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On curve estimation under order restrictions

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  • Pettersson, Kjell

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

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    Abstract

    Robust regression is of interest in many problems where assumptions of a parametric function may be inadequate. In this thesis, we study regression problems where the assumptions concern only whether the curve is increasing or decreasing. Examples in economics and public health are given. In a forthcoming paper, the estimation methods presented here will be the basis for likelihood based surveillance systems for detecting changes in monotonicity. Maximum likelihood estimators are thus derived. Distributions belonging to the regular exponential family, for example the normal and Poisson distributions, are considered. The approach is semiparametric, since the regression function is nonparametric and the family of distributions is parametric. In Paper I, “Unimodal Regression in the Two-parameter Exponential Family with Constant or Known Dispersion Parameter”, we suggest and study methods based on the restriction that the curve has a peak (or, equivalently, a trough). This is of interest for example in turning point detection. Properties of the method are described and examples are given. The starting point for Paper II, “Semiparametric Estimation of Outbreak Regression”, was the situation at the outbreak of a disease. A regression may be constant before the outbreak. At the onset, there is an increase. We construct a maximum likelihood estimator for a regression which is constant at first but then starts to increase at an unknown time. The consistency of the estimator is proved. The method is applied to Swedish influenza data and some of its properties are demonstrated by a simulation study.

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    File URL: http://hdl.handle.net/2077/9514
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    Bibliographic Info

    Paper provided by Statistical Research Unit, Department of Economics, School of Business, Economics and Law, University of Gothenburg in its series Research Reports with number 2007:15.

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    Length: 32 pages
    Date of creation: 04 Feb 2008
    Date of revision:
    Handle: RePEc:hhs:gunsru:2007_015

    Contact details of provider:
    Postal: Statistical Research Unit, University of Gothenburg, Box 640, SE 40530 GÖTEBORG
    Web page: http://www.statistics.gu.se/

    Related research

    Keywords: Non-parametric; Order restrictions; Two-parameter exponential family; Known dispersion parameter; Poisson distribution; Constant Base-line; Monotonic change; Exponential family;

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