# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$tildeepsilon_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(1,x,theta)=x'theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E{tildeepsilon}=int_-infty^+inftyepsilonexp{-epsilon}expleft{-exp{-epsilon}right}depsilon=alpha+sigmagamma,eqno(11){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}tildeu_d=v_d+tildeepsilon_d,quadd=1,ldots,Deqno(1){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$v_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$max_d{epsilon_d}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I{delta(epsilon)=d}=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(epsilon|X)=prod_d=1^Dexp{-epsilon_d}expleft{-exp{-epsilon_d}right}.eqno(8){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar{epsilon(i)}=12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon=(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(theta_0,theta_1,theta_2,theta_3)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}F(x|alpha,sigma)=P{tildeepsilonlex|alpha,sigma}=expleft{-expleft{-(x-alpha)oversigmaright}right}.eqno(12){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon)=d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}f(epsilon)=Kexpleft{-left|epsilonoversqrtsigma^2right|right}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}phi(y)=1oversqrt2piexp{-y^22}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}alpha=sigmalogleft[sum_d=1^Dexp{alpha_dsigma}right]eqno(13){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(epsilon|X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$alpha${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(1,x,theta)+epsilon(1);SPMgt;u(0,x,theta)+epsilon(0)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X=(X_1,ldots,X_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$partialUpartialv_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}partialU(v_1,ldots,v_D,X)overpartialv_d=P{d|X}eqno(6){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Phi(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}U(v_1,ldots,v_D,X)=gamma+logleft[sum_d=1^Dexp{v_d}right].eqno(10){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(1,x,theta)=theta_0+x'theta_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=.577216ldots${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}P{d|X}=exp{v_d}oversum_d'=1^Dexp{v_d'}.eqno(9){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x'theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I{delta(epsilon)=d}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(1,x,theta)+epsilon(1)leu(0,x,theta)+epsilon(0)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatbeta_mboxlad=argmin_betasum_i=1^N|y_i-X_ibeta|.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta)=P{y=1|x,theta}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y_i=X_ibeta+epsilon_i,quadi=1,ldots,N{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(y_i,x_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pleft{d|Xright}=intI{d=delta(epsilon)}f(epsilon|X)depsiloneqno(4){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}partialpartialv_dmax_d=1,ldots,D[v_d+epsilon_d]=I{d=delta(epsilon)}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$int^infty_-inftyf(epsilon)depsilon=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}U(v_1,ldots,v_D,X)=Eleft{max_d=1,ldots,D[v_d+tildeepsilon_d]Big|Xright}=int_epsilon_1cdotsint_epsilon_Dmax_d=1,ldots,D[v_d+epsilon_d]f(epsilon_1,ldots,epsilon_D|X)depsilon_1cdotsdepsilon_Deqno(5){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(alpha_1,ldots,alpha_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}U(y,x,epsilon,theta)=u(y,x,theta)+epsilon(y),quady=0,1{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxcov(epsilon(1),epsilon(0)}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta(epsilon)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${epsilon(0),epsilon(1)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$max(epsilon_1,ldots,epsilon_D)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Psi(x,theta)=F(x'theta){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilon(i)}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_mboxlad${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}v_d=X_dbetaeqno(2){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}delta(epsilon)=mboxitargmax_d=1,ldots,Dleft[v_d+tildeepsilon_dright]eqno(3){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}x'theta=theta_0+theta_1x+theta_2x^2+theta_3x^3.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$P{d|X}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Phi(x)=int^x_-inftyphi(y)dy{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$U(v_1,ldots,v_D,X)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(0,x,theta)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeu_d${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta)=P{y|x,theta}${_inline}/;
$cached_env_img{$key} = ' 
';
1;