\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\@writefile{toc}{\contentsline {begintocitem}{}{}{}}
\@writefile{toc}{\contentsline {jobname}{Doksum}{}{}}
\@writefile{toc}{\contentsline {doi}{0003/0000.0000}{}{}}
\@writefile{toc}{\contentsline {arxiv}{math.PR/0000003}{}{}}
\gdef\hy@title{Semiparametric Models and Likelihood - The Power of Ranks}
\@writefile{toc}{\contentsline {title}{Semiparametric Models and Likelihood - The Power of Ranks}{66}{}}
\thanksnewlabel{e1@email}{{doksum@stat.wisc.edu}{66}}
\thanksnewlabel{e2@email}{{}{66}}
\thanksnewlabel{a1thanks}{{1}{66}}
\thanksnewlabel{t1thanks}{{\ensuremath  {*}}{66}}
\thanksnewlabel{a2thanks}{{2}{66}}
\@writefile{idx}{\indexentry {K. Doksum, \textit {University of Wisconsin, Madison}}{}}
\@writefile{idx}{\indexentry {A. Ozeki, \textit {University of Wisconsin, Madison}}{}}
\gdef\hy@author{Kjell Doksum and Akichika Ozeki}
\gdef\hy@subject{IMS Collections 2009 Vol. 0 66--92}
\gdef\hy@keywords{62G05, 62G20, 62N02, Lehmann model, proportional hazard model, profile NP likelihood, nonparametric maximum likelihood, MM algorithm, copula models, Box-Cox models, }
\@writefile{toc}{\contentsline {author}{Kjell Doksum and Akichika Ozeki}{67}{}}
\@writefile{toc}{\contentsline {endtocitem}{}{}{}}
\gdef\author@num{2}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{67}{section.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Lehmann Type Models. Cox Regression}{67}{subsection.1.1}}
\newlabel{eq1.1}{{1.1}{67}{Lehmann Type Models. Cox Regression\relax }{equation.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Sklar Type Models. Copula Regression}{67}{subsection.1.2}}
\newlabel{eq1.2}{{1.2}{68}{Sklar Type Models. Copula Regression\relax }{equation.1.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Proportional Hazard and Proportional Expected Hazard Rate Models}{68}{section.2}}
\newlabel{eq2.1}{{2.1}{68}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.1}{}}
\newlabel{eq2.2}{{2.2}{68}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.2}{}}
\newlabel{LEHMANN_MODEL}{{2.3}{68}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.3}{}}
\newlabel{HR_COX}{{2.5}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.5}{}}
\newlabel{SINAMI_PLUS}{{2.6}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.6}{}}
\newlabel{SINAMI_MINUS}{{2.7}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.7}{}}
\newlabel{SINAMI}{{2.8}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.8}{}}
\newlabel{SINAMI0}{{2.8}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.8}{}}
\newlabel{FRAILTY}{{2.11}{69}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.11}{}}
\newlabel{SINAMI_HR}{{2.12}{70}{Proportional Hazard and Proportional Expected Hazard Rate Models\relax }{equation.2.12}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Rank, Partial and Marginal Likelihood}{70}{section.3}}
\newlabel{SEC_RANK}{{3}{70}{Rank, Partial and Marginal Likelihood\relax }{section.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  \noindent SINAMI and PEHR hazard ratios for $\theta = -3, -1.5, 1.5, 3$.}}{71}{figure.1}}
\newlabel{FIG_HAZRATIO}{{1}{71}{ \label {FIG_HAZRATIO}\noindent SINAMI and PEHR hazard ratios for $\theta = -3, -1.5, 1.5, 3$}{figure.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Profile NP Likelihood}{72}{section.4}}
\newlabel{}{{4.1}{72}{Profile NP Likelihood\relax }{}{}}
\newlabel{}{{4.1}{72}{Profile NP Likelihood\relax }{}{}}
\newlabel{eq_PROLIK1}{{4.1}{72}{Profile NP Likelihood\relax }{equation.4.1}{}}
\newlabel{eq_PROLIK2}{{4.2}{72}{Profile NP Likelihood\relax }{equation.4.2}{}}
\newlabel{eq_PROLIK3}{{4.3}{73}{Profile NP Likelihood\relax }{equation.4.3}{}}
\newlabel{eq_LM_NP}{{4.4}{73}{Profile NP Likelihood\relax }{}{}}
\newlabel{BRESLOW_EQ}{{4.4}{73}{Profile NP Likelihood\relax }{equation.4.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Profile NP Likelihood for the PEHR Model}{73}{section.5}}
\newlabel{eq_PEHR_PR1}{{5.1}{73}{Profile NP Likelihood for the PEHR Model\relax }{equation.5.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}The MM Algorithm}{74}{subsection.5.1}}
\newlabel{SUR1}{{5.2}{74}{The MM Algorithm\relax }{equation.5.2}{}}
\newlabel{SUR2}{{5.3}{74}{The MM Algorithm\relax }{equation.5.3}{}}
\newlabel{B_A}{{5.4}{74}{The MM Algorithm\relax }{equation.5.4}{}}
\newlabel{UPDATE1}{{5.5}{74}{The MM Algorithm\relax }{equation.5.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)}{74}{subsection.5.2}}
\newlabel{SEC_MM_PLUS}{{5.2}{74}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{subsection.5.2}{}}
\newlabel{LOGLIK1}{{5.6}{74}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.6}{}}
\newlabel{B_org}{{5.7}{74}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.7}{}}
\newlabel{A_org}{{5.8}{74}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.8}{}}
\newlabel{B_h1}{{5.9}{75}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.9}{}}
\newlabel{A_h1}{{5.10}{75}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.10}{}}
\newlabel{MM_MAIN}{{5.11}{75}{The MM Algorithm for the PEHR Model with $\theta \geq 0$ (SINAMI with $\theta \geq 0$)\relax }{equation.5.11}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}The MM Algorithm for the SINAMI Model with $\theta \leq 0$}{75}{subsection.5.3}}
\newlabel{SEC_THETA_NEG}{{5.3}{75}{The MM Algorithm for the SINAMI Model with $\theta \leq 0$\relax }{subsection.5.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}The MM Algorithm for the SINAMI Model with $\theta \in R$}{75}{subsection.5.4}}
\newlabel{SEC_THETA_BOTH}{{5.4}{75}{The MM Algorithm for the SINAMI Model with $\theta \in R$\relax }{subsection.5.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Profile NPMLE Implementation}{75}{subsection.5.5}}
\newlabel{}{{5.12}{75}{Profile NPMLE Implementation\relax }{equation.5.12}{}}
\newlabel{EQ6.20}{{5.13}{75}{Profile NPMLE Implementation\relax }{equation.5.13}{}}
\newlabel{SINAMI_PDF}{{5.14}{76}{Profile NPMLE Implementation\relax }{equation.5.14}{}}
\newlabel{SINAMI_ALG}{{5.15}{76}{Profile NPMLE Implementation\relax }{}{}}
\newlabel{SINAMI_ALG1}{{5.15}{76}{Profile NPMLE Implementation\relax }{equation.5.15}{}}
\newlabel{F_H}{{5.16}{76}{Profile NPMLE Implementation\relax }{equation.5.16}{}}
\newlabel{SINAMI_ALG}{{5.18}{76}{Profile NPMLE Implementation\relax }{equation.5.18}{}}
\newlabel{eq_R5.3}{{5.21}{77}{Profile NPMLE Implementation\relax }{equation.5.21}{}}
\newlabel{eq_R5.3}{{5.22}{77}{Profile NPMLE Implementation\relax }{equation.5.22}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Estimation of the Variance of the Profile NPMLE}{77}{subsection.5.6}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Simulation Results}{77}{section.6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}PEHR Model Estimates}{77}{subsection.6.1}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces mysmallcaption}}{78}{table.1}}
\newlabel{SINAMI_TB1}{{1}{78}{mysmallcaption\relax }{table.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Model Fit for Misspecified Model}{78}{subsection.6.2}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Estimation in the Normal Copula Model}{78}{section.7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The One Covariate Case}{78}{subsection.7.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  \noindent Cox and PEHR estimated hazard ratio when $F_0 \sim EXP(1)$ and $F \sim $ Gamma or Weibull.}}{79}{figure.2}}
\newlabel{FIG_2outside}{{2}{79}{ \label {FIG_2outside}\noindent Cox and PEHR estimated hazard ratio when $F_0 \sim EXP(1)$ and $F \sim $ Gamma or Weibull}{figure.2}{}}
\newlabel{COPULA01}{{7.1}{79}{The One Covariate Case\relax }{}{}}
\newlabel{COPU_L1}{{7.2}{80}{The One Covariate Case\relax }{equation.7.2}{}}
\newlabel{remark7.1eq}{{7.3}{80}{The One Covariate Case\relax }{equation.7.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}The Multivariate Covariate Case}{81}{subsection.7.2}}
\newlabel{SEC_MCOV}{{7.2}{81}{The Multivariate Covariate Case\relax }{subsection.7.2}{}}
\newlabel{EQ_Y_COPULA}{{7.4}{81}{The Multivariate Covariate Case\relax }{equation.7.4}{}}
\newlabel{EQ_X_COPULA}{{7.5}{81}{The Multivariate Covariate Case\relax }{equation.7.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Transformation and NP Models}{81}{section.8}}
\newlabel{EQ8.1}{{8.1}{81}{Transformation and NP Models\relax }{equation.8.1}{}}
\newlabel{EQ8.2}{{8.2}{81}{Transformation and NP Models\relax }{equation.8.2}{}}
\newlabel{EQ8.3NEW}{{8.3}{82}{Transformation and NP Models\relax }{equation.8.3}{}}
\newlabel{EQ8.3}{{8.4}{82}{Transformation and NP Models\relax }{equation.8.4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  \noindent $\mathaccentV {hat}05E{\rho }$ boxplots for correctly specified model (\ref  {eq_sim1}) with n=128. Top 5: $\lambda _1 = \lambda _2=0.5$. Bottom 5: $\lambda _1 = \lambda _2=1$. The horizontal line gives the true value of $\rho $.}}{83}{figure.3}}
\newlabel{FIG_rho}{{3}{83}{ \label {FIG_rho}\noindent $\hat {\rho }$ boxplots for correctly specified model (\ref {eq_sim1}) with n=128. Top 5: $\lambda _1 = \lambda _2=0.5$. Bottom 5: $\lambda _1 = \lambda _2=1$. The horizontal line gives the true value of $\rho $}{figure.3}{}}
\newlabel{EQ_ALPHA_LSE}{{8.5}{83}{Transformation and NP Models\relax }{equation.8.5}{}}
\newlabel{NONPARA1}{{8.6}{83}{Transformation and NP Models\relax }{equation.8.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.1}Simulation Results}{84}{subsection.8.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {8.1.1}Correctly Specified Model}{84}{subsubsection.8.1.1}}
\newlabel{eq_sim1}{{8.7}{84}{Correctly Specified Model\relax }{equation.8.7}{}}
\newlabel{eq_F1F2}{{8.8}{84}{Correctly Specified Model\relax }{equation.8.8}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {8.1.2}Misspecified Model}{84}{subsubsection.8.1.2}}
\newlabel{eq_sim2}{{8.9}{84}{Misspecified Model\relax }{equation.8.9}{}}
\newlabel{EQ8.4}{{8.12}{84}{Misspecified Model\relax }{equation.8.12}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces   \noindent Boxplots of the three estimates of median regression m(x) for model (\ref  {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 0.5). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line.}}{86}{figure.4}}
\newlabel{FIG_L1_a1n0.5_var0.5}{{4}{86}{ \label {FIG_L1_a1n0.5_var0.5} \noindent Boxplots of the three estimates of median regression m(x) for model (\ref {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 0.5). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line}{figure.4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  \noindent Boxplots of the three estimates of median regression m(x) for model (\ref  {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 1). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line.}}{87}{figure.5}}
\newlabel{FIG_L1_a1n0.5_var1}{{5}{87}{ \label {FIG_L1_a1n0.5_var1}\noindent Boxplots of the three estimates of median regression m(x) for model (\ref {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 1). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line}{figure.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  \noindent Boxplots of the three estimates of median regression m(x) for model (\ref  {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 0.5). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line.}}{88}{figure.6}}
\newlabel{FIG_L0.5_a1n0.5_var0.5}{{6}{88}{ \label {FIG_L0.5_a1n0.5_var0.5}\noindent Boxplots of the three estimates of median regression m(x) for model (\ref {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 0.5). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line}{figure.6}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  \noindent Boxplots of the three estimates of median regression m(x) for model (\ref  {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 1). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line.}}{89}{figure.7}}
\newlabel{FIG_L0.5_a1n0.5_var1}{{7}{89}{ \label {FIG_L0.5_a1n0.5_var1}\noindent Boxplots of the three estimates of median regression m(x) for model (\ref {eq_sim2}) with ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 1). I: profile MLE, II: normal scores, and III: NP, spline. The true value of m(x) is the solid line}{figure.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  \noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 0.5). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$.}}{90}{figure.8}}
\newlabel{FIG_3MSE}{{8}{90}{ \label {FIG_3MSE}\noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 0.5). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$}{figure.8}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces  \noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 1). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$.}}{90}{figure.9}}
\newlabel{FIG_4MSE}{{9}{90}{ \label {FIG_4MSE}\noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(1, 1, 0.5, 1). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$}{figure.9}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces  \noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 0.5). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$.}}{90}{figure.10}}
\newlabel{FIG_3MSE}{{10}{90}{ \label {FIG_3MSE}\noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 0.5). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$}{figure.10}{}}
\bibcite{r1}{{1}{}{{}}{{}}}
\bibcite{r2}{{2}{}{{}}{{}}}
\bibcite{r3}{{3}{}{{}}{{}}}
\bibcite{r4}{{4}{}{{}}{{}}}
\bibcite{r5}{{5}{}{{}}{{}}}
\bibcite{r6}{{6}{}{{}}{{}}}
\bibcite{r7}{{7}{}{{}}{{}}}
\bibcite{r8}{{8}{}{{}}{{}}}
\bibcite{r9}{{9}{}{{}}{{}}}
\bibcite{r10}{{10}{}{{}}{{}}}
\bibcite{r11}{{11}{}{{}}{{}}}
\bibcite{r12}{{12}{}{{}}{{}}}
\bibcite{r13}{{13}{}{{}}{{}}}
\bibcite{r14}{{14}{}{{}}{{}}}
\bibcite{r15}{{15}{}{{}}{{}}}
\bibcite{r16}{{16}{}{{}}{{}}}
\bibcite{r17}{{17}{}{{}}{{}}}
\bibcite{r18}{{18}{}{{}}{{}}}
\bibcite{r19}{{19}{}{{}}{{}}}
\bibcite{r20}{{20}{}{{}}{{}}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  \noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 1). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$.}}{91}{figure.11}}
\newlabel{FIG_4MSE}{{11}{91}{ \label {FIG_4MSE}\noindent MSE of the three estimates of m(x) as a function of the misspecification parameter $\gamma $ for ($\lambda _1, \lambda _2,\alpha _1, \sigma ^2$)=(0.5, 0.5, 0.5, 1). $\bigcirc = I$, $\bigtriangleup = II$, $+ = III$}{figure.11}{}}
\@writefile{toc}{\contentsline {section}{Acknowledgements}{91}{section*.3}}
\@writefile{toc}{\contentsline {section}{References}{91}{section*.5}}
\bibcite{r21}{{21}{}{{}}{{}}}
\bibcite{r22}{{22}{}{{}}{{}}}
\bibcite{r23}{{23}{}{{}}{{}}}
\bibcite{r24}{{24}{}{{}}{{}}}
\bibcite{r25}{{25}{}{{}}{{}}}
\bibcite{r26}{{26}{}{{}}{{}}}
\bibcite{r27}{{27}{}{{}}{{}}}
\bibcite{r28}{{28}{}{{}}{{}}}
\bibcite{r29}{{29}{}{{}}{{}}}
\bibcite{r30}{{30}{}{{}}{{}}}
\bibcite{r31}{{31}{}{{}}{{}}}
\bibcite{r32}{{32}{}{{}}{{}}}
\bibcite{r33}{{33}{}{{}}{{}}}
\bibcite{r34}{{34}{}{{}}{{}}}
\bibcite{r35}{{35}{}{{}}{{}}}
\bibcite{r36}{{36}{}{{}}{{}}}
\bibcite{r37}{{37}{}{{}}{{}}}
\bibcite{r38}{{38}{}{{}}{{}}}
\bibcite{r39}{{39}{}{{}}{{}}}
\bibcite{r40}{{40}{}{{}}{{}}}
\bibcite{r41}{{41}{}{{}}{{}}}
\bibcite{r42}{{42}{}{{}}{{}}}
\bibcite{r43}{{43}{}{{}}{{}}}
\bibcite{r44}{{44}{}{{}}{{}}}
\bibcite{r45}{{45}{}{{}}{{}}}
\bibcite{r46}{{46}{}{{}}{{}}}
\global\NAT@numberstrue