Monotone spectral density estimation

Dragi Anevski (1) , Philippe Soulier (2)

1 Skane University Hospital [Lund]
2 MODAL'X - Modélisation aléatoire de Paris X

We propose two estimators of a unimodal or monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.

Mots clés: spectral density; shape restriction; isotonic estimation

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

Dragi Anevski, Philippe Soulier. Monotone spectral density estimation. Annals of Statistics, 2011, 39 (1), pp.418-438. ⟨10.1214/10-AOS804⟩. ⟨hal-00355215v2⟩