# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$Z_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft{P(thetainA|X_1,ldots,X_N+1)big|X_1,ldots,X_Nright}=P(thetainA|X_1,ldots,X_N).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}A(L)X_t=B(L)epsilon_t{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${p_1,ldots,p_K}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${b_1,ldots,b_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}widehattheta_N=argmax_thetainThetaQ_N(theta).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p_j${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI_tsupset(tildeZ_1,ldots,tildeZ_t)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p^hboxrmth${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}L^kX_t=X_t-k{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Omega=E{h(tildey,tildex,theta^*)h(tildey,tildex,theta^*)'}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Jtimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeZ_t=P(thetainA|tildeX_1ldots,X_t)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ktimes1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1=sum_i=1^Ktheta_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$B(theta^*,varepsilon)={thetainR^kbig||theta-theta^*|;SPMlt;epsilon}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${X_t}={1,2,3}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatOmega_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(y_t,x_t)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${tildeZ_t}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${X_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}H_N(theta)=1overNsum_i=1^Nh(y_i,x_i,theta),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$b_4=K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*=(theta^*_1,ldots,theta^*_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(x|theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i=1,ldots,N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hattheta_N=argmin_thetainThetaH_N(theta)[hatOmega_N]^-1H_N(theta),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Eleft{tildeZ_t+1|calI_tright}=tildeZ_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_i,x_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}p(theta)=Gamma(alpha_1+cdots+alpha_K)overGamma(alpha_1)cdotsGamma(alpha_K)theta_1^alpha_1-1cdotstheta_K^alpha_K-1{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_t,epsilon_s${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pleft(widehattheta_NnotinB(theta^*,varepsilon)right)stackrelprightarrow0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q(theta^*);SPMgt;sup_thetanotinB(theta^*,varepsilon)Q(theta){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$b_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI_t${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_i;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*_j(p_1,ldots,p_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}NH_N(hattheta_N)[hatOmega_N]^-1H_N(hattheta_N)_Longrightarrowatopdchi^2(J-K),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sup_thetainThetaleft|Q_N(theta)-Q(theta)right|stackrelprightarrow0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatbeta^2_T=sum_t=1^Tx_ty_toversum_t=1^Tx^2_t{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_iin(0,1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^k${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar(epsilon_t|x_t)=sigma^2|x_t|^theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tnes${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}A(L)=alpha_0+alpha_1L+alpha_2L^2+cdots+alpha_qL^q{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(X_1,ldots,X_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(alpha_0sigma,ldots,alpha_qsigma)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$b_1=2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${X_t}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$thetainR^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=(theta_1,ldots,theta_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P(thetainA|X_1,ldots,X_N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$AsubsetTheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}B(L)=beta_0+beta_1L+beta_2L^2+cdots+beta_pL^p{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(alpha,beta_1,ldots,beta_K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilon_t}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$chi^2(J-K)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}theta^*_j(p_1,ldots,p_K)=expleft{beta_j+alphap_jright}oversum_k=1^Kexpleft{beta_k+alphap_kright}{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatbeta^1_T=sum_t=1^Ty_toversum_t=1^Tx_t{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$q^hboxrmth${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntoinfty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilon_t|x_t}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha_i;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta^*,theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i=1,ldots,K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$k=1,ldots,K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pr{X_i=k}=theta_k,quadk=1,ldots,K.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$chi^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y_t=betax_t+epsilon_t{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${epsilon_t}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*_k${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_t${_inline}/;
$cached_env_img{$key} = ' 
';
1;