Scandinavian Working Papers in Economics

Research Reports,
University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law

No 2007:13: Semiparametric estimation of outbreak regression

Marianne Frisén (), Eva Andersson () and Kjell Pettersson ()
Additional contact information
Marianne Frisén: Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Statistical Research Unit, Göteborg University, Box 640, SE 40530 GÖTEBORG
Eva Andersson: Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Statistical Research Unit, Göteborg University, Box 640, SE 40530 GÖTEBORG
Kjell Pettersson: Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Statistical Research Unit, Göteborg University, Box 640, SE 40530 GÖTEBORG

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.

Keywords: Constant Base-line; Monotonic change; Exponential family

JEL-codes: C10

16 pages, February 4, 2008

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