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Likelihood Based Uncertainty Bounding in Prediction Error Identification using ARX models A Simulation Study ECC 2007, Kos, Greece Arjan den Dekker, Xavier Bombois and Paul Van den Hof July 4, 2007 1 Delft Center for Systems and Control


  1. Likelihood Based Uncertainty Bounding in Prediction Error Identification using ARX models A Simulation Study ECC 2007, Kos, Greece Arjan den Dekker, Xavier Bombois and Paul Van den Hof July 4, 2007 1 Delft Center for Systems and Control

  2. Confidence regions • 1 0.95 0.9 0.85 0.8 0.75 b 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 2 Delft Center for Systems and Control

  3. Outline July 4, 2007 3 Delft Center for Systems and Control

  4. Data generating system and predictor model July 4, 2007 4 Delft Center for Systems and Control

  5. Statistical inference July 4, 2007 5 Delft Center for Systems and Control

  6. Statistical inference 1 0.95 0.9 0.85 0.8 b 0.75 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 6 Delft Center for Systems and Control

  7. Construction of confidence regions 1 0.95 0.9 0.85 0.8 0.75 b 0.7 0.65 0.6 0.55 0.5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 a July 4, 2007 7 Delft Center for Systems and Control

  8. Test statistics July 4, 2007 8 Delft Center for Systems and Control

  9. ARX modelling July 4, 2007 9 Delft Center for Systems and Control

  10. Confidence regions for ARX parameters July 4, 2007 10 Delft Center for Systems and Control

  11. Result from asymptotic theory ( θ 0 known) July 4, 2007 11 Delft Center for Systems and Control

  12. Simulation experiment July 4, 2007 12 Delft Center for Systems and Control

  13. observed coverage rates 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0 50 100 150 200 250 300 350 400 number of data points N July 4, 2007 13 Delft Center for Systems and Control

  14. observed coverage rates 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0 50 100 150 200 250 300 350 400 number of data points N July 4, 2007 14 Delft Center for Systems and Control

  15. Conclusions July 4, 2007 15 Delft Center for Systems and Control

  16. ARX modelling July 4, 2007 16 Delft Center for Systems and Control

  17. Result from asymptotic theory ( θ 0 known) July 4, 2007 17 Delft Center for Systems and Control

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