M. D. Ruiz Medina
Limit theorems in long-range dependence (LRD) functional sequences is a challenging topic. Central and functional central limit theorems under non-summability of the covariance operator norm sequence, and for the sample covariance operator have been recently derived in Düker (2018, 2020) in the time domain. On the other hand, in the functional spectral domain, Ruiz--Medina (2021) characterizes LRD in Hilbert-valued time series. Minimum contrast estimation is extended to this domain, under a Gaussian scenario, in a weak-consistent way. The present talk formulates reduction theorems in an infinite-dimensional framework to obtain some central and non-central limit results for stationary functional sequences displaying LRD.
Palabras clave: Central limit theorem, functional spectral analysis, non-central limit theorem, LRD functional sequences
Programado
GT17 Procesos Estocásticos y sus Aplicaciones I
7 de junio de 2022 12:00
A24
