Abstract #302255

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JSM 2003 Abstract #302255
Activity Number: 90
Type: Contributed
Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302255
Title: Early Detection Statistics with Online Possibly Multivariate Data
Author(s): Keh-Shin Lii*+ and Ashis SenGupta
Companies: University of California, Riverside and Indian Statistical Institute
Address: Dept. of Statistics, Riverside, CA, 92521-0002,
Keywords: change point detection ; multivariate ; Fisher information ; Roberts-Shiryayev
Abstract:

We study the online early detection of an abrupt change in the shift of parameter value in the underlying multiparameter multivariate exponential family distribution. It is shown that a similar optimality property holds for the Gaussian case when a shift in the mean vector is considered. The role of the Fisher information matrix is exposed here. This leads to a relationship between the dimensionality and the dispersion matrix of the random variable resulting in the same detection delay. Sensitivity analyses done for the univariate case establishes the need for the construction of distribution-specific RS statistics and their corresponding thresholds for the multivariate nonexponential family case. However, similar results as for the Gaussian case are shown to hold by extensive simulation studies for several multiparameter nonexponential families. Nomograms are presented to facilitate the construction of an optimal detection mechanism when some flexibility is available with the dimension and correlation structure of the vector random variable to be observed.

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