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Wavelet methods to estimate an integrated quadratic functional: Adaptivity and asymptotic law

Author

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  • Gayraud, Ghislaine
  • Tribouley, Karine

Abstract

Using wavelet thresholding methods, we give an adaptive estimator of [theta]=[integral operator]f2, where f is coming from the white noise model. We estimate the random bias term, which is the dominating term in the decomposition of the quadratic error, and state a central limit theorem. This estimator has two advantages: it is centered around [theta] and the rate does not require the knowledge on the regularity of f. Moreover, using our procedure, we provide explicit confidence intervals and critical regions for parametric tests on [theta].

Suggested Citation

  • Gayraud, Ghislaine & Tribouley, Karine, 1999. "Wavelet methods to estimate an integrated quadratic functional: Adaptivity and asymptotic law," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 109-122, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:2:p:109-122
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    Cited by:

    1. Christophe Chesneau, 2011. "On adaptive wavelet estimation of a quadratic functional from a deconvolution problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 405-429, April.

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