On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions
We study sample quantiles of distributions indexed by estimated parameters, with a on Value-at-Risk related to linear projections of financial returns that whose underlying probability law is heavy-tailed. In this setting, the projection direction and the empirical quantile threshold are estimated from the data, so the standard Bahadur representation under a fixed distribution does not separate the distinct sources of instability. A canonical starting point is Bahadur's representation, which expresses the sample quantile through the empirical distribution function plus a remainder term \cite{bahadur1966}. Empirical-process theory provides a usable scaffolding through the mechanics of half...
| Authors | Choudur Lakshminarayan |
|---|---|
| Primary category | stat.ML |
| Published | 18 May 2026 |
| Last updated at source | 22 May 2026 |
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