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Minimum Area Confidence Set (MACS) Criterion for Confidence bands in Simple Linear Regression

Minimum Area Confidence Set (MACS) Criterion for Confidence bands in Simple Linear Regression. W. Liu, University of Southampton, UK A.J. Hayter, University of Denver, USA. Outline. Confidence bands Confidence set of a confidence band MACS criterion Best 3-segment band

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Minimum Area Confidence Set (MACS) Criterion for Confidence bands in Simple Linear Regression

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  1. Minimum Area Confidence Set (MACS) Criterion for Confidence bands in Simple Linear Regression W. Liu, University of Southampton, UK A.J. Hayter, University of Denver, USA

  2. Outline • Confidence bands • Confidence set of a confidence band • MACS criterion • Best 3-segment band • Best 2-segment band • Comparison of best 3-segment band and hyperbola band • Discussion

  3. Confidence bands

  4. Hyperbola band over (a, A)

  5. 3-segment band

  6. 2-segment band

  7. Confidence set of a band

  8. Confidence set of the 3-segment band

  9. Confidence set of the 2-segment band

  10. MACS criterion

  11. Best 3-segment band

  12. Best 2-segment band

  13. Comparison of the best 3-segment band and hyperbola band

  14. Discussion • MACS criterion is related to the D-optimality in design of experiments • The average width criterion is the other criterion • Future research

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