Semiparametric M-estimation with non-smooth criterion functions

Laurent Delsol () and Ingrid Van Keilegom ()
Additional contact information
Laurent Delsol: Université d’Orléans, Université de Tours, CNRS
Ingrid Van Keilegom: KU Leuven

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 2, No 10, 577-605

Abstract: Abstract We are interested in the estimation of a parameter $$\theta $$θ that maximizes a certain criterion function depending on an unknown, possibly infinite-dimensional nuisance parameter h. A common estimation procedure consists in maximizing the corresponding empirical criterion, in which the nuisance parameter is replaced by a nonparametric estimator. In the literature, this research topic, commonly referred to as semiparametric M-estimation, has received a lot of attention in the case where the criterion function satisfies certain smoothness properties. In certain applications, these smoothness conditions are, however, not satisfied. The aim of this paper is therefore to extend the existing theory on semiparametric M-estimators, in order to cover non-smooth M-estimators as well. In particular, we develop ‘high-level’ conditions under which the proposed M-estimator is consistent and has an asymptotic limit. We also check these conditions for a specific example of a semiparametric M-estimator coming from the area of classification with missing data.

Keywords: Asymptotic distribution; Classification; Empirical processes; M-Estimation; Missing data; Nonstandard asymptotics; Nuisance parameter; Semiparametric regression (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10463-018-0700-y 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:72:y:2020:i:2:d:10.1007_s10463-018-0700-y

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

DOI: 10.1007/s10463-018-0700-y

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 ().