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On minimum L1-norm estimate of the parameter of the Ornstein--Uhlenbeck process

Author

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  • Kutoyants, Y.
  • Pilibossian, P.

Abstract

We consider the problem of [theta]-parameter estimation by observations of the linear process dXt=[theta]Xt dt+[var epsilon]dWt, XO=xO, O[less-than-or-equals, slant]t[less-than-or-equals, slant]T, where [var epsilon] is a "small" parameter. The asymptotics ([var epsilon] --> 0) of minimum L1-norm estimate is investigated. Here xt([theta]) = x0exp([theta]t). It is proved that this estimate is consistant and the difference [var epsilon]-1([theta]*[var epsilon] - [theta]) converges in probability to a random variable which is (for large T) asymptotically normal.

Suggested Citation

  • Kutoyants, Y. & Pilibossian, P., 1994. "On minimum L1-norm estimate of the parameter of the Ornstein--Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 117-123, May.
    • Handle: RePEc:eee:stapro:v:20:y:1994:i:2:p:117-123
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    Cited by:

    1. Stefano Maria IACUS, 2010. "On Lasso-type estimation for dynamical systems with small noise," Departmental Working Papers 2010-12, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Diop, Aliou & Yode, Armel Fabrice, 2010. "Minimum distance parameter estimation for Ornstein-Uhlenbeck processes driven by Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 122-127, January.
    3. Zhao, Huiyan & Zhang, Chongqi, 2019. "Minimum distance parameter estimation for SDEs with small α-stable noises," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 301-311.

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