\usepackage{eurosym, graphicx, amsmath, amssymb, bbm, color, bm}
\usepackage{graphics, epsfig, verbatim, latexsym, geometry}
\usepackage{fancyhdr, nopageno, amsthm, eucal, eufrak, setspace, rotating}

\setcounter{MaxMatrixCols}{10}

\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
%\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
%\input{tcilatex}
\newcommand{\newoperator}[3]{\newcommand*{#1}{\mathop{#2}#3}}
\newcommand{\renewoperator}[3]{\renewcommand*{#1}{\mathop{#2}#3}}
\newcommand{\SC}{\mathbb{C}}
\newcommand{\SN}{\mathbb{N}}
\newcommand{\SQ}{\mathbb{Q}}
\newcommand{\SR}{\mathbb{R}}
\newcommand{\SZ}{\mathbb{Z}}
\newcommand{\calA}{\mathcal{A}}
\newcommand{\calB}{\mathcal{B}}
\newcommand{\calC}{\mathcal{C}}
\newcommand{\calD}{\mathcal{D}}
\newcommand{\calE}{\mathcal{E}}
\newcommand{\calF}{\mathcal{F}}
\newcommand{\calG}{\mathcal{G}}
\newcommand{\calH}{\mathcal{H}}
\newcommand{\calI}{\mathcal{I}}
\newcommand{\calJ}{\mathcal{J}}
\newcommand{\calK}{\mathcal{K}}
\newcommand{\calL}{\mathcal{L}}
\newcommand{\calM}{\mathcal{M}}
\newcommand{\calN}{\mathcal{N}}
\newcommand{\calO}{\mathcal{O}}
\newcommand{\calP}{\mathcal{P}}
\newcommand{\calQ}{\mathcal{Q}}
\newcommand{\calR}{\mathcal{R}}
\newcommand{\calS}{\mathcal{S}}
\newcommand{\calT}{\mathcal{T}}
\newcommand{\calU}{\mathcal{U}}
\newcommand{\calV}{\mathcal{V}}
\newcommand{\calW}{\mathcal{W}}
\newcommand{\calX}{\mathcal{X}}
\newcommand{\calY}{\mathcal{Y}}
\newcommand{\calZ}{\mathcal{Z}}
\newcommand{\mA}{\bm A}
\newcommand{\va}{\bm a}
\newcommand{\vb}{\bm b}
\newcommand{\mC}{\bm C}
\newcommand{\vc}{\bm c}
\newcommand{\mD}{\bm D}
\newcommand{\vd}{\bm d}
\newcommand{\mE}{\bm E}
\newcommand{\ve}{\bm e}
\newcommand{\mF}{\bm F}
\newcommand{\vf}{\bm f}
\newcommand{\mG}{\bm G}
\newcommand{\vg}{\bm g}
\newcommand{\mH}{\bm H}
\newcommand{\vh}{\bm h}
\newcommand{\mI}{\bm I}
\newcommand{\vi}{\bm i}
\newcommand{\mJ}{\bm J}
\newcommand{\vj}{\bm j}
\newcommand{\mK}{\bm K}
\newcommand{\vk}{\bm k}
\newcommand{\mL}{\bm L}
\newcommand{\vl}{\bm l}
\newcommand{\mM}{\bm M}
\newcommand{\vm}{\bm m}
\newcommand{\mN}{\bm N}
\newcommand{\vn}{\bm n}
\newcommand{\mO}{\bm O}
\newcommand{\vo}{\bm o}
\newcommand{\mP}{\bm P}
\newcommand{\vp}{\bm p}
\newcommand{\mQ}{\bm Q}
\newcommand{\vq}{\bm q}
\newcommand{\mR}{\bm R}
\newcommand{\vr}{\bm r}
\newcommand{\mS}{\bm S}
\newcommand{\vs}{\bm s}
\newcommand{\mT}{\bm T}
\newcommand{\vt}{\bm t}
\newcommand{\mU}{\bm U}
\newcommand{\vu}{\bm u}
\newcommand{\mV}{\bm V}
\newcommand{\vv}{\bm v}
\newcommand{\mW}{\bm W}
\newcommand{\vw}{\bm w}
\newcommand{\mX}{\bm X}
\newcommand{\vx}{\bm x}
\newcommand{\mY}{\bm Y}
\newcommand{\vy}{\bm y}
\newcommand{\mZ}{\bm Z}
\newcommand{\vz}{\bm z}
\newcommand{\valpha}{\bm \alpha}
\newcommand{\vbeta}{\bm \beta}
\newcommand{\vgamma}{\bm \gamma}
\newcommand{\vdelta}{\bm \delta}
\newcommand{\vepsi}{\bm \epsi}
\newcommand{\vvarepsilon}{\bm \varepsilon}
\newcommand{\vzeta}{\bm \zeta}
\newcommand{\veta}{\bm \eta}
\newcommand{\vtheta}{\bm \theta}
\newcommand{\viota}{\bm \iota}
\newcommand{\vkappa}{\bm \kappa}
\newcommand{\vlambda}{\bm \lambda}
\newcommand{\vmu}{\bm \mu}
\newcommand{\vnu}{\bm \nu}
\newcommand{\vxi}{\bm \xi}
\newcommand{\vpi}{\bm \pi}
\newcommand{\vrho}{\bm \rho}
\newcommand{\vsigma}{\bm \sigma}
\newcommand{\vtau}{\bm \tau}
\newcommand{\vupsilon}{\bm \upsilon}
\newcommand{\vphi}{\bm \phi}
\newcommand{\vchi}{\bm \chi}
\newcommand{\vpsi}{\bm \psi}
\newcommand{\vomega}{\bm \omega}
\newcommand{\mGamma}{\bm \varGamma}
\newcommand{\mDelta}{\bm \varDelta}
\newcommand{\mTheta}{\bm \varTheta}
\newcommand{\mLambda}{\bm \varLambda}
\newcommand{\mXi}{\bm \varXi}
\newcommand{\mPi}{\bm \varPi}
\newcommand{\mSigma}{\bm \varSigma}
\newcommand{\mUpsilon}{\bm \varUpsilon}
\newcommand{\mPhi}{\bm \varPhi}
\newcommand{\mPsi}{\bm \varPsi}
\newcommand{\mOmega}{\bm \varOmega}
\newcommand{\rB}{\ensuremath{\mathrm{B}}}
\newcommand{\rC}{\ensuremath{\mathrm{C}}}
\newcommand{\rD}{\ensuremath{\mathrm{D}}}
\newcommand{\rF}{\ensuremath{\mathrm{F}}}
\newcommand{\rH}{\ensuremath{\mathrm{H}}}
\newcommand{\rL}{\ensuremath{\mathrm{L}}}
\newcommand{\rN}{\ensuremath{\mathrm{N}}}
\newcommand{\rt}{\ensuremath{\mathrm{t}}}
\newcommand{\rU}{\ensuremath{\mathrm{U}}}
\newcommand{\bin}{\ensuremath{\mathrm{bin}}}
\newcommand{\eu}{\ensuremath{\mathrm{e}}}
\newcommand{\iu}{\ensuremath{\mathrm{i}}}
\newcommand{\LN}{\ensuremath{\mathrm{LN}}}
\newcommand{\Po}{\ensuremath{\mathrm{Po}}}
\newcommand{\ped}[1]{\ensuremath{_\mathrm{#1}}}
\newcommand{\ap}[1]{\ensuremath{^\mathrm{#1}}}
\renewoperator{\Re}{\mathrm{Re}}{\nolimits}
\renewoperator{\Im}{\mathrm{Im}}{\nolimits}
\makeatletter
\newcommand{\rd}{\@ifnextchar^{\DIfF}{\DIfF^{}}}
\def\DIfF^#1{   \mathop{\mathrm{\mathstrut d}}   \nolimits^{#1}\gobblespace}
\def\gobblespace{\futurelet\diffarg\opspace}
\def\opspace{   \let\DiffSpace\!   \ifx\diffarg(   \let\DiffSpace\relax
   \else
   \ifx\diffarg[   \let\DiffSpace\relax
   \else
   \ifx\diffarg\{   \let\DiffSpace\relax
   \fi\fi\fi\DiffSpace}
\newcommand{\deriv}[3][]{\frac{\rd^{#1}#2}{\rd #3^{#1}}}
\newcommand{\pderiv}[3][]{\frac{\partial^{#1}#2}{\partial #3^{#1}}}
\newcommand{\bias}{\operatorname{bias}}
\newcommand{\col}{\operatorname{col}}
\newcommand{\corr}{\operatorname{corr}}
\newcommand{\cov}{\operatorname{cov}}
\newcommand{\dg}{\operatorname{dg}}
\newcommand{\diag}{\operatorname{diag}}
\newcommand{\E}{\operatorname{E}}
\newcommand{\etr}{\operatorname{etr}}
\newoperator{\ip}{\mathrm{int}}{\nolimits}
\newcommand{\kur}{\operatorname{kur}}
\newcommand{\MSE}{\operatorname{MSE}}
\newcommand{\plim}{\operatorname{plim}}
\newcommand{\rk}{\operatorname{rk}}
\newcommand{\sgn}{\operatorname{sgn}}
\newcommand{\tr}{\operatorname{tr}}
\newcommand{\var}{\operatorname{var}}
\renewcommand{\vec}{\operatorname{vec}}
\newcommand{\vech}{\operatorname{vech}}
\newcommand{\distr}{\sim}
\newcommand{\adistr}{\stackrel{a}{\distr}}
\newcommand{\diff}{\bigtriangledown}
\newcommand{\fordiff}{\bigtriangleup}
\newcommand{\mply}{\cdot}
\newcommand{\widebar}{\overline}
\newcommand{\eps}{\epsilon}
\newcommand{\epsi}{\varepsilon}
\newcommand{\longto}{\longrightarrow}
\newcommand{\pto}{\stackrel{p}{\longrightarrow}}
\newcommand{\dto}{\stackrel{d}{\longrightarrow}}
\newcommand{\wto}{\stackrel{w}{\longrightarrow}}
\newcommand{\vvarsigma}{\bm \varsigma}
\newcommand{\score}{\vvarsigma}
\newcommand{\Infmat}{\bm\calI}
\newcommand{\Hesmat}{\bm\calH}
\newcommand{\vones}{\bm\imath}
\newcommand{\vzeros}{\boldsymbol{0}}
\newcommand{\mzeros}{\mathbf{O}}
\newcommand{\bcdot}{\raisebox{1pt}{\textbf{\large .}}}
\newcommand{\interior}[1]{\overset{\circ}{#1}}
\newcommand{\hspacesymbols}   {$\{x: x \in S, x$ satisfies $P\}\;\;$}
\newcommand{\type}[1]{{\tt$\backslash$#1}}
\pagestyle{fancy} \fancyhf{} \rhead{\thepage}
\renewcommand{\headrulewidth}{0pt}
%\numberwithin{equation}{section}
\setlength{\textwidth}{16.5cm}
\setlength{\oddsidemargin}{0cm}
\setlength{\evensidemargin}{0cm}
\setlength{\topmargin}{0.5cm}
