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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\\
  4:15 p.m., Tuesday, March 18, 2008\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Brian Marx} \\
  Department of Experimental Statistics\\
  Louisiana State University
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  \subsection*{Bilinear varying-coefficient surface models with an application to death counts}
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In monthly counts of deaths, we often find strong seasonal patterns,
and the strength of such patterns varies over both year and age. A
structure like this lends itself to varying-coefficient surfaces
(over year and age) modulating the coefficients of (annual harmonic)
cosine and sine regressors. However, in many cases, these modulation
models can be too simplistic: they perhaps cannot handle relatively
sharp peaks in the winter and relatively flat troughs in the summer.

Rather than adding higher harmonics, we assume that there exists a
general {\it carrier wave} (a term borrowed from radio technology),
modulated over time and age. We assume the carrier wave is an
unknown period twelve vector. This leads to a bilinear model, which
we estimate as follows: (1) For a fixed carrier wave, we have a
varying-coefficient surface model. (2) For fixed varying
coefficients, we estimate the carrier wave using generalized linear
regression.

We estimate varying-coefficient surfaces using tensor product
P-splines, avoiding backfitting. Penalties are attached on both the
row and columns of the tensor product coefficients, and optimization
of the penalty tuning parameters is based on minimization of a
quasi-likelihood criterion. As the data are on a grid, efficient
computation can be achieved using array regression techniques. An
illustrative example is provided by monthly death counts due to
respiratory diseases, for US females during 1959-1999.

This is joint work with Paul Eilers, Jutta Gampe, and Roland Rau.

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