Semiparametric M-Estimation with Non-Smooth Criterion Functions
(2011) , 28 pages
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- Authors
- Abstract
- We are interested in the estimation of a parameter 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 M 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-estimation problems, in order to cover non-smooth M-estimation problems 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 in detail for a specific example of a semiparametric M-estimation problem, which comes from the area of classification with missing data, and which cannot be dealt with using the existing results in the literature.
- Affiliations
Universite d'Orleans, France MAPMO
Citations
Delsol, L., & Van Keilegom, I. (2011). Semiparametric M-Estimation with Non-Smooth Criterion Functions (ISBA Discussion Paper 2011/41). https://hdl.handle.net/2078.5/209127