Edgeworth expansions for infinite triangular arrays with applications to short and long memory processes

Gilles Fay (1) , Eric Moulines (2) , Philippe Soulier (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 MODAL'X - Modélisation aléatoire de Paris X

The validity of the Edgeworth expansion for densities of linear statistics of linear processes is proved. In contrast with previous works on Edgeworth expansions for dependent processes, this result is valid under long-range dependence.

Mots clés: Edgeworth expansions; Linear statistics; Linear processes; Long-range dependence

Domaines: Statistiques [math.ST]

Gilles Fay, Eric Moulines, Philippe Soulier. Edgeworth expansions for infinite triangular arrays with applications to short and long memory processes. Statistics and Probability Letters, 2004, 66 (3), pp.275-288. ⟨10.1016/j.spl.2003.09.009⟩. ⟨hal-00147627⟩