Wavelet Thresholding: Beyond the Gaussian I.I.D. Situation

  • With this article we first like to give a brief review on wavelet thresholding methods in non-Gaussian and non-i.i.d. situations, respectively. Many of these applications are based on Gaussian approximations of the empirical coefficients. For regression and density estimation with independent observations, we establish joint asymptotic normality of the empirical coefficients by means of strong approximations. Then we describe how one can prove asymptotic normality under mixing conditions on the observations by cumulant techniques.; In the second part, we apply these non-linear adaptive shrinking schemes to spectral estimation problems for both a stationary and a non-stationary time series setup. For the latter one, in a model of Dahlhaus on the evolutionary spectrum of a locally stationary time series, we present two different approaches. Moreover, we show that in classes of anisotropic function spaces an appropriately chosen wavelet basis automatically adapts to possibly different degrees of regularity for the different directions. The resulting fully-adaptive spectral estimator attains the rate that is optimal in the idealized Gaussian white noise model up to a logarithmic factor.

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Metadaten
Verfasserangaben:Michael H. Neumann, Rainer von Sachs
URN (Permalink):urn:nbn:de:hbz:386-kluedo-5338
Schriftenreihe (Bandnummer):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (133)
Dokumentart:Wissenschaftlicher Artikel
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:1995
Jahr der Veröffentlichung:1995
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):03.04.2000
Freies Schlagwort / Tag:Non-linear wavelet thresholding ; evolutionary spectrum; non-Gaussia non-i.i.d. errors ; nonparametric regression and (spectral) density estimation
Quelle:Wavelets and Statistics (A. Antoniadis, G. Oppenheim, eds.) Springer LN Statistics 103, 301-329 (1995)
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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