%\setlength\topmargin{-0.25in} \setlength\oddsidemargin{-0.25in}
%\setlength\textheight{9.0in} \setlength\textwidth{7.0in}
%\setlength\columnsep{0.375in} \newlength\titlebox
%\setlength\titlebox{2.25in} \setlength\headheight{0pt}
%\setlength\headsep{0pt}

\setlength\headheight{13.6pt}
\setlength{\evensidemargin}{-0.25 in} \setlength{\oddsidemargin}{-0.25 in}
\setlength{\textwidth}{6.9 in} \setlength{\topmargin}{-0.75 in}
\setlength{\textheight}{9.3 in}

\renewcommand{\baselinestretch}{0.9}

\renewcommand{\labelenumi}{\arabic{enumi}}
\renewcommand{\labelenumii}{(\alph{enumii})}
\renewcommand{\labelenumiii}{(\roman{enumiii})}

\makeatletter
\let\orig@Itemize =\itemize
\let\orig@Enumerate =\enumerate
\let\orig@Description =\description % Zero the vertical spacing parameters
\def\MySpacing{\itemsep=0.0ex\topsep=0.0ex\partopsep=0.0ex\parskip=0.0ex\parsep=0.0ex}
\def\WideSpacing{\itemsep=2.0ex\topsep=0.5ex\partopsep=0.0ex\parskip=0.0ex\parsep=0.0ex}
% Redefine the environments in terms of the original values
\renewenvironment{itemize}{\orig@Itemize\MySpacing}{\endlist}
\newenvironment{Myenumerate}{\orig@Enumerate\MySpacing}{\endlist}
\newenvironment{enumerateWide}{\orig@Enumerate\WideSpacing}{\endlist}
\newenvironment{itemizeWide}{\orig@Itemize\WideSpacing}{\endlist}
\renewenvironment{description}{\orig@Description\MySpacing}{\endlist}

\newenvironment{qenumerate}{\parindent 0in \orig@Enumerate}{\endlist}

\def\qitemize{%
  \ifnum \@itemdepth >\thr@@\@toodeep\else
    \advance\@itemdepth\@ne
    \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
    \expandafter
    \list
      \csname\@itemitem\endcsname
%      {\def\makelabel##1{\hss\llap{##1}}}%
       {\def\makelabel##1{\llap{##1}}}%
  \fi}

\def\hsp{\vspace{0.1 in}}
\def\fsp{\vspace{0.2 in}}

\makeatother


\renewcommand\rmdefault{ppl}

\newcommand\textsclarge[1]{\fontshape{sc}\fontsize{14}{15} \selectfont{#1}}
\newcommand\textscnormal[1]{\fontshape{sc}\fontsize{12}{15} \selectfont{#1}}

\newcommand{\dst}{\displaystyle}
\newcommand{\bigone}{{\rm 1\hspace{-3 pt}l}}

%\newcommand{\mathsfsmall}{\fontshape{sf}\fontsize{12}{15} \selectfont{#1}}
%\def\transpose{{\mathsfsmall{T}}}
\DeclareOldFontCommand{\sf}{\small\it\sffamily}{\mathsf}
\def\transpose{{\sf{T}}}


\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
\DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E}
\DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A}
\DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52}
\DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51}
\DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49}
\DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43}


\def\X{\mathbb{X}}
\def\CalC{\mathscr{C}}

\def\P{\text{Pr}}

\def\dsum#1#2{\displaystyle{\sum_{#1}^{#2}}~}
\def\dint#1#2{\displaystyle{\int_{#1}^{#2}}}
\def\Prob#1{\mbox{P}\left (~#1~\right )}
\def\Exp#1#2{\mbox{E}_{#1} [~#2~]}
\def\bigchoose#1#2{\displaystyle{#1 \choose #2}}

\newcommand{\undertilde}[1]{\underset{\widetilde{}}{#1}}

\newcommand\Xvec{{\skew0\utilde{X}}}

\def\Xvecn{{\undertilde{X_n}}}
\def\Yvec{{\undertilde{Y}}}
\def\Tvec{{\utilde{T}}}
\def\xvec{{\utilde{x}}}
\def\yvec{{\utilde{y}}}
\def\zvec{{\utilde{z}}}
\def\tvec{{\utilde{t}}}
\def\qvec{{\utilde{q}}}
\def\gvec{{\utilde{g}}}
\def\hvec{{\utilde{h}}}
\def\lvec{{\utilde{l}}}
\def\thvec{{\skew0\utilde{\theta}}}
\def\thveczero{{\skew0\utilde{\theta}_0}}
\def\thvecone{{\skew0\utilde{\theta}_1}}
\def\thvectwo{{\skew0\utilde{\theta}_2}}
\def\phivec{{\skew0\utilde{\phi}}}
\def\etavec{{\undertilde{\eta}}}
\def\betavec{{\skew0\utilde{\beta}}}
\def\omegavec{{\skew0\utilde{\omega}}}
\def\wvec{{\undertilde{w}}}
\def\Svec{{\undertilde{S}}}
\def\zerovec{{\undertilde{0}}}
\def\Psimat{{\bm{\Psi}}}
\def\avec{{\undertilde{a}}}

\def\Xveca{{\skew0\utilde{X}}_1}
\def\Xvecb{{\skew0\utilde{X}}_2}
\def\xveca{{\skew0\utilde{x}}_1}
\def\xvecb{{\skew0\utilde{x}}_2}
\def\mvec{{\skew0\utilde{m}}}
\def\nvec{{\skew0\utilde{n}}}
\def\cvec{{\skew0\utilde{c}}}
\def\fvec{{\skew0\utilde{f}}}
\def\hvec{{\skew0\utilde{h}}}
\def\Dvec{{\skew0\utilde{D}}}
\def\xivec{{\skew0\utilde{\xi}}}


\def\lvec{{\skew0\utilde{l}}}
\def\lvecn{{\skew0\utilde{l}_n}}
\def\dotlvec{{\skew0\utilde{\dot{l}}}}
\def\dotlvecn{{\skew0\utilde{\dot{l}}_n}}
\def\ddotlvecn{{\skew0\utilde{\ddot{l}}_n}}
\def\dddotlvecn{{\skew0\utilde{\dddot{l}}_n}}

\def\lra{\longrightarrow}
\def\Lra{\Longrightarrow}

\def\calA{\mathcal{A}}
\def\calB{\mathcal{B}}
\def\calC{\mathcal{C}}
\def\calD{\mathcal{D}}
\def\calE{\mathcal{E}}
\def\calF{\mathcal{F}}
\def\calG{\mathcal{G}}

\def\bmt{\tvec}
\def\bmf{\fvec}
\def\bmx{\xvec}
\def\bmh{\hvec}
\def\bmxzero{\xvec_0}

\def\bmphi{\bm{\phi}}
\def\bmphizero{\bm{\phi_0}}

\def\bmth{\thvec}
\def\bmphi{\bm{\phi}}

\def\bmx{\bm{x}}
\def\bmg{\bm{g}}

\def\alphaline{\overline{\alpha}}
\def\betaline{\overline{\beta}}

\def\betadag{{\beta^\dag}}
\def\betastar{{\beta^\star}}

\def\transpose{{\textsf{T}}}

\def\bmZn{\bm{Z}_n}
\def\bmZ{\bm{Z}}
\def\bmD{\bm{D}}

\def\bZ{\mathbf{Z}}
\def\bA{\mathbf{A}}
\def\Ident{\mathbf{I}}

%\def\dddot#1{\stackrel{\ldots}{#1}}

\setcounter{section}{2}
\newcounter{mytheorem}
\setcounter{mytheorem}{1}

\def\lra{\longrightarrow}
\def\Lra{\Longrightarrow}
\def\Llra{\Longleftrightarrow}

\def\eqdef{\stackrel{def}{=}}
\def\eqdist{\stackrel{d}{=}}

\def\tildethn{\skew2\tilde{\thvec}_n}
\def\hatthn{\skew2\hat{\thvec}_n}
\def\tildephin{\skew2\tilde{\bmphi}_n}

\def\thnstar{\bm{\theta}_n^\star}

\def\th{\theta}

\def\Exp{\text{E}}
\def\Var{\text{Var}}
\newcommand{\SET}[1]{\left\{#1\right\}}

\def\muX{\muvec^\text{\tiny{$X$}}}
\def\muY{\muvec^\text{\tiny{$Y$}}}
\def\muXgy{\muvec^\text{\tiny{$X|y$}}}
\def\muXgY{\muvec^\text{\tiny{$X|Y$}}}

\def\Loss{\mathcal{L}}



\newcommand\argmin[1]{\underset{#1}{\textrm{argmin}}}
\newcommand\argmax[1]{\underset{#1}{\textrm{argmax}}}


\newcommand\Xbarn{{\overline{X}_n}}
\newcommand\xbarn{{\overline{x}_n}}
\newcommand\Xbar{{\overline{X}}}
\newcommand\xbar{{\overline{x}}}

\def\thetahat{\widehat{\theta}}
\def\sigmahat{\widehat{\sigma}}
\def\tauhat{\widehat{\tau}}

\newcommand\muvec{{\skew0\undertilde{\mu}}}
\newcommand\pivec{{\skew0\utilde{\pi}}}

\def\lra{\longrightarrow}
\def\Lra{\Longrightarrow}
\def\Llra{\Longleftrightarrow}
\def\iif{\Longleftrightarrow}


\def\CiP{\stackrel{p}{\lra}}
\def\CiR{\stackrel{r}{\lra}}
\newcommand\CRM[1]{\stackrel{r = #1}{\lra}}
\newcommand\Cqm{\stackrel{q.m.}{\lra}}
\def\Cas{\stackrel{a.s.}{\lra}}
\def\CiL{\stackrel{\mathfrak{L}}{\lra}}
\def\eqdef{\stackrel{def}{=}}
\def\CiD{\stackrel{d}{\lra}}
\def\Cae{\stackrel{a.e.}{\lra}}
\def\Cwp{\stackrel{w.p. 1}{\lra}}

\def\nlra{\nrightarrow}

\def\nCas{\stackrel{a.s.}{\nlra}}
\def\nCiP{\stackrel{p}{\nlra}}


\def\approxsim{\; \; \raisebox{-0.3ex}{.} \\ \hspace{-0.11in} \sim \\ \hspace{-0.105in} \raisebox{0.95ex}{.} \; \; }

\newcommand\Xvecsub[1]{{\skew0\utilde{X}}_{\! #1}}
\newcommand\Zvecsub[1]{{\skew0\utilde{Z}}_{\! #1}}
\newcommand\Zvec{{\skew0\utilde{Z}}}

\newcommand\Xbarvecn{{\overline{\skew0\utilde{X}}_{\!n}}}

\def\Xmean{\overline{X}}
\def\xmean{\overline{x}}
\def\Ymean{\overline{Y}}
\def\ymean{\overline{y}}


\def\Xseq{X_1,\ldots,X_n}
\def\xseq{x_1,\ldots,x_n}
\def\Yseq{Y_1,\ldots,Y_n}
\def\yseq{y_1,\ldots,y_n}
\def\Zseq{Z_1,\ldots,Z_n}
\def\zseq{z_1,\ldots,z_n}

\def\eqindist{\stackrel{d}{=}}

\def\O{\text{O}}
\def\o{\text{o}}
\def\E{\mathbb{E}}
\def\Var{\text{Var}}
\def\Cov{\text{Cov}}

\def\Cramer{Cram\'{e}r}

\def\FisherI{\mathcal{I}}
\def\FisherItilde{\widetilde{\mathcal{I}}}

\def\MSE{\text{MSE}}

\def\calR{\mathcal{R}}
\def\calW{\mathcal{W}}
\def\calX{\mathcal{X}}
\def\calH{\mathcal{H}}

\def\thetapr{\theta^\prime}

\def\boldl{\lvec}

\def\thnstar{\thvec_n^\star}

\def\tildethn{\skew2\widetilde{\thvec}_n}
\def\hatthn{\skew2\hat{\thvec}_n}
\def\tildephin{\skew2\widetilde{\bmphi}_n}

\def\thnstar{\bm{\theta}_n^\star}

\def\thtilde{\widetilde{\thvec}_n}
\def\thhat{\widehat{\thvec}_n}
\def\thhatzero{\widehat{\thvec}_{n0}}
\def\thhatone{\widehat{\thvec}_{n1}}

%\def\thhatzeroone{\widehat{\thvec}_{n01}}
\def\thhatzeroone{{\skew0\utilde{\widehat{\theta}}_{n01}}}
\def\thhatonezero{{\skew0\utilde{\widehat{\theta}}_{n10}}}
\def\thhatoneone{{\skew0\utilde{\widehat{\theta}}_{n11}}}

\def\thtilzero{\widetilde{\thvec}_{n0}}
\def\thtilone{\widetilde{\thvec}_{n1}}

\def\thtilzeroone{{\skew0\utilde{\widetilde{\theta}}_{n01}}}
\def\thtilonezero{{\skew0\utilde{\widetilde{\theta}}_{n10}}}
\def\thtiloneone{{\skew0\utilde{\widetilde{\theta}}_{n11}}}


\def\dotlike{\dot{\bm{l}}_n}
\def\ddotlike{\ddot{\bm{l}}_n}

\def\thhatNewt{\widehat{\thvec}^{\dagger}}
\def\thhatScor{\widehat{\thvec}^{\star}}
\def\thddag{{\thvec}_n^{\ddag}}

\def\FisherIhat{\widehat{I}_n}
\def\FisherIhatzzo{\widehat{I}_{n00.1}}
\def\FisherIhatzz{\widehat{I}_{n00}}
\def\FisherIhatzo{\widehat{I}_{n01}}
\def\FisherIhatoz{\widehat{I}_{n10}}
\def\FisherIhatoo{\widehat{I}_{n11}}

\def\xtilde{\widetilde{x}}
\def\Xtilde{\widetilde{X}}

\def\bth{\thvec}

\def\Prob#1{\mbox{P}\left[~#1~\right]}
\def\prob#1{\mbox{P}\left(~#1~\right)}

\def\CProb#1#2{\mbox{P}\left[~#1~|~#2~\right]}
\def\Cprob#1#2{\mbox{P}\left(~#1~|~#2~\right)}

\def\calY{\mathcal{Y}}
\def\Ind{\mathbb{1}}

\def\given{\; | \;}

\def\bx{\mathbf{x}}
\def\bX{\mathbf{X}}
\def\bM{\mathbf{M}}
\def\bD{\mathbf{D}}
\def\expit{\text{expit}}

\def\bL{\mathbf{L}}
\def\by{\mathbf{y}}
\def\bx{\mathbf{x}}

\def\bp{\mathbf{p}}

\def\thetavec{\boldsymbol{\theta}}
\def\bu{\mathbf{u}}
\def\bU{\mathbf{U}}
\def\bY{\mathbf{Y}}
\def\bX{\mathbf{X}}
\def\bH{\mathbf{H}}
\def\bV{\mathbf{V}}

\def\calS{\mathcal{S}}
\def\calR{\mathcal{R}}
\def\pihat{\widehat{\pi}}
\def\Rpack{\texttt{R}}
\def\thetavec{\boldsymbol{\theta}}
\def\bu{\mathbf{u}}
\def\Ihat{\widehat{I}}
\def\Zhat{\widehat{Z}}

\def\pitilde{\widetilde{\pi}}
\def\ptilde{\widetilde{p}}
\def\ybar{\overline{y}}
\def\phat{\widehat{p}}
\def\Lhat{\widehat{\mathcal{L}}}

\def\Post{\pi}
\def\Prop{q}

\def\btheta{\boldsymbol{\theta }}
\def\balpha{\boldsymbol{\alpha }}
\def\bbeta{\boldsymbol{\beta }}
\def\bvarphi{\boldsymbol{\varphi }}
\def\bx{\mathbf{x}}
\def\by{\mathbf{y}}
\def\bu{\mathbf{u}}
\def\bv{\mathbf{v}}
\def\bg{\mathbf{g}}
\def\bh{\mathbf{h}}
\def\bt{\mathbf{t}}
\def\bz{\mathbf{z}}
\def\bc{\mathbf{c}}

\def\bA{\mathbf{A}}
\def\bW{\mathbf{W}}

\def\R{\mathbb{R}}

\def\dint{\displaystyle{\int}}
\def\dsum{\displaystyle{\sum}}

\def\pitilde{\widetilde{\pi}}
\def\ptilde{\widetilde{p}}
\def\qtilde{\widetilde{q}}

\def\bomega{\mathbf{\omega}}
\def\bkappa{\mathbf{\kappa}}

\def\calX{\mathcal{X}}

\newcommand\IndState[1][1]{\State\hspace{#1\algorithmicindent}}

\def\ftilde{\widetilde{f}}

\def\Dset{\mathcal{D}}
\def\cald{\delta}
\def\calN{\mathcal{N}}