# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.
$key = q/{_inline}$E{eta^k}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H(theta^*)^-1calI(theta^*)H(theta^*)^-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar(hatdelta^2)=1.9481500${_inline}/;
$cached_env_img{$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} = ' 
';
$key = q/{_inline}$ainR^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=theta^o${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E[fracpartiallnf(x|theta)partialthetafracpartiallnf(x|theta)partialtheta']=-E[fracpartial^2lnf(x|theta)partialthetapartialtheta']{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylrrrrrrrmboxParameter;SPMamp;beta_0;SPMamp;beta_1;SPMamp;beta_2;SPMamp;beta_3;SPMamp;sigma^2;SPMamp;mu;SPMamp;delta^2mboxTrueValue;SPMamp;-3.000;SPMamp;2.000;SPMamp;-4.000;SPMamp;-0.010;SPMamp;0.015;SPMamp;0.000;SPMamp;1.000mboxMLEhfil;SPMamp;-3.259;SPMamp;2.228;SPMamp;-2.571;SPMamp;-0.971;SPMamp;0.015;SPMamp;-0.047;SPMamp;0.974mboxStd.Dev.;SPMamp;0.194;SPMamp;0.809;SPMamp;0.836;SPMamp;0.304;SPMamp;.00055;SPMamp;0.025;SPMamp;0.036array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g(y|x,beta,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_mboxfgls${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylrrrrrmboxParameter;SPMamp;mboxTruth;SPMamp;mboxMLE;SPMamp;mboxStd.Error;SPMamp;mboxFGLS;SPMamp;mboxStd.Errorbeta_0;SPMamp;-3.000;SPMamp;-3.256;SPMamp;0.190;SPMamp;-3.256;SPMamp;0.190beta_1;SPMamp;2.000;SPMamp;2.209;SPMamp;0.777;SPMamp;2.200;SPMamp;0.789beta_2;SPMamp;-4.000;SPMamp;-2.558;SPMamp;0.819;SPMamp;-2.548;SPMamp;0.833beta_3;SPMamp;-0.010;SPMamp;-0.966;SPMamp;0.295;SPMamp;-0.962;SPMamp;0.300gamma_0;SPMamp;-4.000;SPMamp;-4.012;SPMamp;0.044;SPMamp;-4.022;SPMamp;0.050gamma_1;SPMamp;0.000;SPMamp;0.030;SPMamp;0.053;SPMamp;0.006;SPMamp;0.069gamma_2;SPMamp;-0.200;SPMamp;-0.254;SPMamp;0.026;SPMamp;-0.239;SPMamp;0.039gamma_3;SPMamp;0.000;SPMamp;-0.010;SPMamp;0.014;SPMamp;0.002;SPMamp;0.025array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${partialf(x_i|theta_N)partialtheta}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L_N(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hattheta=argminQ_n(theta)rightarrow_ptheta^o=argminQ(theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E(epsilon_i|X_i)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig1.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$-H(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_i=(1,x_i,x_i^2,x_i^3)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinet_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q_n(theta)=frac1nsum_i=1^Nfrac12(Y_i-f(X_i|theta))^2{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(beta,;sigma^2,;mu,;delta^2right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtnfracpartialQ_n(theta^o)partialthetarightarrow_dNleft(0,Eleft((Y_i-f(X_i|theta^o))^2fracpartialpartialthetaf(X_i|theta^o)fracpartialpartialtheta'f(X_i|theta^o)right)right)equivN(0,B(theta^o)){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_i=left(1,x_i,x_i^2,x_i^3right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}1oversqrtNsum_i=1^Ny_i,N_LongrightarrowatopDN(0,sigma^2).{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartial^2lnf(x|theta)partialthetapartialtheta'=frac1f(x|theta)fracpartial^2f(x|theta)partialthetapartialtheta'-fracpartiallnf(x|theta)partialthetafracpartiallnf(x|theta)partialtheta'{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft{exp{toversqrtNsum_i=1^Ny_i,N}right}=left[1+1over2M''_y_i,N(overlinet_N)t^2Nright]^N.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$H(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatdelta^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$KtimesK${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(;mu,;delta^2right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_1,N,ldots,y_N,N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{sigma^2(tildex)}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mathcalIleft(theta^astright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}=left[arrayccccfrac1sigma^2Eleft(Z_iX_iright);SPMamp;0;SPMamp;0;SPMamp;00;SPMamp;-frac12sigma^4;SPMamp;0;SPMamp;00;SPMamp;0;SPMamp;-frac1delta^2;SPMamp;00;SPMamp;0;SPMamp;0;SPMamp;-frac12delta^4arrayright],{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$N(0,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,gamma)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Q(theta)=E(frac12(Y_i-f(X_i|theta))^2){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatgamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mathcalIleft(theta^astright)=-Hleft(theta^astright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x)=exp{-4-.2x^2}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i=1,ldots,N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$N(0,sigma^2(x))${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft[arrayccpartial^2lngleft(y|x;;left(beta,;sigma^2right)right)overpartial(beta,sigma^2)partial(beta,sigma^2)';SPMamp;00;SPMamp;partial^2lnhleft(x;;left(;mu,;delta^2right)right)overpartial(mu,delta^2)partial(mu,delta^2)'arrayright]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(Theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mathcalIleft(theta^astright).${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(X_i|theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtn(hattheta-theta^o)=-[fracpartial^2Q_n(overlinetheta)partialthetapartialtheta']^-1sqrtnfracpartialQ_n(theta^o)partialtheta{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma^*${_inline}/;
$cached_env_img{$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/{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} = ' 
';
$key = q/{_inline}$hatsigma^2(x_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma=left(gamma_0,gamma_1,gamma_2,gamma_3right)^prime.${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{epsilon^3}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$N(mbox$boldmath0$,Sigma)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar(y_i,N)=sigma^2_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^c_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(y_i,x_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^o=theta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}A(theta^o)=fracpartial^2Q_n(overlinetheta)partialthetapartialtheta'rightarrow_pEleft(fracpartialpartialthetaf(X_i|theta^o)fracpartialpartialtheta'f(X_i|theta^o)right){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$partial^2L^c_N(beta,gamma)partialbetapartialgamma'=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^o${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}widehatHleft(widehattheta_MLright)^-1widehatmathcalIleft(widehattheta_MLright)widehatHleft(widehattheta_MLright)^-1=left[arraycccc0.0374;SPMamp;-0.0872;SPMamp;0.0255;SPMamp;0.0157-0.0872;SPMamp;0.6543;SPMamp;-0.5643;SPMamp;-0.22150.0255;SPMamp;-0.5643;SPMamp;0.6998;SPMamp;0.25180.0157;SPMamp;-0.2215;SPMamp;0.2518;SPMamp;0.0923arrayright]{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2(x)ge0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^m_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig3.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$M''_y_i,N(0)=E{y_i,N^2}=sigma^2_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(y_i,x_iright)${_inline}/;
$cached_env_img{$key} = ' ';
$key = q/{_inline}$lim_Ntoinftya_N=a${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$-H(theta^*)=calI(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tsqrtN${_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)mbox.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}lim_NtoinftyM''_y_i,N(overlinet_N)=sigma^2.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mboxvar(hatsigma^2)=[hatmu_4-hatsigma^4]N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylccccmboxParameter;SPMamp;gamma_0;SPMamp;gamma_1;SPMamp;gamma_2;SPMamp;gamma_3mboxTrueValue;SPMamp;-4.0;SPMamp;0.0;SPMamp;-0.2;SPMamp;0.0mboxNLSestimatehfil;SPMamp;-4.022;SPMamp;0.006;SPMamp;-0.240;SPMamp;0.002mboxStandardDeviation;SPMamp;0.050;SPMamp;0.069;SPMamp;0.039;SPMamp;0.025array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$partialL_N^c(beta,hatgamma)partialbeta=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}hatmu_r=1overNsum_i=1^N(x_i-hatmu)^4.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$delta^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Ntoinfty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta_N=theta^*+fracdeltaN${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon_isimNleft(0,expleft(gamma_0+gamma_1x_i+gamma_2x_i^2right)right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon;SPMgt;0,${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$mu${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}y_i=exp{X_ibeta}exp{epsilon_i}{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}$4times1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$exp{X_igamma}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeX${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$nabla_thetalogf(x_i|theta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta^*,gamma^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Z_iequivleft[y_i-2expleft(X_ibetaright)right]expleft(X_ibetaright)X_i^prime${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2=0.015${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtn(hattheta-theta^o)rightarrow_dNleft(0,A(theta^o)^-1B(theta^o)A(theta^o)^-1right){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2(x_i)=exp{X_ihatgamma}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatmu_4${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L_N^c(hatbeta,gamma)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(beta,;sigma^2,;mu,;delta^2right),${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$eta=(x-mu^*)simN(0,delta^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*in${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$N(0,a'Sigmaa)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinethetarightarrow_ptheta^o${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$h(x|mu,delta^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^c_N(beta,gamma)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L_N^c(beta,gamma)${_inline}/;
$cached_env_img{$key} = ' ';
$key = q/{_inline}$mboxstd(hatsigma^2)=0.0005499${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$fracpartialQ_n(hattheta)partialtheta=o_p(n^-12)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$g(X_i)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatepsilon_i^2=(y_i-exp{X_ihatbeta})^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_isimNleft(mu,delta^2right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${a'y_i,N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$y_i,N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$lnf(x|theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^ast${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}arraylccccmboxParameter;SPMamp;widehatbeta_0;SPMamp;widehatbeta_1;SPMamp;widehatbeta_2;SPMamp;widehatbeta_3mboxTruevalues;SPMamp;-3.000;SPMamp;2.000;SPMamp;-4.000;SPMamp;-0.010mboxModelI(MLE);SPMamp;-3.259;SPMamp;2.228;SPMamp;-2.570;SPMamp;-0.971mboxModelII(OLS);SPMamp;-2.543;SPMamp;0.118;SPMamp;-0.152;SPMamp;-0.033array{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatsigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(cdot|theta_N)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta=left(beta_0,beta_1,beta_2,beta_3right)^prime${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$E{y_i,N}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$lim_Ntoinftysigma^2_N=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E[fracpartial^2lnf(x|theta)partialthetapartialtheta']=E[frac1f(x|theta)fracpartial^2f(x|theta)partialthetapartialtheta']-E[fracpartiallnf(x|theta)partialthetafracpartiallnf(x|theta)partialtheta']{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtNleft(widehattheta_N-theta_Nright)stackreldrightarrowNleft[0,calI^-1(theta^*)right].{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$i=sqrt-1${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Sigma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_i^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft((Y_i-f(X_i|theta^o))fracpartial^2partialthetapartialtheta'f(X_i|theta^o)right)=Eleft(epsilon_ifracpartial^2partialthetapartialtheta'f(X_i|theta^o)right)=0{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_i,N}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$A(theta^o)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,beta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$fracpartialQ_n(hattheta)partialthetaapprox0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(hatbeta_mboxfgls,hatgamma_mboxfgls)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$lim_Ntoinftysigma^2_N=sigma^2;SPMgt;0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$widehattheta_Nstackrelprightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinetheta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$R^K${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1,ldots,N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$X_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartialQ_n(hattheta)partialtheta=0=fracpartialQ_n(theta^o)partialtheta+fracpartial^2Q_n(overlinetheta)partialthetapartialtheta'(hattheta-theta^o){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$gamma${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig2.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$f(y,x|theta)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatthetarightarrow_ptheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left{left(y_i,x_iright)right}_i=1^N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$tildeepsilon_isimN(0,sigma^2(x_i))${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$M_y_i,N(t)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}ln(y_i)=X_ibeta+epsilon_i{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}calI_betabeta(theta^*)=Eleft{sigma^2(x)exp{Xbeta^*}XX'oversigma^4right}ne-Eleft{-exp{2Xbeta^*}XX'oversigma^2right}=-H_betabeta(theta^*){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}Eleft{left[ln(y)-Xbetaright]^2I{y;SPMgt;0}right}.{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta_3=-.97${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta_3^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1oversqrtNsum_i=1^Ny_i,N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${x_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$1,ldots,infty${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$exp{Xbeta}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L_N${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${epsilon_i}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(;beta,;gammaright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$Hleft(theta^astright)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}sqrtn(hattheta-theta^o)rightarrow_dNleft(0,sigma^2Eleft(fracpartialpartialthetaf(X_i|theta^o)fracpartialpartialtheta'f(X_i|theta^o)right)^-1right){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta=(beta,gamma,mu,delta^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$theta^*+fracdeltaNrightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$beta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${hatepsilon_i^2}${_inline}/;
$cached_env_img{$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}widehatmathcalI^-1left(widehattheta_MLright)=left[arraycccc114.9;SPMamp;-254.7;SPMamp;9.0;SPMamp;95.8-254.7;SPMamp;2155.5;SPMamp;-2045.8;SPMamp;-810.59.0;SPMamp;-2045.8;SPMamp;3765.1;SPMamp;6.295.8;SPMamp;-810.5;SPMamp;6.2;SPMamp;1721.5arrayright],{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}${y_i,N}={partialf(x_i|theta_N)partialtheta}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}E{left[y-exp(Xbeta)right]^2},{displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$M'_y_i,N(0)=E{y_i,N}=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$L^c_N(beta,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$hatbeta${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(mu,delta^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$varepsilon_isimNleft(0,sigma^2right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$exp{t^2sigma^22}${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$left(beta,;sigma^2right)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}theta^o=argminE((g(X_i)-f(X_i|theta))^2){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$calI_betabeta(theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$lim_Ntoinfty[1+a_NN]^N=expa${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,gamma)=(beta^*,gamma^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{}psfigfile=fig4.eps,angle=-90,height=2.5in{}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sqrtN(hattheta-theta^*)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon=(y-exp{Xbeta})${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$epsilon_isimN(0,sigma^2)${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x)=sigma^2${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{displaymath}fracpartial^2Q_n(overlinetheta)partialthetapartialtheta'rightarrow_pEleft(fracpartialpartialthetaf(X_i|theta^o)fracpartialpartialtheta'f(X_i|theta^o)right)-Eleft((Y_i-f(X_i|theta^o))fracpartial^2partialthetapartialtheta'f(X_i|theta^o)right)equivA(theta^o){displaymath}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$(beta,gamma)=0${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$overlinethetastackrelprightarrowtheta^*${_inline}/;
$cached_env_img{$key} = ' 
';
$key = q/{_inline}$sigma^2(x)${_inline}/;
$cached_env_img{$key} = ' 
';
1;