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


  • Milstein, G. N.
  • Nussbaum, M.


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.

Suggested Citation

  • Milstein, G. N. & Nussbaum, M., 2001. "Maximum likelihood estimation of a nonparametric signal in white noise by optimal control," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 193-203, November.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:193-203

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    References listed on IDEAS

    1. Rychlik, Tomasz, 1992. "Stochastically extremal distributions of order statistics for dependent samples," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 337-341, April.
    2. Masaaki Sibuya, 1991. "Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 261-285, June.
    3. Caraux, G. & Gascuel, O., 1992. "Bounds on distribution functions of order statistics for dependent variates," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 103-105, May.
    4. Gascuel, O. & Caraux, G., 1992. "Bounds on expectations of order statistics via extremal dependences," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 143-148, September.
    5. Rychlik, Tomasz, 1995. "Bounds for order statistics based on dependent variables with given nonidentical distributions," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 351-358, June.
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