Abstract
A general many quantiles + noise model is studied in the robust formulation (allowing non-normal, non-independent observations), where the identifiability requirement for the noise is formulated in terms of quantiles rather than the traditional zero expectation assumption. We propose a penalisation method based on the quantile loss function with appropriately chosen penalty function making inference on possibly sparse high-dimensional quantile vector. We apply a local approach to address the optimality by comparing procedures to the oracle sparsity structure. We establish that the proposed procedure mimics the oracle in the problems of estimation and uncertainty quantification (under the so-called EBR condition). Adaptive minimax results over sparsity scale follow from our local results.
Original language | English |
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Pages (from-to) | 60-77 |
Number of pages | 18 |
Journal | Journal of Nonparametric Statistics |
Volume | 36 |
Issue number | 1 |
Early online date | 22 Jun 2023 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Volume 36, 2024 - Issue 1: 2022 International Symposium on Nonparametric Statistics. Guest editors: Stathis Paparoditis and Ingrid Van Keilegom.Publisher Copyright:
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- Estimation
- oracle rate
- oracle sparsity structure
- quantile loss
- uncertainty quantification