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Moment convergence of M ‐estimators
Author(s) -
Nishiyama Yoichi
Publication year - 2010
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2010.00469.x
Subject(s) - estimator , mathematics , moment (physics) , convergence (economics) , rate of convergence , residual , statistics , maximum likelihood , convergence of random variables , random variable , algorithm , computer science , economics , computer network , channel (broadcasting) , physics , classical mechanics , economic growth
This study extends the rate of convergence theorem of M ‐estimators presented by van der V aart and W ellner (weak convergence and empirical processes: with applications to statistics, Springer‐Verlag, Newyork, 1996) who gave a result of the form r to a result of the form sup n E | r , for any p ≥1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.