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:10.48550/arxiv.1011.4370

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A Short Simulation Study1

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2012

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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: 80%

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: 80%