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), Mielniczuk (1997) and 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.

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Keywords Confidence band, Empirical process, Limit theorem, Mean integrated squared error
Persistent URL
Journal Statistics and Probability Letters
Ould Haye, M, & Philippe, A. (Anne). (2011). Marginal density estimation for linear processes with cyclical long memory. Statistics and Probability Letters, 81(9), 1354–1364. doi:10.1016/j.spl.2011.04.010