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Weak-stationarity conditions for wavelet processes

✍ Scribed by Shu-Ji Kawasaki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
603 KB
Volume
335
Category
Article
ISSN
0016-0032

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✦ Synopsis

Weak-stationarity criteria are obtained for second-order processes which have Karhunen-Loeve type canonical representation with respect to wavelets, for each case that the translation-measure in the representation of the covariance is (i) discrete, (ii) absolutely continuous or has (iii) discrete and absolutely continuous parts,

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Let X 1 ; : : : ; X n be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator P n; H and establish weak convergence of the empirical process √ n(P n; H -P)(f) f∈F under sharp conditions. If