We investigate whether several families of generalized quantiles (expectiles, Lp-quantiles and M-quantiles) respect various stochastic orders (the usual stochastic order, the convexity order, the s-convexity orders). We employ techniques from monotone comparative statics developed in Topkis (1978) and Milgrom and Shannon (1994), in order to provide sufficient as well as necessary conditions for isotonicity. We show that expectiles with < 1/2 are basically the only generalized quantiles that are isotonic with respect to the icv ordering; more generally, the Lp-quantiles are isotonic with respect to the s-convex order.

Bellini, F. (2012). Isotonicity properties of generalized quantiles [Working paper del dipartimento].

Isotonicity properties of generalized quantiles

BELLINI, FABIO
2012

Abstract

We investigate whether several families of generalized quantiles (expectiles, Lp-quantiles and M-quantiles) respect various stochastic orders (the usual stochastic order, the convexity order, the s-convexity orders). We employ techniques from monotone comparative statics developed in Topkis (1978) and Milgrom and Shannon (1994), in order to provide sufficient as well as necessary conditions for isotonicity. We show that expectiles with < 1/2 are basically the only generalized quantiles that are isotonic with respect to the icv ordering; more generally, the Lp-quantiles are isotonic with respect to the s-convex order.
Working paper del dipartimento
expectiles, generalized quantiles, stochastic orders, isotonicity,submodularity, single crossing condition
English
2012
Bellini, F. (2012). Isotonicity properties of generalized quantiles [Working paper del dipartimento].
open
File in questo prodotto:
File Dimensione Formato  
Rapporto 227.pdf

accesso aperto

Dimensione 194.73 kB
Formato Adobe PDF
194.73 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/29717
Citazioni
  • Scopus 13
  • ???jsp.display-item.citation.isi??? ND
Social impact