Quantile/expectile regression, and extreme data analysis
Quantile/expectile regression, and extreme data analysis
Quantile/expectile regression, and extreme data analysis
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Expectile <strong>regression</strong><br />
Interrelationship between <strong>expectile</strong>s <strong>and</strong> quantiles† I<br />
“Expectiles have properties that are similar to quantiles” (Newey <strong>and</strong><br />
Powell, 1987). The reason is that <strong>expectile</strong>s of a distribution F are<br />
quantiles a distribution G which is related to F (Jones, 1994).<br />
The main details are as follows.<br />
Let<br />
P(s) =<br />
∫ s<br />
−∞<br />
y f (y) dy<br />
ρ [1]<br />
τ (u) = τ − I (u ≤ 0),<br />
ρ [2]<br />
ω (u) = |u|(ω − I (u < 0)).<br />
the (first) partial moment,<br />
© T. W. Yee (University of Auckl<strong>and</strong>) <strong>Quantile</strong>/<strong>expectile</strong> <strong>regression</strong>, <strong>and</strong> <strong>extreme</strong> <strong>data</strong> <strong>analysis</strong> 18 July 2012 @ Cagliari 36/101/
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