• Corpus ID: 237433460

Estimation of the covariate conditional tail expectation : a depth-based level set approach

@inproceedings{Elisabeth2021EstimationOT,
  title={Estimation of the covariate conditional tail expectation : a depth-based level set approach},
  author={Armaut Elisabeth and Diel Roland and Laloe Thomas},
  year={2021}
}

• Armaut Elisabeth, Diel Roland, Laloe Thomas
• Published 7 September 2021
• Mathematics

The aim of this paper is to study the asymptotic behavior of a particular multivariate risk measure, the Covariate-Conditional-TailExpectation (CCTE), based on a multivariate statistical depth function. Depth functions have become increasingly powerful tools in nonparametric inference for multivariate data, as they measure a degree of centrality of a point with respect to a distribution. A multivariate risks scenario is then represented by a depth-based lower level set of the risk factors, meaning that we consider a non-compact setting. More precisely, given a probability measure P on R and a depth function D(·, P ), we are interested in the α-lower level set LD(α) := { z ∈ R : D(z, P ) ≤ α } . First, we present a plug-in approach in order to estimate LD(α). In a second part, we provide a consistent estimator of our CCTE for a general depth function with a rate of convergence, and we consider the particular case of the Mahalanobis depth. A simulation study complements the performances of our estimator. Key-Words. Plug-in estimation, multivariate depth function, Mahalanobis depth, risk theory. ∗[e-mail] †[e-mail] ‡[e-mail] 1 ar X iv :2 10 9. 03 01 7v 1 [ m at h. ST ] 7 S ep 2 02 1