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Robust oracle estimation and uncertainty quantification for possibly sparse quantiles

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  • Eduard Belitser
  • Paulo Serra
  • Alexandra Vegelien

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.

Suggested Citation

  • Eduard Belitser & Paulo Serra & Alexandra Vegelien, 2024. "Robust oracle estimation and uncertainty quantification for possibly sparse quantiles," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 36(1), pages 60-77, January.
    • Handle: RePEc:taf:gnstxx:v:36:y:2024:i:1:p:60-77
    DOI: 10.1080/10485252.2023.2226779
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