Parametric rst - order Edgeworth expansion for Markov additive functionals . Application to M - estimations . D . FERRE ∗ février 2012
نویسنده
چکیده
We give a spectral approach to prove a parametric rst-order Edgeworth expansion for bi-variate additive functionals of strongly ergodic Markov chains. In particular, given any V-geometrically ergodic Markov chain (X n) n∈IN whose distribution depends on a parameter θ, we prove that {ξ p (X n−1 , X n); p ∈ P, n ≥ 1} satises a uniform (in (θ, p)) rst-order Edge-worth expansion provided that {ξ p (·, ·); p ∈ P} satises some non-lattice condition and an almost optimal moment domination condition. Furthermore, the sequence (X n) n∈IN need not be stationary. This result is applied to M-estimations.
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تاریخ انتشار 2012