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

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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

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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

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Confidence bands

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Hyperbola band over (a, A)

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3-segment band

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2-segment band

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Confidence set of a band

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Confidence set of the 3-segment band

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Confidence set of the 2-segment band

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MACS criterion

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Best 3-segment band

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Best 2-segment band

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Comparison of the best 3-segment band and hyperbola band

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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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