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Maximum likelihood estimation of a nonparametric signal in white noise by optimal control

✍ Scribed by G.N. Milstein; M. Nussbaum

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
115 KB
Volume
55
Category
Article
ISSN
0167-7152

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✦ Synopsis

We study extremal problems related to nonparametric maximum likelihood estimation (MLE) of a signal in white noise. The aim is to reduce these to standard problems of optimal control which can be solved by iterative procedures. This reduction requires a preliminary data smoothing; stability theorems are proved which justify such an operation on the data as a perturbation of the originally sought nonparametric (nonlinear) MLE. After this, classical optimal control problems appear; in the basic case of a signal with bounded ΓΏrst derivative one obtains the well-known problem of the optimal road proΓΏle.

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