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Optimal local estimation is formulated in the minimax sense for inverse problems and nonlinear regression. This theory provides best mean squared finite sample error bounds for some popular statistical learning algorithms and also for several optimal improvements of other existing learning algorithms such as smoothing splines and kernel regularization. The bounds and improved algorithms are not based...
We develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids. We seek an estimate that minimizes the worst-case estimation error over the given parameter set. Since this problem is intractable, we approximate it using semidefinite relaxation, and refer to the resulting estimate as the relaxed Chebyshev...
In air surveillance systems, Kalman filter and its derives have been largely used for real-time multiple target tracking, where minimization of calculation burdens is greatly desired. While non-maneuvering targets can be accurately tracked by using a Kalman filter with a constant velocity model, a maneuvring target might be miss-tracked since prediction errors increase significantly. The H∞ filter...
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