Premium
Preliminary test estimation in uniformly locally asymptotically normal models
Author(s) -
Paindaveine Davy,
Rasoafaraniaina Joséa,
Verdebout Thomas
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12516
Subject(s) - estimator , mathematics , goodness of fit , covariance , asymptotic analysis , statistical hypothesis testing , statistics
Preliminary test estimation is a methodology that combines goodness‐of‐fit testing and estimation. It is a classical procedure when it is suspected that the parameter to be estimated satisfies some prespecified constraints. In the present paper, we establish general results on the asymptotic behavior of preliminary test estimators. More precisely, we show that, in uniformly locally asymptotically normal (ULAN) models, a general asymptotic theory can be derived for preliminary test estimators based on estimators admitting generic Bahadur‐type representations. This allows for a detailed comparison between classical estimators and preliminary test estimators in ULAN models. Our results, that, in standard linear regression models, are shown to reduce to some classical results, are also illustrated in more modern and involved setups, such as the multisample one where m covariance matrices ∑ 1 , … , ∑ mare to be estimated when it is suspected that these matrices might be equal, might be proportional, or might share a common “scale”. Simulation results confirm our theoretical findings and an illustration on a real data example is provided.