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

Ghislaine Gayraud and Karine Tribouley

Statistics & Probability Letters, 1999, vol. 44, issue 2, 109-122

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].

Keywords: Adaptive; estimation; Confidence; bands; Minimax; risk; Wavelet; thresholding; methods (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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