# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{displaymath}widehatg_N(widehattheta_N)=widehatg_N(theta^*)-widehatG_N(overlinetheta)(widehattheta_N-theta^*){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q(beta)=-Evarepsilon_i^4-6(beta-beta^*)^2Evarepsilon_i^2Ex_i^2-(beta-beta^*)^4Ex_i^4.{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}nabla_betaQ_N(widehatbeta_N)=-frac1Nsum_i=1^N4(y_i-widehatbeta_Nx_i)^3x_i=0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}nabla_thetal_N(widehattheta_N)=frac1Nsum_i=1^Nnabla_thetalogf(x_i|widehattheta_N)=0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_NinTheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatg_N(widehattheta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*in${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Q(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$thetaneqtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W=Omega^-1=E[g(x,theta^*)g(x,theta^*)^prime]^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W_N=[frac1Nsum_i=1^Ng(x_i,widehattheta)g(x_i,widehattheta)^prime]^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtN(widehatbeta_N-beta^*)stackreldrightarrowNleft[0,frac16Evarepsilon_i^6Ex_i^2left(12Evarepsilon_i^2Ex_i^2right)^2right]=Nleft[0,frac19fracEvarepsilon_i^6Ex_i^2left(Evarepsilon_i^2Ex_i^2right)^2right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtN(widehatbeta_N-beta^*)=left[frac1Nsum_i=1^N12(y_i-overlinebetax_i)^2x_i^2right]^-1frac1sqrtNsum_i=1^N4(y_i-beta^*x_i)^3x_itext.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtNleft(widehattheta_N-theta_Nright)stackreldrightarrowNleft[0,calI^-1(theta^*)right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q_N(theta)=-widehatg_N(theta)^primeW_Nwidehatg_N(theta){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_N=argmax_thetainThetaQ_N(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Q(theta)=-left[W^frac12primeg_0(theta)right]^primeleft[W^frac12primeg_0(theta)right];SPMlt;Q(theta^*)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sup_thetainThetaleft|frac1Nsum_i=1^Ng(x_i,theta)-E[g(x,theta)]right|stackrelprightarrow0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E[g(x,theta)]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}g_0(theta)=E[g(x,theta)].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_Nstackrelprightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinetheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtN(widehattheta_N-theta_N)=left[frac1Nsum_i=1^Nnabla_thetathetalogf(x_i|overlinetheta)right]^-1frac1sqrtNsum_i=1^Nnabla_thetalogf(x_i|theta_N)text.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}V(widehatbeta_OLS)=fracsigma^2Ex_i^2=sigma^2;SPMlt;frac53sigma^2=V(widehatbeta).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinebeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(Theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}left[widehatG_N(widehattheta_N)^primeW_NwidehatG_N(overlinetheta)right]^-1widehatG_N(widehattheta_N)^primeW_Nstackrelprightarrow(G^primeWG)^-1G^primeW,{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}0=-widehatG_N(widehattheta_N)^primeW_Nleft[widehatg_N(theta^*)-widehatG_N(overlinetheta)(widehattheta_N-theta^*)right]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q(theta)=-g_0(theta)^primeWg_0(theta){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}V(widehatbeta)=frac19fracEvarepsilon_i^6E1^2left(Evarepsilon_i^2E1^2right)^2=frac19frac15left(sigma^2right)^3left(sigma^2right)^2=frac53sigma^2.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}lim_NrightarrowinftyS_N^-2sum_i=1^Nint_|y_iN|;SPMgt;varepsilonS_Ny_iN^2f(x_i|theta_N)dx_i=0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}frac1Nsum_i=1^Nnabla_thetathetalogf(x_i|overlinetheta)stackrelprightarrowEleft[nabla_thetathetalogf(x_i|theta^*)right]=calI(theta^*).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Evarepsilon_i^3=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sup_thetainThetaleft|Q_N(theta)-Q(theta)right|stackrelprightarrow0.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g(x,theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtN(widehattheta_N-theta^*)=left[widehatG_N(widehattheta_N)^primeW_NwidehatG_N(overlinetheta)right]^-1widehatG_N(widehattheta_N)^primeW_NsqrtNwidehatg_N(theta^*)text.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Omega=E[g(x,theta^*)g(x,theta^*)^prime]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinebetastackrelprightarrowbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${x_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtNleft(widehattheta_N-theta^*right)stackreldrightarrowNleft[0,(G^primeWG)^-1G^primeWOmegaWG(G^primeWG)^-1right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pleft((X_N-X)^prime(X_N-X);SPMgt;varepsilon^2right)leqfracE(X_N-X)^prime(X_N-X)varepsilon^2rightarrow0qquadtextasNrightarrowinfty{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Wg_0(theta)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W^frac12primeg_0(theta)neq0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*+fracdeltaNrightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatbeta_Nstackrelprightarrowbeta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}frac1Nsum_i=1^N12(y_i-overlinebetax_i)^2x_i^2stackrelprightarrow12Evarepsilon_i^2Ex_i^2.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}frac1sqrtNsum_i=1^Nnabla_thetalogf(x_i|theta_N)stackreldrightarrowNleft[0,calI(theta^*)right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}nabla_thetaQ_N(widehattheta_N)=-left[nabla_thetawidehatg_N(widehattheta_N)right]^primeW_Nwidehatg_N(widehattheta_N)=-widehatG_N(widehattheta_N)^primeW_Nwidehatg_N(widehattheta_N)=0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_i=1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$G=E[nabla_thetag(x,theta^*)]${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatbeta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Evarepsilon_i^6=15left(sigma^2right)^3${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta=beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_N=theta^*+fracdeltaN${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(G^primeOmegaG)^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon;SPMgt;0,${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left|g(x,theta)right|leqd(x)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}0=-frac1Nsum_i=1^N4(y_i-beta^*x_i)^3x_i-left[frac1Nsum_i=1^N12(y_i-overlinebetax_i)^2x_i^2right](widehatbeta_N-beta^*){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$I-Omega^-frac12G(G^primeOmegaG)^-1G^primeOmega^-frac12${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtNwidehatg_N(theta^*)stackreldrightarrowNleft[0,Omegaright].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Pleft(left|X_N-Xright|;SPMgt;varepsilonright)leqfracE(X_N-X)^2varepsilon^2rightarrow0qquadtextasNrightarrowinfty{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}0=frac1Nsum_i=1^Nnabla_thetalogf(x_i|theta_N)+frac1Nsum_i=1^Nnabla_thetathetalogf(x_i|overlinetheta)(widehattheta_N-theta_N){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$lim_NrightarrowinftyW_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}frac1sqrtNsum_i=1^N4varepsilon_i^3x_istackreldrightarrowNleft[0,16Evarepsilon_i^6Ex_i^2right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$W_N=I${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinethetastackrelprightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$nabla_thetalogf(x_i|theta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
1;