Lp-quantiles are a class of generalised quantiles defined as the minimisers of an expected asymmetric power function. For p=1p=1 and p=2p=2 they correspond respectively to the quantiles and the expectiles. In this contribution we show that for the class of Student t distributions with p degrees of freedom, the Lp-quantile and the quantile coincide for any confidence level τ∈(0,1)τ∈(0,1). The proof involves concepts from combinatorial analysis as well as a recursive formula for the truncated moments of the Student t distribution. This work extends the contribution of Koenker (1993) that shows a similar result for the expectiles
On the Lp-quantiles for the Student t distribution / Mauro, Bernardi; Valeria, Bignozzi; Petrella, Lea. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 128:(2017), pp. 77-83. [https://doi.org/10.1016/j.spl.2017.04.017]
On the Lp-quantiles for the Student t distribution
PETRELLA, Lea
2017
Abstract
Lp-quantiles are a class of generalised quantiles defined as the minimisers of an expected asymmetric power function. For p=1p=1 and p=2p=2 they correspond respectively to the quantiles and the expectiles. In this contribution we show that for the class of Student t distributions with p degrees of freedom, the Lp-quantile and the quantile coincide for any confidence level τ∈(0,1)τ∈(0,1). The proof involves concepts from combinatorial analysis as well as a recursive formula for the truncated moments of the Student t distribution. This work extends the contribution of Koenker (1993) that shows a similar result for the expectilesFile | Dimensione | Formato | |
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