Stability Analysis in the Exponential Families and Generalized Linear Model

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Ying Lu*+
• Companies: University of Minnesota
• Keywords: Cumulative Sum ; Sequential Change Detection ; Stability ; Exponential Family ; Generalized Linear Model

Abstract

In many modern applications of Statistics,the data arrives in a sequential order, and the question of interest is whether the parameters of the data generating system have remained stable through the entire time-length of data collection. We construct a likelihood ratio test statistic to study the stability of parameters, which turns out to be the well-known CUSUM statistic. We study the effectiveness of using our distribution-specific test statistic, as opposed to the normality-driven CUSUM statistic. The conclusion is that when the underlying distribution belongs to the exponential family, our likelihood-ratio statistic generally works better than the normal CUSUM statistic, especially when the potential change in parameters is small in size. Another observation is that the likelihood-ratio statistic has a stable performance in detection whether the change point lies at the beginning, in the middle or at the end of the data collection time. We extend our study to test for changes in parameters in the generalized linear model setting. Finally, we conduct a detailed study on the Atlantic hurricane data over the past 150 years, and the validity of our methodology is strengthened.