\contentsline {begintocitem}{}{}{}
\contentsline {jobname}{Doksum}{}{}
\contentsline {doi}{0003/0000.0000}{}{}
\contentsline {arxiv}{math.PR/0000003}{}{}
\contentsline {title}{Semiparametric Models and Likelihood - The Power of Ranks}{66}{}
\contentsline {author}{Kjell Doksum and Akichika Ozeki}{67}{}
\contentsline {endtocitem}{}{}{}
\contentsline {section}{\numberline {1}Introduction}{67}{section.1}
\contentsline {subsection}{\numberline {1.1}Lehmann Type Models. Cox Regression}{67}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}Sklar Type Models. Copula Regression}{67}{subsection.1.2}
\contentsline {section}{\numberline {2}Proportional Hazard and Proportional Expected Hazard Rate Models}{68}{section.2}
\contentsline {section}{\numberline {3}Rank, Partial and Marginal Likelihood}{70}{section.3}
\contentsline {section}{\numberline {4}Profile NP Likelihood}{72}{section.4}
\contentsline {section}{\numberline {5}Profile NP Likelihood for the PEHR Model}{73}{section.5}
\contentsline {subsection}{\numberline {5.1}The MM Algorithm}{74}{subsection.5.1}
\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}
\contentsline {subsection}{\numberline {5.3}The MM Algorithm for the SINAMI Model with $\theta \leq 0$}{75}{subsection.5.3}
\contentsline {subsection}{\numberline {5.4}The MM Algorithm for the SINAMI Model with $\theta \in R$}{75}{subsection.5.4}
\contentsline {subsection}{\numberline {5.5}Profile NPMLE Implementation}{75}{subsection.5.5}
\contentsline {subsection}{\numberline {5.6}Estimation of the Variance of the Profile NPMLE}{77}{subsection.5.6}
\contentsline {section}{\numberline {6}Simulation Results}{77}{section.6}
\contentsline {subsection}{\numberline {6.1}PEHR Model Estimates}{77}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Model Fit for Misspecified Model}{78}{subsection.6.2}
\contentsline {section}{\numberline {7}Estimation in the Normal Copula Model}{78}{section.7}
\contentsline {subsection}{\numberline {7.1}The One Covariate Case}{78}{subsection.7.1}
\contentsline {subsection}{\numberline {7.2}The Multivariate Covariate Case}{81}{subsection.7.2}
\contentsline {section}{\numberline {8}Transformation and NP Models}{81}{section.8}
\contentsline {subsection}{\numberline {8.1}Simulation Results}{84}{subsection.8.1}
\contentsline {subsubsection}{\numberline {8.1.1}Correctly Specified Model}{84}{subsubsection.8.1.1}
\contentsline {subsubsection}{\numberline {8.1.2}Misspecified Model}{84}{subsubsection.8.1.2}
\contentsline {section}{Acknowledgements}{91}{section*.3}
\contentsline {section}{References}{91}{section*.5}