PreprintCC BY 4.0arXiv
Estimation risk in conditional expectiles
Abstract
We establish the consistency and asymptotic normality of a two-step estimator of conditional expectiles in the context of conditional scale models. We first estimate the conditional variance parameters by quasi-maximum likelihood and then compute the unconditional expectile of the innovations using the empirical distribution of the standardized residuals. We show how replacing true innovations with standardized residuals affects the asymptotic variances of both conditional and unconditional expectile estimators. Finally, our empirical analysis reveals that conditional expectiles assess tail risk in cryptomarkets in a more robust manner than traditional quantile-based risk measures, such as value at risk and expected shortfall.
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BibTeX
@misc{fernandes2026estimation,
title = {{Estimation risk in conditional expectiles}},
author = {Marcelo Fernandes and Vitor Henriques and Eduardo Fonseca Mendes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02673},
eprint = {2609.02673},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02673},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Estimation risk in conditional expectiles
AU - Marcelo Fernandes
AU - Vitor Henriques
AU - Eduardo Fonseca Mendes
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02673
UR - https://arxiv.org/abs/2609.02673
AB - We establish the consistency and asymptotic normality of a two-step estimator of conditional expectiles in the context of conditional scale models. We first estimate the conditional variance parameters by quasi-maximum likelihood and then compute the unconditional expectile of the innovations using the empirical distribution of the standardized residuals. We show how replacing true innovations with standardized residuals affects the asymptotic variances of both conditional and unconditional expectile estimators. Finally, our empirical analysis reveals that conditional expectiles assess tail risk in cryptomarkets in a more robust manner than traditional quantile-based risk measures, such as value at risk and expected shortfall.
ER -