Lp-quantiles are a class of generalised quantiles defined as the minimisers of an expected asymmetric power function. For p=1 and p=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). 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.
Bernardi, M., Bignozzi, V., Petrella, L. (2017). On the Lp-quantiles for the Student t distribution. STATISTICS & PROBABILITY LETTERS, 128, 77-83 [10.1016/j.spl.2017.04.017].
On the Lp-quantiles for the Student t distribution
Bignozzi, V
;
2017
Abstract
Lp-quantiles are a class of generalised quantiles defined as the minimisers of an expected asymmetric power function. For p=1 and p=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). 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.
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