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Test of tails based on extreme regression quantiles

✍ Scribed by Jana Jurečková

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
108 KB
Volume
49
Category
Article
ISSN
0167-7152

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✦ Synopsis

The extreme regression quantiles, as analogues of the extreme-order statistics in the linear regression model, were ÿrst considered by Smith (1994, Biometrika 81, 173-183) and studied by Portnoy and JureÄ ckovà a (1999, Extremes, to appear). They may have various important applications, parallel to those of the extreme value theory. We propose the test of the Pareto-type tail with index m, 0 ¡ m6m0 of the distribution of errors in the linear regression model, based on the extreme regression quantiles. The asymptotic null distribution of the test criterion is normal and the test is consistent against the Pareto-type tails with a greater index as well as against the exponential (Weibull) tails.

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✍ Maurizio Guida; Maurizio Longo 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 944 KB

For high reliability devices or structures it is not uncommon that the probabilities to be estimated are lower than 10 -6 . In such cases the standard methods of the empirical fit approach and the counting approach may become impractical. In this paper the estimation problem is handled by extrapolat