# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$sigma^2(x)=Phi(xtheta^*)[1-Phi(xtheta^*)]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}widehatPsi(x)=fracsum_i=1^NK_hleft(x_i-xright)y_isum_i=1^NK_hleft(x_i-xright),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$F_N(hattheta^1_N,hattheta^2_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$;h,${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu_1-mu_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11=1=sigma_22${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11=sigma_22=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$K_hleft(x_i-xright)=frac1hKleft(fracx_i-xhright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$-H_N(hattheta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L_N(hattheta_N)=-.5751${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta_1=0.095360${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=(theta_0,theta_1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_N(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$haty_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_12=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Phi${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$|H_N(theta)-H(theta)|to0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma_mboxnlsgeSigma_mboxmle${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y_i=theta_0+theta_1x_i+theta_2x^2_i+theta_3x^3_i+eta_i{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig1.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma_mboxmle${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildetheta^2_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${0,1}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxstd(hattheta_2)=0.102891${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}theta^0=argmin_thetainR^4Eleft{[Psi(x|theta)-mboxPr{y=1|x}]^2right}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(i,x,theta)=xtheta_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI(theta^*)=-H(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2(x)=Phi(xhattheta^1_N)[1-Phi(xhattheta^1_N)]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_12=-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta^1_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta^2_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxPr{y=1|x}=Phi(xtheta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$F_N(alpha,beta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^1_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma_mboxnls${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtN(hattheta_N-theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatW=102.15${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatW=2.788${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtsigma_11-2sigma_12+sigma_22=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hath=.3037${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta_2=0.096739${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu_0=mu_1=mune0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11=12=sigma_22${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11=sigma_22=.5${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig2.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H_N(tildetheta^2_N)toH(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta_Ntotheta^0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Phi(xtheta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta)=mboxPr{1|x,theta}=Phi(xtheta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Phi(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxPr{y=1|x}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y=Phi(xtheta^*)+eta,{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI_N(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu_0=mu_1=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2(x_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}left(epsilon_0atopepsilon_1right)simN(mu,Sigma),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_0=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_11=1.5=sigma_22${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}(theta_1-theta_0)oversqrt2-2sigma_12=beta,{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatW${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$u(i,x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI_N(hattheta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{eta|x}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${eta_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(8),ldots,(12)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatSigma_N=H^-1_N(hattheta_N)calI_N(hattheta_N)H^-1_N(hattheta_N),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatW=N(hattheta_N-theta^*)'hatSigma_N^-1(hattheta_N-theta^*),{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}-H(theta^*)=Eleft{partialoverpartialthetaPhi(xtheta^*)partialoverpartialtheta'Phi(xtheta^*)right},{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_1-epsilon_0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$;widehath=caststd(x)astn^-frac15,,${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E{y|x}=1timesmboxPr{y=1|x}+0timesmboxPr{y=0|x}=mboxPr{y=1|x}=Phi(xtheta^*).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig3.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildetheta^2_Ntotheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x|theta^0)=exp{xtheta^0)(1+exp(xtheta^0))${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(theta_0,theta_1,sigma_12)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}calI(theta^*)=Eleft{Phi(xtheta*)[1-Phi(xtheta^*)]partialoverpartialthetaPhi(xtheta^*)partialoverpartialtheta'Phi(xtheta^*)right},{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$phi(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylrrrrmboxParameter;SPMamp;theta_0;SPMamp;theta_1;SPMamp;theta_2;SPMamp;theta_3mboxTrueValue;SPMamp;0.500;SPMamp;0.200;SPMamp;0.100;SPMamp;-0.050mboxProbitMLEhfil;SPMamp;0.543;SPMamp;0.173;SPMamp;0.083;SPMamp;-0.038mboxStd.Dev.;SPMamp;0.031;SPMamp;0.040;SPMamp;0.020;SPMamp;0.011mboxLogitMLEhfil;SPMamp;0.877;SPMamp;0.295;SPMamp;0.144;SPMamp;-0.065mboxStd.Dev.;SPMamp;0.051;SPMamp;0.068;SPMamp;0.034;SPMamp;0.019array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$F_N(theta^*,theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu_1=mu_0=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Kleft(cdotright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxstd(hattheta_2)=0.094864${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxstd(hattheta_1)=.030680${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxstd(hattheta_1)=.030548${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma_22${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatWLongrightarrowchi^2(4)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$p=Phi(x_i|theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sigma^2(x_i)=Psi(x_i|theta^*)[1-Psi(x_i|theta^*)],{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatSigma_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*2=0.1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${-Phi(xtheta^*),1-Phi(xtheta^*)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i=Psi(x_i|theta^*)+eta_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig4.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$3.4times10^-21${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_1-epsilon_0simN(mu_1-mu_0,sigma_11-2sigma_12+sigma_22)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtN[hattheta^1_N-theta^*]=O_p(1)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi(x,theta^*)=mboxPr{y=1|x}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$cinlbrack0.5,2.5].${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}theta=partialoverpartialx[u(1,x,theta)-u(0,x,theta)].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylrrrrmboxParameter;SPMamp;theta_0;SPMamp;theta_1;SPMamp;theta_2;SPMamp;theta_3mboxTrueValue;SPMamp;0.500;SPMamp;0.200;SPMamp;0.100;SPMamp;-0.050mboxProbitNLShfil;SPMamp;0.542;SPMamp;0.174;SPMamp;0.085;SPMamp;-0.038mboxStd.Dev.;SPMamp;0.030;SPMamp;0.040;SPMamp;0.020;SPMamp;0.011mboxLogitNLShfil;SPMamp;0.876;SPMamp;0.295;SPMamp;0.145;SPMamp;-0.064mboxStd.Dev.;SPMamp;0.051;SPMamp;0.068;SPMamp;0.034;SPMamp;0.019array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Psi=Phi${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x)=Phi(xtheta^*)[1-Phi(xtheta^*)]=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
1;