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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1133-1143 |
| Number of pages | 11 |
| Journal | Nonlinear Processes in Geophysics |
| Volume | 21 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 28 2014 |
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Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms. / Lu, Y.; Chatterjee, S.
In: Nonlinear Processes in Geophysics, Vol. 21, No. 6, 28.11.2014, p. 1133-1143.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms
AU - Lu, Y.
AU - Chatterjee, S.
PY - 2014/11/28
Y1 - 2014/11/28
N2 - 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.
AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=84913584621&partnerID=8YFLogxK
U2 - 10.5194/npg-21-1133-2014
DO - 10.5194/npg-21-1133-2014
M3 - Article
AN - SCOPUS:84913584621
VL - 21
SP - 1133
EP - 1143
JO - Nonlinear Processes in Geophysics
JF - Nonlinear Processes in Geophysics
SN - 1023-5809
IS - 6
ER -