Browsing by Author "Pettersson, Kjell"

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Explorative analysis of spatial aspects on the Swedish influenza data
(2007-12-20T13:50:55Z) Bock, David; Pettersson, Kjell
The spatial aspects on the Swedish influenza data are analyzed. During the influenza period, reports on laboratory diagnosed cases and influenza-like-illness are obtained from viral and microbiological laboratories and from sentinel physicians, respectively, in different regions of Sweden. Information about the spatio-temporal patterns might give insight in the way the influenza spreads over Sweden. It might also be used in automated surveillance systems for outbreak and peak detection of the influenza. We describe the regional patterns in Swedish influenza data in different ways. Several natural hypotheses about geographical patterns are examined but can not be verified as consistent over the years. However, we find that, for a group of large cities, the outbreak of the influenza occurs at least four weeks earlier than for the rest of Sweden. The possibilities to utilize this in surveillance systems are briefly discussed.
On curve estimation under order restrictions
(2008-02-04T13:08:30Z) Pettersson, Kjell
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.
Semiparametric estimation of outbreak regression
(2008-07-02T10:11:11Z) Frisén, Marianne; Andersson, Eva; Pettersson, Kjell
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.
Unimodal regression in the two-parameter exponential family with constant or known dispersion parameter
(2008-02-04T13:00:17Z) Pettersson, Kjell
In this paper we discuss statistical methods for curve-estimation under the assumption of unimodality for variables with distributions belonging to the two-parameter exponential family with known or constant dispersion parameter. We suggest a non-parametric method based on monotonicity properties. The method is applied to Swedish data on laboratory verified diagnoses of influenza and data on inflation from an episode of hyperinflation in Bulgaria.