# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{displaymath}fracpartial^2partialtheta_k^2l_N(theta)=-fracN_ktheta_k^2-fracleft(N-N_1-cdots-N_K-1right)left(1-theta_1-cdots-theta_K-1right)^2{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}widehattheta_k=fracN_kN.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}calI(beta)^-1=left(X^primeOmega^-1Xright)^-1.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Sigma=mboxcov(widehattheta)=frac1Nleft[arraycccctheta_1(1-theta_1);SPMamp;-theta_1theta_2;SPMamp;cdots;SPMamp;-theta_1theta_K-1-theta_1theta_2;SPMamp;theta_2(1-theta_2);SPMamp;cdots;SPMamp;-theta_2theta_K-1cdots;SPMamp;cdots;SPMamp;cdots;SPMamp;cdotscdots;SPMamp;cdots;SPMamp;cdots;SPMamp;cdots-theta_1theta_K-1;SPMamp;theta_2theta_K-1;SPMamp;cdots;SPMamp;theta_K-1(1-theta_K-1)arrayright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}N_k=sum_i=1^NI{x_i=k},qquadsum_k=1^KN_k=N{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft[widehattheta_kwidehattheta_lright]=frac1N^2Eleft[N_kN_lright]=frac(N-1)theta_ktheta_lN{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft[widehattheta_kright]=Eleft[fracN_kNright]=frac1NEleft[N_kright]=frac1NNtheta_k=theta_k.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma=calI_N^-1(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$N_k${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}varepsilon=y-XbetasimNleft(0,Omegaright),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartial^2partialtheta_kpartialtheta_ll_N(theta)=-fracleft(N-N_1-cdots-N_K-1right)left(1-theta_1-cdots-theta_K-1right)^2{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartialpartialtheta_kl_N(theta)=fracN_ktheta_k-fracleft(N-N_1-cdots-N_K-1right)left(1-theta_1-cdots-theta_K-1right)=0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$kneql${_inline}/;
$cached_env_img{$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}Eleft[N_kright]=sum_i=1^NEI{x_i=k}=sum_i=1^Ntheta_k=Ntheta_k{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} = ' 
';
$key = q/{_inline}$k=1,ldots,K-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft[widehattheta_k^2right]=frac1N^2Eleft[N_k^2right]=fractheta_kN+frac(N-1)theta_k^2N.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_k${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$SigmatimescalI_N(theta)=I${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Eleft[I{x_i=k}I{x_i=l}right]=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildeX_1,ldots,tildeX_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(x_1,ldots,x_N|theta)=prod_k=1^Ktheta_k^N_k.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I{x_i=k}${_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} = ' 
';
$key = q/{_inline}$I{x_i=l}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(x_i|theta)=prod_k=1^Ktheta_k^I{x_i=k},{displaymath}/;
$cached_env_img{$key} = ' 
';
1;