# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{displaymath}R_it=gamma+beta_i(R_mt-gamma)+epsilon_it,quadi=1,ldots,K,quadt=1,ldots,T,eqno(1){displaymath}/;
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$key = q/{_inline}${p_1,ldots,p_K}${_inline}/;
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$key = q/{displaymath}logleft{P(d|x)right}=x_dtheta-logleft{sum_j=1^Jexp{x_jtheta}right}.{displaymath}/;
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$key = q/{_inline}$hatthetatotheta^*${_inline}/;
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$key = q/{_inline}$126times126${_inline}/;
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$key = q/{_inline}$theta=(q_2,q_3)${_inline}/;
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$key = q/{_inline}$theta${_inline}/;
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$key = q/{displaymath}left[Sigmaright]^-1=left[arraycccc1overp_1;SPMamp;0;SPMamp;cdots;SPMamp;00;SPMamp;1overp_2;SPMamp;cdots;SPMamp;0cdots;SPMamp;cdots;SPMamp;cdots;SPMamp;cdotscdots;SPMamp;cdots;SPMamp;1overp_K-2;SPMamp;00;SPMamp;cdots;SPMamp;cdots;SPMamp;1overp_K-1arrayright]+1over(1-p_1-p_2-cdots-p_K-1)left[arraycccc1;SPMamp;1;SPMamp;cdots;SPMamp;11;SPMamp;1;SPMamp;cdots;SPMamp;11;SPMamp;cdots;SPMamp;cdots;SPMamp;11;SPMamp;cdots;SPMamp;cdots;SPMamp;11;SPMamp;1;SPMamp;cdots;SPMamp;1arrayright].{displaymath}/;
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$key = q/{_inline}$i=1,ldots,2000${_inline}/;
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$key = q/{_inline}$x=(x_1,x_2,x_3)${_inline}/;
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$key = q/{_inline}$18times1${_inline}/;
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$key = q/{_inline}$beta${_inline}/;
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$key = q/{_inline}$mboxmed(epsilon_t|X_t)=0${_inline}/;
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$key = q/{_inline}$tildeD_i${_inline}/;
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$key = q/{_inline}$Ktimes1${_inline}/;
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$key = q/{_inline}$v_j${_inline}/;
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$key = q/{_inline}$theta=(theta_2,theta_3)${_inline}/;
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$key = q/{_inline}$tildeG_i${_inline}/;
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$key = q/{_inline}$q_1${_inline}/;
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$key = q/{_inline}$x_j${_inline}/;
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$key = q/{_inline}$Gamma${_inline}/;
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$key = q/{_inline}$q_3${_inline}/;
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$key = q/{displaymath}tildeG_i=tildeE_1+cdotstildeE_alpha{displaymath}/;
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$key = q/{_inline}$W(rho,Omega)${_inline}/;
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$key = q/{_inline}${tildeX_1,ldots,tildeX_N}${_inline}/;
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$key = q/{_inline}$sigma_ij=E{epsilon_itepsilon_jt}${_inline}/;
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$key = q/{_inline}$beta;SPMgt;0${_inline}/;
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$key = q/{_inline}$rho=70${_inline}/;
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$key = q/{_inline}$R_it${_inline}/;
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$key = q/{_inline}$mboxboldmath$tildeD$=(tildeD_1,ldots,tildeD_K)${_inline}/;
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$key = q/{_inline}$Sigma${_inline}/;
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$key = q/{_inline}$R_mt${_inline}/;
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$key = q/{_inline}$(epsilon_1,epsilon_2)${_inline}/;
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$key = q/{_inline}$H_N(hattheta)toH(theta^*)${_inline}/;
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$key = q/{displaymath}partiallogleft{P(d|x)right}partialtheta=sum_j=1^Jleft[I{j=d}-P(j|x)right]x_j{displaymath}/;
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$key = q/{_inline}$E{epsilon_itepsilon_js}=0${_inline}/;
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$key = q/{_inline}$KtimesK${_inline}/;
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$key = q/{displaymath}mboxttpubJohn_Rustcoursesecon161statsstocksdat{displaymath}/;
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$key = q/{_inline}$x_1times3${_inline}/;
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$key = q/{_inline}$theta_k${_inline}/;
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$key = q/{displaymath}Sigma=left[arrayccccp_1(1-p_1);SPMamp;-p_1p_2;SPMamp;cdots;SPMamp;-p_1p_K-1-p_1p_2;SPMamp;p_2(1-p_2);SPMamp;cdots;SPMamp;-p_2p_K-1cdots;SPMamp;cdots;SPMamp;cdots;SPMamp;cdotscdots;SPMamp;cdots;SPMamp;cdots;SPMamp;cdots-p_1p_K-1;SPMamp;p_2p_K-1;SPMamp;cdots;SPMamp;p_K-1(1-p_K-1)arrayright],{displaymath}/;
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$key = q/{_inline}$gamma${_inline}/;
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$key = q/{displaymath}v_j=xtheta_j+epsilon_j,quadj=1,2,3eqno(6){displaymath}/;
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$key = q/{displaymath}partial^2logleft{P(d|x)right}partialthetapartialtheta'=-sum_j=1^Jx_jx_j'P(j|x)+left[sum_j=1^Jx_jP(j|x)right]left[sum_j=1^Jx_jP(j|x)right]'{displaymath}/;
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$key = q/{_inline}$[Sigma]^-1${_inline}/;
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$key = q/{_inline}$alpha${_inline}/;
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$key = q/{_inline}$2times2${_inline}/;
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$key = q/{displaymath}Sigma=[sigma_ij],eqno(2){displaymath}/;
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$key = q/{displaymath}hatbeta=argmin_beta1overTsum_t=1^T|y_t-X_tbeta|eqno(8){displaymath}/;
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$key = q/{_inline}$754times65${_inline}/;
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$key = q/{_inline}$f(x)=betaexp{-betax}${_inline}/;
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$key = q/{_inline}$Omega=I${_inline}/;
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$key = q/{_inline}$63times63${_inline}/;
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$key = q/{_inline}$xge0${_inline}/;
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$key = q/{_inline}$theta=p(lambda)${_inline}/;
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$key = q/{_inline}$epsilon_it${_inline}/;
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$key = q/{_inline}$(K-1)times(K-1)${_inline}/;
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$key = q/{_inline}$theta_21${_inline}/;
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$key = q/{_inline}$tnes${_inline}/;
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$key = q/{_inline}${tildeX_1,ldots,tildeX_1000}${_inline}/;
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$key = q/{_inline}$(tildeG_1,ldots,tildeG_K)${_inline}/;
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$key = q/{_inline}$theta_kge0${_inline}/;
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$key = q/{_inline}$sup_thetainTheta|H_N(theta)-H(theta)|to0${_inline}/;
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$key = q/{_inline}$thetainDelta^K-1${_inline}/;
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$key = q/{_inline}$theta^*${_inline}/;
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$key = q/{_inline}$(alpha,beta)${_inline}/;
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$key = q/{_inline}$R^2${_inline}/;
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$key = q/{_inline}$q_2${_inline}/;
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$key = q/{displaymath}f(x_i|theta)=prod_k=1^Ktheta_k^I{x_i=k},eqno(4){displaymath}/;
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$key = q/{_inline}$sum_k=1^Ktheta_k=1${_inline}/;
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$key = q/{_inline}$beta^*${_inline}/;
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$key = q/{displaymath}sum_k=1^Kp_k=1.{displaymath}/;
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$key = q/{_inline}$thetainR^K${_inline}/;
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$key = q/{_inline}$126times1${_inline}/;
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$key = q/{_inline}$x=(x_1,ldots,x_J)${_inline}/;
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$key = q/{_inline}$E{epsilon_it|R_mt}=0${_inline}/;
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$key = q/{displaymath}R_it=alpha_i+beta_iR_mt+epsilon_it,quadi=1,ldots,K,quadt=1,ldots,Teqno(3){displaymath}/;
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$key = q/{_inline}$(tildeE_1,ldots,tildeE_alpha)${_inline}/;
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$key = q/{_inline}$theta^*=(.1,.2,.4,.3)${_inline}/;
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$key = q/{displaymath}y_t=X_tbeta^*+epsilon_t,quadt=1,ldots,Teqno(7){displaymath}/;
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$key = q/{_inline}$(alpha',beta')'${_inline}/;
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$key = q/{_inline}$theta_32${_inline}/;
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$key = q/{_inline}$(Sigma,alpha,beta)${_inline}/;
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$key = q/{_inline}$mboxboldmath$alpha$=(alpha_1,ldots,alpha_K)${_inline}/;
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$key = q/{_inline}$lambda${_inline}/;
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$key = q/{_inline}$alpha_k;SPMgt;0${_inline}/;
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$key = q/{_inline}$k=1,ldots,K${_inline}/;
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$key = q/{_inline}$alphainR^K_+${_inline}/;
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$key = q/{displaymath}tildeD_i=tildeG_iover(tildeG_1+cdots+tildeG_K){displaymath}/;
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$key = q/{_inline}$alpha=(3,1,4,4)${_inline}/;
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$key = q/{_inline}$(x_1,x_2,x_3)${_inline}/;
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$key = q/{_inline}$3times1${_inline}/;
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$key = q/{_inline}$theta_1${_inline}/;
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$key = q/{_inline}$(alpha_i,beta)${_inline}/;
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$key = q/{displaymath}theta_k=p_k(lambda)=exp{lambda_k}oversum_k'=1^Kexp{lambda_k'}.eqno(5){displaymath}/;
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$key = q/{_inline}$6times1${_inline}/;
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1;