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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  %% Time of talk, Weekday, Date of talk\\
  %% Example: 4:15 p.m., Tuesday, November 20th, 2007\\
  4:15 p.m., Tuesday, January 15th, 2008\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{Inchi Hu} \\
  Department of Information and Systems Management\\
  Hong Kong University of Science and Technology, Hong Kong, China
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  \subsection*{The coupling spline model and stochastic approximation}
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\noindent
The seminal work of Robbins and Monro (1951) brought into being a 
sequential nonparametric procedure to find the root of a
regression function. The nonparametric nature of Robbins-Monro
scheme allows broad applicability but also causes slower convergence.
This talk introduces a new semi-parametric model and an algorithm to 
generate a sequence of approximations to the root. The simulation study 
demonstrates computational efficiency and faster convergence of the 
proposed method. With moderate sample sizes, the method is as accurate 
as the optimal Robbins-Monro procedure in the linear case. In a few 
nonlinear examples, it is 10 to over 1000 times more accurate as 
measured by mean square error. We then apply the algorithm to compute MLE 
in some spatial models and generalized linear mixed models and report some   
encouraging results. 
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