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

G. N. Milstein and M. Nussbaum

Statistics & Probability Letters, 2001, vol. 55, issue 2, 193-203

Abstract: 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 first derivative one obtains the well-known problem of the optimal road profile.

Keywords: Nonparametric; signal; in; white; noise; Maximum; likelihood; Smoothness; classes; Extremal; problems; Optimal; control; Iterative; solution (search for similar items in EconPapers)
Date: 2001
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