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Semiparametric estimation of outbreak regression

Author

Listed:
  • Frisén, Marianne

    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Andersson, Eva

    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Pettersson, Kjell

    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

A regression may be constant for small values of the independent variable (for example time), but then a monotonic increase starts. Such an “outbreak” regression is of interest for example in the study of the outbreak of an epidemic disease. We give the least square estimators for this outbreak regression without assumption of a parametric regression function. It is shown that the least squares estimators are also the maximum likelihood estimators for distributions in the regular exponential family such as the Gaussian or Poisson distribution. The approach is thus semiparametric. The method is applied to Swedish data on influenza, and the properties are demonstrated by a simulation study. The consistency of the estimator is proved.

Suggested Citation

  • Frisén, Marianne & Andersson, Eva & Pettersson, Kjell, 2008. "Semiparametric estimation of outbreak regression," Research Reports 2007:13, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    • Handle: RePEc:hhs:gunsru:2007_013
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    File URL: http://hdl.handle.net/2077/10526
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    References listed on IDEAS

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    1. Efromovich S., 2001. "Density Estimation Under Random Censorship and Order Restrictions: From Asymptotic to Small Samples," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 667-684, June.
    2. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    3. N/A, 1999. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 169(1), pages 111-120, July.
    4. E. Andersson, 2002. "Monitoring cyclical processes. A non-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 973-990.
    5. Christian Sonesson & David Bock, 2003. "A review and discussion of prospective statistical surveillance in public health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 5-21, February.
    6. N/A, 1999. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 170(1), pages 106-115, October.
    7. N/A, 1999. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 167(1), pages 118-127, January.
    8. -, 1999. "Major statistical publications: abstracts," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 27448, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    9. N/A, 1999. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 168(1), pages 117-126, April.
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    More about this item

    Keywords

    Constant Base-line; Monotonic change; Exponential family;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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    This paper has been announced in the following NEP Reports:

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