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    Large scale reduction principle and application to hypothesis testing

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    Date Issued
    2015-01-01
    Publisher Version
    10.1214/15-EJS987
    Author(s)
    Clausel, Marianne
    Roueff, Francois
    Taqqu, Murad S.
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    Permanent Link
    https://hdl.handle.net/2144/37501
    Version
    First author draft
    Citation (published version)
    Marianne Clausel, Francois Roueff, Murad S Taqqu. 2015. "Large scale reduction principle and application to hypothesis testing." ELECTRONIC JOURNAL OF STATISTICS, Volume 9, Issue 1, pp. 153 - 203 (51). https://doi.org/10.1214/15-EJS987
    Abstract
    Consider a non–linear function G(Xt) where Xt is a stationary Gaussian sequence with long–range dependence. The usual reduction principle states that the partial sums of G(Xt) behave asymptotically like the partial sums of the first term in the expansion of G in Hermite polynomials. In the context of the wavelet estimation of the long–range dependence parameter, one replaces the partial sums of G(Xt) by the wavelet scalogram, namely the partial sum of squares of the wavelet coefficients. Is there a reduction principle in the wavelet setting, namely is the asymptotic behavior of the scalogram for G(Xt) the same as that for the first term in the expansion of G in Hermite polynomial? The answer is negative in general. This paper provides a minimal growth condition on the scales of the wavelet coefficients which ensures that the reduction principle also holds for the scalogram. The results are applied to testing the hypothesis that the long-range dependence parameter takes a specific value.
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    • CAS: Mathematics & Statistics: Scholarly Papers [263]
    • BU Open Access Articles [3664]


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