Asymptotic linear expansion of regularized M-estimators

Tino Werner ()
Additional contact information
Tino Werner: Carl von Ossietzky University Oldenburg

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 1, No 8, 167-194

Abstract: Abstract Parametric high-dimensional regression requires regularization terms to get interpretable models. The respective estimators correspond to regularized M-functionals which are naturally highly nonlinear. Their Gâteaux derivative, i.e., their influence curve linearizes the asymptotic bias of the estimator, but only up to a remainder term which is not guaranteed to tend (sufficiently fast) to zero uniformly on suitable tangent sets without profound arguments. We fill this gap by studying, in a unified framework, under which conditions the M-functionals corresponding to convex penalties as regularization are compactly differentiable, so that the estimators admit an asymptotically linear expansion. This key ingredient allows influence curves to reasonably enter model diagnosis and enable a fast, valid update formula, just requiring an evaluation of the corresponding influence curve at new data points. Moreover, this paves the way for optimally-robust estimators, bounding the influence curves in a suitable way.

Keywords: Asymptotic linear expansion; Regularized M-estimators; Influence curves (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-021-00792-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:74:y:2022:i:1:d:10.1007_s10463-021-00792-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-021-00792-5

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().