Quantile/expectile regression, and extreme data analysis

LMS quantile regression
Third Method: The Yeo-Johnson transformation† I
Yeo and Johnson (2000) introduce a new power transformation which is
well defined on the whole real line, and potentially useful for improving
normality:
ψ(λ, y) =
⎧
⎪⎨
⎪⎩
λ = 1 = the identity transformation.
(y + 1) λ − 1
(y ≥ 0, λ ≠ 0),
λ
log(y + 1) (y ≥ 0, λ = 0),
− (−y + 1)2−λ − 1
(y < 0, λ ≠ 2),
2 − λ
− log(−y + 1) (y < 0, λ = 2).
The Yeo-Johnson transformation is equivalent to the generalized Box-Cox
transformation for y > −1 where the shift constant 1 is included.
© T. W. Yee (University of Auckland) Quantile/expectile regression, and extreme data analysis 18 July 2012 @ Cagliari 14/101/ 101