WIAS Preprint No. 596, (2000)

Maximum likelihood estimate for nonparametric signal in white noise by optimal control


  • Milstein, Grigori N.
  • Nussbaum, Michael

2010 Mathematics Subject Classification

  • 62G05 60H10 49K15


  • nonparametric diffusion model, maximum likelihood method, optimal estimation.




The paper is devoted to questions of constructing the maximum likelihood estimate for a nonparametric signal in white noise by considering corresponding problems of optimal control. For signals with bounded derivatives, sensitivity theorems are proved. The theorems state a stability of the maximum likelihood estimate with respect to changing output data. They make possible to reduce the original problem to a standard problem of optimal control which is solved by iterative procedure. For signals of Sobolev type the maximum likelihood estimate is obtained to within a parameter which can be found from a transcendental equation.

Appeared in

  • Statistic and Probability Letters, vol. 55/2 (2001), pp. 193-203

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