Monte Carlo Experiments on the Detection of Trends in Extreme Values

Xuebin Zhang Climate Research Branch, Meteorological Service of Canada, Downsview, Ontario, Canada

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Francis W. Zwiers Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, British Columbia, Canada

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Guilong Li Climate Research Branch, Meteorological Service of Canada, Downsview, Ontario, Canada

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Abstract

Using Monte Carlo simulations, several methods for detecting a trend in the magnitude of extreme values are compared. Ordinary least squares regression is found to be the least reliable method. A Kendall's tau–based method provides some improvement. The advantage of this method over that of least squares diminishes when the sample size is moderate to small. Explicit consideration of the extreme value distribution when computing trend always outperforms the above two methods. The use of the r largest values as extremes enhances the power of detection for moderate values of r; the use of larger values of r may lead to bias in the magnitude of the estimated trend.

Corresponding author address: Xuebin Zhang, Climate Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada. Email: xuebin.zhang@ec.gc.ca

Abstract

Using Monte Carlo simulations, several methods for detecting a trend in the magnitude of extreme values are compared. Ordinary least squares regression is found to be the least reliable method. A Kendall's tau–based method provides some improvement. The advantage of this method over that of least squares diminishes when the sample size is moderate to small. Explicit consideration of the extreme value distribution when computing trend always outperforms the above two methods. The use of the r largest values as extremes enhances the power of detection for moderate values of r; the use of larger values of r may lead to bias in the magnitude of the estimated trend.

Corresponding author address: Xuebin Zhang, Climate Research Branch, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada. Email: xuebin.zhang@ec.gc.ca

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