Modile as a conservative tail risk measurer: the solution of an optimisation problem with 0-1 loss function

by   Keming Yu, et al.

Quantiles and expectiles, which are two important concepts and tools in tail risk measurements, can be regarded as an extension of median and mean, respectively. Both of these tail risk measurers can actually be embedded in a common framework of L_p optimization with the absolute loss function (p=1) and quadratic loss function (p=2), respectively. When 0-1 loss function is frequently used in statistics, machine learning and decision theory, this paper introduces an 0-1 loss function based L_0 optimisation problem for tail risk measure and names its solution as modile, which can be regarded as an extension of mode. Mode, as another measure of central tendency, is more robust than expectiles with outliers and easy to compute than quantiles. However, mode based extension for tail risk measure is new. This paper shows that the proposed modiles are not only more conservative than quantiles and expectiles for skewed and heavy-tailed distributions, but also providing or including the unique interpretation of these measures. Further, the modiles can be regarded as a type of generalized quantiles and doubly truncated tail measure whcih have recently attracted a lot of attention in the literature. The asymptotic properties of the corresponding sample-based estimators of modiles are provided, which, together with numerical analysis results, show that the proposed modiles are promising for tail measurement.


page 1

page 2

page 3

page 4


A new method for estimating the tail index using truncated sample sequence

This article proposes a new method of truncated estimation to estimate t...

Tail Gini Functional under Asymptotic Independence

Tail Gini functional is a measure of tail risk variability for systemic ...

Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics

We propose a generalized formulation of the Huber loss. We show that wit...

The risk function of the goodness-of-fit tests for tail models

This paper contributes to answering a question that is of crucial import...

Robust Dynamic Mode Decomposition

The paper develops a robust estimation method that makes the dynamic mod...

Head-tail Loss: A simple function for Oriented Object Detection and Anchor-free models

This paper presents a new loss function for the prediction of oriented b...

On Tail Decay Rate Estimation of Loss Function Distributions

The study of loss function distributions is critical to characterize a m...

Please sign up or login with your details

Forgot password? Click here to reset