Marginal density estimation for linear processes with cyclical long memory

Mohamedou Ould Haye (1) , Anne Philippe (2)

1 Carleton University
2 UN - Université de Nantes

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular we extend the results of Ho and Hsing (1996) and Mielniczuk (1997); Hall and Hart (1990) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limiting distribution may be different in this context.

Mots clés: Confidence band; Empirical process; Limit theorem; Mean integrated squared error

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Mohamedou Ould Haye, Anne Philippe. Marginal density estimation for linear processes with cyclical long memory. Statistics and Probability Letters, 2011, ⟨10.1016/j.spl.2011.04.010⟩. ⟨hal-00762901⟩