
THE GEOFFREY S. WATSON LECTURE SERIES Geoffrey S. Watson was previously chair of the Department of Statistics in the School of Arts and Sciences at Johns Hopkins University. In that role, he stimulated active interactions among statisticians and biostatisticians across the Hopkins campuses. In honor of his contributions to statistical sciences, the Departments of Mathematical Sciences in the School of Arts and Sciences and Biostatistics in the School of Public Health have created an annual Watson Lecture to be jointly sponsored in the spring term of each academic year. A joint committee of faculty will select the lecturer, who will present a research lecture that honors the spirit of original investigation typified by Geoff Watson. An honor roll of past Watson Lecturers will be presented at each year’s meeting. 1999 Watson Lecturer:
Rudolf Beran,
UCBerkeley Department of Statistics 1998 Watson Lecturer:
Susan Murphy,
University of Michigan ABSTRACT: In high dimensional models, interest often lies primarily in a vector parameter and the nuisance parameter is a function, such as a distribution function or a smooth regression function. This talk concerns the verification of the intuitive practice of profiling the nuisance parameter out of the likelihood and using the resulting profile likelihood as if it is a likelihood for the vector parameter. That is, will maximizing the profile likelihood yield an asymptotically normal estimator of the parameter of interest? Can the profile likelihood be used to make likelihood ratio tests and confidence intervals? Can minus the second derivative matrix of the profile likelihood be used to estimate the information matrix? In the parametric setting these properties follow from a quadratic approximation to the likelihood. This work give sufficient conditions for the above approximation to hold in a semiparametric setting and shows how the quadratic approximation leads to an affirmative answer to the above questions. The conditions are sufficiently simple so as to be satisfied in a variety of semiparametric models, for example, the proportional hazards model for current status data, the proportional odds model for right censored survival data, gamma frailty model, errors in variables for a logistic regression model, and a semiparametric logistic regression.
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