Some strong limit theorems for M-estimators
Using the Talagrand isoperimetric inequality, the author establishes some laws of the iterated logarithm for empirical processes rescaled in the ``time'' parameter. These laws are applied to obtain the LIL for \(M\)- estimators with unusual rates of convergence (in particular, with cubic root asymptotics instead of the usual rate \(((n/2) \log \log n)^{1/2})\). Some Bahadur-Kiefer representations for \(M\)-estimators are also given even when the rate is not the standard one.
scientific article; zbMATH DE number 713905
scientific article