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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Application of one-step method to parameter estimation in ODE models.

Itai Dattner1, Shota Gugushvili2

  • 1Department of Statistics University of Haifa 199 Aba Khoushy Ave., Mount Carmel Haifa 3498838 Israel.

Statistica Neerlandica
|June 26, 2018
PubMed
Summary
This summary is machine-generated.

Le Cam's one-step method offers a computationally simple alternative for parameter estimation in ordinary differential equation models. This approach provides accurate point and interval estimates, outperforming traditional methods.

Keywords:
62G20Levenberg–Marquardt algorithmSecondary: 62G08integral estimatornon‐linear least squaresone‐step estimator.AMS 2000 classifications: Primary: 62F12ordinary differential equationssmooth and match estimator

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Area of Science:

  • Statistics
  • Computational Mathematics
  • Applied Mathematics

Background:

  • Parameter estimation in ordinary differential equation (ODE) models is crucial for scientific understanding.
  • Non-linear least squares (NLS) is a popular but computationally intensive method requiring iterative algorithms and ODE integration.
  • Existing methods for ODE parameter estimation can be complex and time-consuming.

Purpose of the Study:

  • To introduce and evaluate Le Cam's one-step method as an efficient alternative for parameter estimation in ODE models.
  • To demonstrate the method's ability to provide both point and interval estimates.
  • To present a data-driven approach for selecting tuning parameters for the preliminary estimator.

Main Methods:

  • Application of Le Cam's one-step method, starting from a preliminary consistent estimator.
  • Utilizing non-parametric smoothing for the initial estimator.
  • Developing a data-driven methodology for tuning parameter selection.
  • Extensive simulations and real data analysis to assess performance.

Main Results:

  • The one-step estimator achieves asymptotic equivalence to the least squares estimator.
  • The method is computationally simpler than traditional iterative NLS estimators.
  • Demonstrated effectiveness through simulations and real-world data examples.
  • Successful generation of both point and interval estimates.

Conclusions:

  • Le Cam's one-step method provides a computationally efficient and effective alternative for parameter estimation in ODE models.
  • The proposed data-driven tuning parameter selection enhances practical applicability.
  • This method simplifies the process of obtaining reliable parameter estimates for ODE systems.