Marginal density estimation for linear processes with cyclical long memory

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

1 School of Mathematics and Statistics [Ottawa]
2 LMJL - Laboratoire de Mathématiques Jean Leray

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) 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 limit distribution may be different in this context.

Mots clés: mean integrated squared error; Confidence band; empirical process; kernel density estimator; limit theorem; mean integrated squared error.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Mohamedou Ould Haye, Anne Philippe. Marginal density estimation for linear processes with cyclical long memory. 2011. ⟨hal-00550119v3⟩