Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Kouamo, Olaf; Lévy‐Leduc, Céline; Moulines, Éric

doi:10.3150/11-bej398

Cited by 3 publications

(3 citation statements)

References 28 publications

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“…Several types of expectiles are investigated. When the discretized sample path of the fBm is contaminated by outliers, we recover the results already shown in Coeurjolly (2008), Achard and Coeurjolly (2010) or Kouamo et al (2010): methods based on medians or trimmed-means are very efficient which is in agreement with the fact that quantiles have a finite gross error sensitivity. The inefficiency of expectiles for such a contamination is also coherent since expectiles have infinite gross error sensitivity.…”

Section: A Short Simulation Studysupporting

confidence: 86%

Expectiles for subordinated Gaussian processes with applications

Coeurjolly¹,

Kortas²

2012

Electron. J. Statist.

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International audienceIn this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample expectiles of subordinated stationary Gaussian processes with unit variance and correlation function satisfying $\rho(i)\sim \kappa|i|^{-\alpha}$ ($\kappa\in \RR$) with $\alpha>0$. Via a simulation study, we demonstrate the relevance of the expectile-based estimation method and show that the suggested estimators are more robust to data rounding than their sample quantile-based counterparts

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Section: A Short Simulation Studysupporting

confidence: 86%

Expectiles for subordinated Gaussian processes with applications

Coeurjolly¹,

Kortas²

2012

Electron. J. Statist.

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“…It is worth noticing that the role of these experiments concerns the relevancy of a spectrum estimated from data and do not concern "parameter estimation from a given spectrum estimate". For more details on parameter estimators (in wavelet and the Fourier domain), the reader can refer to [44], [45], [46], see also [47], [48] for the robust estimation of the autocorrelation function in presence of a long memory parameter.…”

Section: Identification Of a Singular Wavelet Packet Pathmentioning

confidence: 99%

Wavelet Packets of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation

Atto¹,

Berthoumieu

2012

IEEE Trans. Inform. Theory

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International audienceThe paper addresses the analysis and interpretation of second order random processes by using the wavelet packet transform. It is shown that statistical properties of the wavelet packet coefficients are specific to the filtering sequences characterizing wavelet packet paths. These statistical properties also depend on the wavelet order and the form of the cumulants of the input random process. The analysis performed points out the wavelet packet paths for which stationarization, decorrelation and higher order dependency reduction are effective among the coefficients associated with these paths. This analysis also highlights the presence of singular wavelet packet paths: the paths such that stationarization does not occur and those for which dependency reduction is not expected through successive decompositions. The focus of the paper is on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet packet domain. This is addressed with respect to semi-analytical cumulant expansions for modeling different types of nonstatonarity and correlation structures. The characterization obtained eases the interpretation of random signals and time series with respect to the statistical properties of their coefficients on the different wavelet packet paths

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“…Abry and Veitch, 1998;Bardet et al, 2000;Moulines et al, 2007a,b;Roueff and Taqqu, 2009;Fay et al, 2009) for wavelet-based estimators of LRD are for gap free series, use a decimated wavelet transform, do not discuss uncertainty estimates, and the estimator (although not the asymptotic theory) assumes that coefficients over different wavelet scales are uncorrelated. Kouamo et al (2013) proposes an interpolation-wavelet-based method for possibly gappy nonstationary Gaussian series and Knight et al (2016) develop an estimation method based on wavelet lifting.…”

Section: Introductionmentioning

confidence: 99%

Estimation of long-range dependence in gappy Gaussian time series

Craigmile

Mondal

2019

Stat Comput

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Knowledge of the long range dependence (LRD) parameter is critical to studies of self-similar behavior. However, statistical estimation of the LRD parameter becomes difficult when the observed data are masked by short range dependence and other noise, or are gappy in nature (i.e., some values are missing in an otherwise regular sampling). Currently there is a lack of theory for spectral-and wavelet-based estimators of the LRD parameter for gappy data. To address this, we estimate the LRD parameter for gappy Gaussian semiparametric time series based upon undecimated wavelet variances. We develop estimation methods by using novel estimators of the wavelet variances, providing asymptotic theory for the joint distribution of the wavelet variances and our estimator of the LRD parameter. We introduce sandwich estimators to compute standard errors for our estimates. We demonstrate the efficacy of our methods using Monte Carlo simulations, and provide guidance on practical issues such as how to select the range of wavelet scales. We demonstrate the methodology using two applications: one for gappy Arctic sea-ice draft data, and another for gap free and gappy daily average temperature data collected at 17 locations in south central Sweden.

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Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

Cited by 3 publications

References 28 publications

Expectiles for subordinated Gaussian processes with applications

Expectiles for subordinated Gaussian processes with applications

Wavelet Packets of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation

Estimation of long-range dependence in gappy Gaussian time series

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