# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$beta_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i=X_ibeta^*+epsilon_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2_xy${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W=Zgamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[tildeX_2-P(tildeX_2|tildeX_1)]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(tildeX_2|tildeX_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$ainR^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$a_1ne0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$D_ii${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2_x${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon=y-Xbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_1;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1timesK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_2SLS=hatbeta_OLS${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A^12A^12=A${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_IVphantom._longrightarrowatoppbeta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^-1leOmega^*-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$langletildey,tildexrangle=E{tildey,tildex}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ=(tildeW,tildeX_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=gamma^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeepsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=(I|0)'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_SIV${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(P_W-P_Z)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$betainR^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,sigma^2_epsilon,sigma^2_u,E{x^*2})${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$JgeK_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=gamma^*=[E{tildeZ'tildeZ}]^-1E{tildeZ'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[E{tildeX'_1tildeX_1}]^-1E{tildeX'_1tildey}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$JtimesK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeW'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$KtimesK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i^mboxth${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxboldmath$0$${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$NtimesK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$K_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeZ'tildev}=E{tildeZ'(etabeta_0+tildeepsilon)}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeeta=tildeX_1[beta_1+gammabeta_2]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{yv_1}=E{yv_2}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y-P(y|X_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{X'_itildeepsilon_i}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatgamma=[Z'Z]^-1Z'X${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$JleK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1D_ii${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeW${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(K_1timesK_2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(alpha_1,alpha_2,sigma^2_epsilon_d,sigma^2_epsilon_s)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$nu=tildeX_2beta_2+epsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X'Xa=mboxboldmath$0$${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A^-12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$J=(J-K_1)+K_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gammabeta_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildey,tildeX,tildeZ}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma^*=[E{tildeZ'tildeZ}]^-1E{tildeZ'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[A^-1]'=[A']^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${(y_1,X_1,Z_1),ldots,(y_N,X_N,Z_N)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbetalongrightarrowbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X_1,ldots,X_N)'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtN[hatbeta_IV-beta_0]_LongrightarrowatopscriptstyledN(0,Omega)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2_y${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX_2-P(tildeX_2|tildeX_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(y|X)=Xhatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_iinH${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$R^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$K_1=K_2=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatepsilon_i=y_i-X_ihatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_2-P(X_2|X_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatepsilon_i=epsilon_i+X_i(hatbeta-beta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$D^12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$J;SPMgt;K_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A^-1leB^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(tildeX_2|tildeX_1)=tildeX_1gamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildev=tildeetabeta_0+tildeepsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeepsilon^2tildeX'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{x^*v}=E{x^*u}=E{y^*u}=E{y^*v}=E{vu}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_IV${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatepsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2_IV=hatsigma^2_2SLS${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntoinfty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeZ'tildey}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Xbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'tildeepsilon}ne0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$R^N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A^12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2;SPMlt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$j^rmth${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX=(tildeX_1,ldots,tildeX_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1times1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_SIV${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$langley,xrangle=sum_i=1^Ny_ix_iN${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$D^+${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1timesK_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$langleX_i,epsilonrangle=langleX_i,y-Xbetarangle=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Xhatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$D^-12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$q_d=q_s${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'epsilon}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeW^*=P(tildeX|tildeZ)=tildeZgamma^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeepsilon=tildey-tildeXbeta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'_1tildeepsilon}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'_1tildeeta}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[X'X]^+${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[E{tildeW^*'tildeW^*}]^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeepsilon|tildeX}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_2SLS${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildey=tildeX_1beta_1+nu${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$M^mboxth${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Jtimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(y^*,x^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P_WP_Z=P_ZP_W=P_W${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ktimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2SLS${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilon_d}=E{epsilon_s}=E{epsilon_depsilon_s}=E{epsilon_dy}=E{epsilon_sy}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X^j${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxlin(X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilonu}=E{epsilonv}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatepsilon_i^2=(y_i-X_ihatbeta_SIV)^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=[E{tildeX'_1tildeX_1}]^-1E{tildeX'_1tildeX_2}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX_2'epsilon}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$OmegageOmega^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_1+gammabeta_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|tildey|^2equivlangletildey,tildeyrangle${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X^1,ldots,X^K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'_1xi}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$anemboxboldmath$0$${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{v}=E{u}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta=epsilon-betau+v${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(tildey,tildeX)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha_i=-a_ia_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtN(hatbeta-beta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeW=tildeZgamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|y|^2equivlangley,yrangle${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^*-1=E{P(tildeX|tildeZ)'P(tildeX|tildeZ)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A^-12A^-12=A^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_IV${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildey-P(tildey|tildeX_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$R^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{(tildey-tildeXbeta)^2}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_IV=beta_2SLS=beta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X^1ldots,X^K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$JgeK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_2SLS=hatbeta_SIV${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_0nebeta^*=[E{tildeX'tildeX}]^-1E{tildeX'tildey}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeW^*=tildeZgamma^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'_1tildeX_2}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^-1=E{P(tildeX|tildeW)'P(tildeX|tildeW)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_o${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${(y_1,X_1),ldots,(y_N,X_N)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ex^*epsilon=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildey|tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W=Zhatgamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$AgeB${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1timesK_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(tildeepsilon|tildeX_1)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(pi_1,pi_2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Nlongrightarrowinfty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[E{tildeX'_1tildeX_1}]^-1E{tildeX'_1tildeX_2}beta_2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildexi${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma^*=[E{tildeZ'tildeZ}]^-1E{tildeZ'tildey}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildey=tildeXbeta_0+tildeepsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g_nlongrightarrowg${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_SIV=beta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatLambdalongrightarrowLambda${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y^*x${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_1=[X'_1X_1]^-1X'_1y${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y=(y_1,ldots,y_N)'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1timesJ${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeepsilon|tildeZ}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Lambda${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(tildey,tildeX_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_nlongrightarrowbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$WD^-12W'${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(tildeX|tildeZ)=tildeZgamma^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$bullet${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P_Z${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar{tildeepsilon|tildeZ}=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$[E{tildeW'tildeX}]^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildey${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X_1,ldots,X_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$yinR^N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeXbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar(tildeepsilon|tildeX}=E{tildeepsilon^2|tildeX}=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(tildeX|tildeZ)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$JtimesJ${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$KtimesJ${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$yinH${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$langleX_i,X_jrangle${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX'tildey}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma;SPMlt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$NtimesJ${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeZ'tildeX}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeyinL^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatLambda${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$NtimesN${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega^*-1geOmega^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{tildeX_1'epsilon}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_2SLS=beta_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$omega${_inline}/;
$cached_env_img{$key} = ' 
';
1;