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Maximum modulus confidence bands

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  • Christopher Withers
  • Saralees Nadarajah

Abstract

A family of confidence bands (simultaneous confidence regions) is given for EY= x′ β that are piecewise-linear in x. Normality is assumed. These confidence bands are advocated over the usual hyperbolic band when the region of prime interest is distant from $${\overline{\bf x}}$$ . In particular, this is the case when x = x(t) for time t and future time is of primary interest, that is for the prediction problem. For the case x′ = (1, t), the family of bands includes that of Graybill and Bowden (J Am Stat Assoc 62:403–408, 1967 ). Copyright Springer-Verlag 2012

Suggested Citation

  • Christopher Withers & Saralees Nadarajah, 2012. "Maximum modulus confidence bands," Statistical Papers, Springer, vol. 53(4), pages 811-819, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:811-819
    DOI: 10.1007/s00362-011-0384-3
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    References listed on IDEAS

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    1. Mark Bebbington & Chin-Diew Lai & Ričardas Zitikis, 2010. "Life expectancy of a bathtub shaped failure distribution," Statistical Papers, Springer, vol. 51(3), pages 599-612, September.
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    3. Liu, W. & Hayter, A.J. & Piegorsch, W.W. & Ah-Kine, P., 2009. "Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1432-1439, August.
    4. Wei Liu & Shan Lin & Walter W. Piegorsch, 2008. "Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model," International Statistical Review, International Statistical Institute, vol. 76(1), pages 39-57, April.
    5. Walter W. Piegorsch & R. Webster West & Wei Pan & Ralph L. Kodell, 2005. "Low dose risk estimation via simultaneous statistical inferences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 245-258, January.
    6. Liu, W. & Hayter, A.J., 2007. "Minimum Area Confidence Set Optimality for Confidence Bands in Simple Linear Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 181-190, March.
    7. Obaid M. Al-Saidy & Walter W. Piegorsch & R. Webster West & Daniela K. Nitcheva, 2003. "Confidence Bands for Low-Dose Risk Estimation with Quantal Response Data," Biometrics, The International Biometric Society, vol. 59(4), pages 1056-1062, December.
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    Cited by:

    1. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.

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    Keywords

    Confidence band; Prediction; Regression; 62J05; 62G13;
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