# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{displaymath}hatbeta=left[arrayc(X_(1)^primeX_(1))^-1X_(1)^primey_(1)vdots(X_(p)^primeX_(p))^-1X_(p)^primey_(p)arrayright]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}V(hatbeta)=(X^primeX)^-1(X^primeSigma^-1X)(X^primeX)^-1{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}l(beta)=-Nlog(2sqrtsigma^2)-frac1sqrtsigma^2sum_i=1^Nleft|y_i-X_ibetaright|.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Nleft(hatbeta,A_N^-1right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$z_isimN(0,1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$max_d=1,ldots,Dleft[upsilon_d+varepsilon_dright]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}varepsilon=y-XbetasimNleft(0,Omegaright),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Sigma=left[arraycccOmega;SPMamp;;SPMamp;0;SPMamp;ddots;SPMamp;0;SPMamp;;SPMamp;Omegaarrayright]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartiall(hatbeta)partialbeta=X^primeOmega^-1(y-Xhatbeta)=0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatbeta=argmaxl(beta)Rightarrowhatbeta=argminsum_i=1^Nleft|y_i-X_ibetaright|=hatbeta_LAD.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i=1,ldots,k${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(Omega^-1)f(y|beta,Omega^-1,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha+sigmagamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(beta|Omega^-1,y,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Wleft(N+rho_0,R_Nright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}calI(beta)^-1=left(X^primeOmega^-1Xright)^-1.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(varepsilon)=frac12sqrtsigma^2expleft{-left|fracvarepsilonsqrtsigma^2right|right},{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}X_i=left[arraycccX_i1;SPMamp;;SPMamp;0;SPMamp;ddots;SPMamp;0;SPMamp;;SPMamp;X_iparrayright]qquad,X=left[arraycX_1vdotsX_Narrayright]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,y,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^-1,y,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(beta)f(y|beta,Omega^-1,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Y^primeSigma^-1Y=Y^primeP^-1primeP^-1Y=Z^primeZ=sum_i=1^kz_i^2simchi^2(k).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}l(beta)=-fracN2log(2pi)-frac12logleft|Omegaright|-frac12left((y-Xbeta)^primeOmega^-1(y-Xbeta)right).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}V(hatbeta)-V(hatbeta_GLS)geq0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}K=frac12sqrtsigma^2.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ktimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}V(hatbeta_GLS)=(X^primeSigma^-1X)^-1{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}F(x)=expleft{-expleft{-frac(x-alpha)sigmaright}right}{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(Omega^-1|beta,y,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}X_(i)=left[arraycX_1ivdotsX_Niarrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Z=P^-1YsimN(0,I)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}X^primeOmega^-1y=X^primeOmega^-1XhatbetaRightarrowhatbeta=(X^primeOmega^-1X)^-1X^primeOmega^-1y=hatbeta_GLS.{displaymath}/;
$cached_env_img{$key} = ' 
';
1;