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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Wednesday, May 9, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Mikhail Moklyachuk}
\centerline{\sl Department of Probability Theory and Mathematical 
Statistics}
\centerline{\sl Kyiv Taras Shevchenko University}
\centerline{\sl Kyiv 01033, Ukraine}
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\centerline{\bf Game theory and convex optimization methods in robust 
estimation problems}

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With the help of the traditional methods of extrapolation, interpolation
and filtering of stochastic processes the spectral characteristic $h(f,g)$
and the mean square error $\Delta(f,g)$ of the optimal estimate of a 
linear
transformation  $A\xi$ of the unknown values of a stochastic process
$\xi(t)$ from observations of the process $\xi(t)+\eta(t)$ can be found in
the case where the spectral densities $f(\lambda)$ and $g(\lambda)$ of the
processes $\xi(t)$ and $\eta(t)$ are known. In practice, however, problems
of estimation arise where it is necessary to search the estimate which has
the least value of the error for all densities from a certain class of
possible spectral densities (see a survey by S.A.~Kassam and H.V.~Poor
(1985)). The spectral characteristic of such an estimate is called
minimax-robust. We apply convex optimization and game theory methods to
determine the least favorable spectral densities and the minimax-robust
spectral characteristics of the optimal estimates of the transformation
$A\xi.$

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