On the Lp-quantiles for the Student t distribution

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.