Articles | Volume 21, issue 6
Nonlin. Processes Geophys., 21, 1133–1143, 2014
https://doi.org/10.5194/npg-21-1133-2014

Special issue: Physics-driven data mining in climate change and weather...

Nonlin. Processes Geophys., 21, 1133–1143, 2014
https://doi.org/10.5194/npg-21-1133-2014

Research article 28 Nov 2014

Research article | 28 Nov 2014

Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms

Y. Lu1 and S. Chatterjee2 Y. Lu and S. Chatterjee
  • 1Amazon.com, Inc., Seattle, Washington, USA
  • 2University of Minnesota, School of Statistics, Minneapolis, Minnesota, USA

Abstract. Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.

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Short summary
It is rarely ensured that the parameters of statistical distributions are stable through the entire duration of a data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes. We propose testing for stability of parameters of exponential family distributions and generalized linear models. We study Atlantic tropical storms using the techniques developed here.