Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms
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 ge...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2014-11-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/21/1133/2014/npg-21-1133-2014.pdf |
| Summary: | 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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| ISSN: | 1023-5809 1607-7946 |