Wavelet Methods for Curve Estimation

Antoniadis, Anestis; Grègoire, Gèrard; McKeague, Ian W.

doi:10.2307/2290996

Cited by 60 publications

(66 citation statements)

References 2 publications

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“…See, for example, Antoniadis et al (1994Antoniadis et al ( , 1997, Donoho et al (1996), Gao (1993), and Johnstone et al (1992). This leaves open a question which is a natural one to ask within a statistical perspective, namely, can these new classes of functions be used to advantage to solve statistical problems which are purely of a parametric nature?…”

mentioning

confidence: 99%

Wavelet-Based Estimation for Univariate Stable Laws

Antoniadis

Feuerverger

Gonçalvès

2006

AISM

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Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data from stable distributions and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem rather than a nonparametric one, which is the more typical context in wavelet applications.

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confidence: 99%

Wavelet-Based Estimation for Univariate Stable Laws

Antoniadis

Feuerverger

Gonçalvès

2006

AISM

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“…A j E m (t, s)ds, under the assumptions (A4)-(A7) and by the relation (11) of the proof of Theorem 3.2 in [15], we obtain…”

Section: Corollary 22 Under the Conditions Of Theorem 22 Withmentioning

confidence: 81%

Berry-Esseen bounds for wavelet estimator in semiparametric regression model with linear process errors

Cheng-dong

2012

J Inequal Appl

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“…Various methods such as Akaike's Information Criterion [8] and cross-validation can be used for choosing M . Antoniadis [11] suggested linear shrunk wavelet estimators where theŵ jk are linearly shrunk by appropriately chosen level-dependent factors instead of truncation. We should point out that: the linear regression approach here is similar to the dimensionality reduction by keeping the first several wavelet coefficients discussed in section 5.3.…”

Section: Linear Regressionmentioning

confidence: 99%

A survey on wavelet applications in data mining

Zhu

et al. 2002

SIGKDD Explor. Newsl.

182

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Recently there has been significant development in the use of wavelet methods in various data mining processes. However, there has been written no comprehensive survey available on the topic. The goal of this is paper to fill the void. First, the paper presents a high-level data-mining framework that reduces the overall process into smaller components. Then applications of wavelets for each component are reviewd. The paper concludes by discussing the impact of wavelets on data mining research and outlining potential future research directions and applications.

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Wavelet Methods for Curve Estimation

Cited by 60 publications

References 2 publications

Wavelet-Based Estimation for Univariate Stable Laws

Wavelet-Based Estimation for Univariate Stable Laws

Berry-Esseen bounds for wavelet estimator in semiparametric regression model with linear process errors

A survey on wavelet applications in data mining

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