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Title:Asymptotic theory for M estimators for martingale differences with applications to GARCH models
Authors:Tinkl, Fabian
Issue Date:2010
Series/Report no.:IWQW discussion paper series 09/2010
Abstract:We generalize the results for statistical functionals given by [Fernholz, 1983] and [Serfling, 1980] to M estimates for samples drawn for an ergodic and stationary martingale sequence. In a first step, we take advantage of some recent results on the uniform convergency of the empirical distribution given by [Adams & Nobel, 2010] to prove consistency of M estimators, before we assume Hadamard differentiability of our estimators to prove their asymptotic normality. Further we apply the results to the LAD estimator of [Peng & Yao, 2003] and the maximum-likelihood estimator for GARCH processes to show the wide field of possible applications of this method.
Subjects:Hadamard differential
M estimator
von Mises Calculus
martingale differences
GARCH models
Document Type:Working Paper
Appears in Collections:IWQW Discussion Paper Series, FAU Erlangen-Nürnberg

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