UNIFORM-CONVERGENCE OF THE EMPIRICAL SPECTRAL DISTRIBUTION FUNCTION

Authors
MIKOSCH T NORVAISA R
Citation
T. Mikosch et R. Norvaisa, UNIFORM-CONVERGENCE OF THE EMPIRICAL SPECTRAL DISTRIBUTION FUNCTION, Stochastic processes and their applications, 70(1), 1997, pp. 85-114
Citations number
28
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Stochastic processes and their applications → ACNP
ISSN journal
03044149
Volume
70
Issue
1
Year of publication
1997
Pages
85 - 114
Database
ISI
SICI code
0304-4149(1997)70:1<85:UOTESD>2.0.ZU;2-Q
Abstract
Let X be a linear process having a finite fourth moment. Assume F is a class of square-integrable functions. We consider the empirical spect ral distribution function J(n,X) based on X and indexed by F. If F is totally bounded then J(n,X) satisfies a uniform strong law of large nu mbers. If, in addition, a metric entropy condition holds, then J(n,X) obeys the uniform central limit theorem. (C) 1997 Elsevier Science B.V .