand{\qed}{\mbox{\hspace{1em}\rule{2mm}{2mm}}}
\def\to{\rightarrow}

\newenvironment{fminipage}%
    {\begin{Sbox}\begin{minipage}}%
    {\end{minipage}\end{Sbox}\fbox{\TheSbox}}

\def\endm{\end{equation}}
\def\endeq{\end{eqnarray}}
%\def\proof{\mbox{P{\small ROOF~~}}}
\def\proof{{\bf Proof~~}}

\def\ft{\footnote}

\def\hi{\parindent=0pt\hangindent=20pt\hangafter=1}
\def\noi{\noindent}
\def\non{\nonumber}

\def\weakconv{\Rightarrow}
\def\Lconv{\stackrel{\cL_1}{\longrightarrow}}
\def\eqind{\stackrel{\cD}{=}}

\def\begfmini{\begin{center}\begin{fminipage}{6in}}
\def\endfmini{\end{fminipage}\end{center}}

%   Curly letters
\def\cA{{\cal A}}
\def\cB{{\cal B}}
\def\cC{{\cal C}}
\def\cD{{\cal D}}
\def\cE{{\cal E}}
\def\cF{{\cal F}}
\def\cG{{\cal G}}
\def\cH{{\cal H}}
\def\cK{{\cal K}}
\def\cI{{\cal I}}
\def\cJ{{\cal J}}
\def\cL{{\cal L}}
\def\cM{{\cal M}}
\def\cN{{\cal N}}
\def\cO{{\cal O}}
\def\cP{{\cal P}}
\def\cR{{\cal R}}
\def\cS{{\cal S}}
\def\cT{{\cal T}}
\def\cU{{\cal U}}
\def\cW{{\cal W}}
\def\cV{{\cal V}}
\def\cX{{\cal X}}
\def\cY{{\cal Y}}
\def\cQ{{\cal Q}}
\def\cZ{{\cal Z}}
\def\el{et. al.}

%   boldface numbers

\def\b1{{\bf 1.}}
\def\b2{{\bf 2.}}
\def\b3{{\bf 3.}}
\def\b4{{\bf 4.}}
\def\b5{{\bf 5.}}
\def\b6{{\bf 6.}}

%   Mathematical abbreviations

\def\langles{\left\langle\!\left\langle\,}
\def\rangles{\,\right\rangle\!\right\rangle}
\def\non{\nonumber}
\def\half{{1\over 2}}
\def\rarr{\rightarrow}
\def\eps{\epsilon}
\def\eeps{\varepsilon}
\def\sig{\sigma}
\def\al{\alpha}
\def\th{\theta}
\def\cS{{\cal {S}}}
\def\cE{{\cal E}}
\def\sgn{\mbox{sgn}}
\def\Det{\mbox{Det}}
\def\Cov{\mbox{Cov}}
\def\rVar{{\rm Var}}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
%--------------------------------------------------------------------
\def\bX{\mbox{\boldmath $X$}}
% Boldface letters

\iffalse
\def\ba{\mbox{\boldmath $a$}}
\def\bb{\mbox{\boldmath $b$}}
\def\bc{\mbox{\boldmath $c$}}
\def\bd{\mbox{\boldmath $d$}}
\def\be{\mbox{\boldmath $e$}}
\def\bff{\mbox{\boldmath $f$}}
\def\bh{\mbox{\boldmath $h$}}
\def\bg{\mbox{\boldmath $g$}}
\def\bl{\mbox{\boldmath $l$}}
\def\bm{\mbox{\boldmath $m$}}
\def\bp{\mbox{\boldmath $p$}}
\def\bq{\mbox{\boldmath $q$}}
\def\br{\mbox{\boldmath $r$}}
\def\bs{\mbox{\boldmath $s$}}
\def\bu{\mbox{\boldmath $u$}}
\def\bv{\mbox{\boldmath $v$}}
\def\bw{\mbox{\boldmath $w$}}
\def\bx{\mbox{\boldmath $x$}}
\def\by{\mbox{\boldmath $y$}}
\def\bz{\mbox{\boldmath $z$}}
\def\bA{\mbox{\boldmath $A$}}
\def\bB{\mbox{\boldmath $B$}}
\def\bC{\mbox{\boldmath $C$}}
\def\bD{\mbox{\boldmath $D$}}
\def\bE{\mbox{\boldmath $E$}}
\def\bF{\mbox{\boldmath $F$}}
\def\bH{\mbox{\boldmath $H$}}
\def\bI{\mbox{\boldmath $I$}}
\def\bG{\mbox{\boldmath $G$}}
\def\bJ{\mbox{\boldmath $J$}}
\def\bL{\mbox{\boldmath $L$}}
\def\bM{\mbox{\boldmath $M$}}
\def\bP{\mbox{\boldmath $P$}}
\def\bQ{\mbox{\boldmath $Q$}}
\def\bR{\mbox{\boldmath $R$}}
\def\bT{\mbox{\boldmath $T$}}
\def\bS{\mbox{\boldmath $S$}}
\def\bU{\mbox{\boldmath $U$}}
\def\bW{\mbox{\boldmath $W$}}
\def\bX{\mbox{\boldmath $X$}}
\def\bY{\mbox{\boldmath $Y$}}
\def\bZ{\mbox{\boldmath $Z$}}
\def\obx{\overline{\bx}}
\fi
% Boldface symbols of Greek letters


\def\bo{\mbox{\boldmath $0$}}
\def\b1{\mbox{\boldmath $1$}}
\def\balpha{\mbox{\boldmath $\alpha$}}
\def\bbeta{\mbox{\boldmath $\eta$}}
\def\bbbeta{\mbox{\boldmath $\beta$}}
\def\beps{\mbox{\boldmath $\eps$}}
\def\beeps{\mbox{\boldmath $\eeps$}}
\def\bxi{\mbox{\boldmath $\xi$}}
\def\blam{\mbox{\boldmath $\lambda$}}
\def\bgamma{\mbox{\boldmath $\gamma$}}
\def\bLam{\mbox{\boldmath $\Lambda$}}
\def\bmu{\mbox{\boldmath $\mu$}}
\def\bTheta{\mbox{\boldmath $\Theta$}}
\def\bgam{\mbox{\boldmath $\gamma$}}
\def\bGam{\mbox{\boldmath $\Gamma$}}
\def\bt{\mbox{\boldmath $\theta$}}
%\def\bthat{{\hat{$\theta$}_n}}
%\def\bthat{\hat{\mathbf{ $\theta$}}_n}
%\def\bth{\mbox{\boldmath $\hat{\theta}$}}
%\def\bth{\mbox{\hat{\boldmath ${\theta}$}}}
\def\bth{\hat{\bt}}
\def\bgamh{\hat{\bgam}}
\def\btet{\mbox{\boldmath $\theta$}}
\def\bxi{\mbox{\boldmath $\xi$}}
%\def\bx{\mbox{\boldmath $x$}}
%\def\by{\mbox{\boldmath $y$}}
\def\bfeta{\mbox{\boldmath $\eta$}}
\def\bphi{\mbox{\boldmath $\phi$}}
\def\bPhi{\mbox{\boldmath $\Phi$}}

%   Theorems, corollaries and the like
%\newtheorem{assumption}{Assumption}[section]
\newtheorem{assumption}{Assumption}
\newtheorem{problem}{Problem}
\newtheorem{definition}{Definition}
%\newtheorem{lemma}{Lemma}[chapter]     % for report style
%\newtheorem{lemma}{Lemma}[section]  %for report style
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
%\newtheorem{corollary}{Corollary}[section]    %report style
\newtheorem{corollary}{Corollary}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newtheorem{remark}{Remark}
\newtheorem{algorithm}{Algorithm}
% \newtheorem{theorem}{~Theorem}[chapter]   % for report style
%\newtheorem{theorem}{Theorem}[section]     % for article style
\newtheorem{theorem}{Theorem}       % for report style
% \newtheorem{theorem}{$\spadesuit$~Theorem}
\newtheorem{exercise}{Exercise}
\newtheorem{claim}{Claim}
\newtheorem{proof.}{Proof.}
