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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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\begin{center}
  4:15 p.m., Tuesday, July 18, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{ Ramani S. Pilla}\\
Case Western Reserve University\\
Visiting Department of Statistics, Stanford University and Stanford Linear Accelerator Center 
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  \textbf{Semiparametric Inference for Correlated Data}
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\noindent In this talk, parameter estimation, building regression
models and testing of hypotheses for correlated data using
quasi-likelihood based techniques is addressed. A semiparametric model
is defined by a set of mean zero estimating functions. Based on a
quadratic form arising from an approximate covariance matrix for the
estimating functions, we can create a pseudo loglikelihood that forms
the basis for the {\em quadratic inference function} (QIF). In a
semiparametric approach, we (1) formulate a unified large-sample
theoretical framework for the QIF; (2) establish a generalization of
the QIF test statistic, along with its asymptotic distribution, for a
general linear hypothesis problem involving correlated data; (3)
propose an {\em iteratively reweighted generalized least squares}
(IRGLS) algorithm for finding the QIF estimator and show its
convergence properties; and (4) discuss novel techniques for building
regression models for correlated data using the IRGLS
algorithm. Furthermore, we present inferential theory for hypothesis
testing under general convex cone alternatives.  This fundamental
problem is addressed by first establishing that a {\em generalized
quasi-score} statistic is asymptotically equivalent to the squared
length of the projection of the standard Gaussian vector onto the
convex cone. We show that the asymptotic null distribution of the test
statistic is a weighted chi-squared distribution and explicit
expressions for these weights are obtained using the volume-of-tube
formula around a convex manifold in the unit sphere. We illustrate
applications to testing under order restricted alternatives for
correlated data.

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