Monitoring spatial maxima |
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| Authors: | Peter Rogerson |
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| Institution: | (1) Department of Geography, Department of Biostatistics, and National Center for Geographic Information and Analysis, University at Buffalo, Wilkeson Hall, Buffalo, NY 14261, USA |
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| Abstract: | When assessing maps consisting of comparable regional values, it is of interest to know whether the peak, or maximum value, is higher than it would likely be by chance alone. Peaks on maps of crime or disease might be attributable to random fluctuation, or they might be due to an important deviation from the baseline process that produces the regional values. This paper addresses the situation where a series of such maps are observed over time, and it is of interest to detect statistically significant deviations between the observed and expected peaks as quickly as possible. The Gumbel distribution is used as a model for the statistical distribution of extreme values; this distribution does not require the underlying distributions of regional values to be either normal, known, or identical. Cumulative sum surveillance methods are used to monitor these Gumbel variates, and these methods are also extended for use when monitoring smoothed regional values (where the quantity monitored is a weighted sum of values in the immediate geographical neighborhood). The new methods are illustrated by using data on breast cancer mortality for the 217 counties of the northeastern United States, and prostate cancer mortality for the entire United States, during the period 1968-1998.The research assistance of Ikuho Yamada is gratefully acknowledged. I also am grateful for the support of Grant 1R01 ES09816-01 from the National Institutes of Health, the support of National Cancer Institute Grant R01 CA92693-0, and the helpful comments made by the referees |
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| Keywords: | Cumulative sum methods Gumbel distribution Spatial maxima Spatial surveillance |
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