Electronic Journal of Statistics

Expectiles for subordinated Gaussian processes with applications

Jean-François Coeurjolly and Hedi Kortas

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Abstract

In this paper, in order to deal with data rounding issues, 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. So as 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 ρ(i)κ|i|α (κℝ) with α>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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 303-322.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1331216628

Digital Object Identifier
doi:10.1214/12-EJS674

Mathematical Reviews number (MathSciNet)
MR2988410

Zentralblatt MATH identifier
1277.60071

Subjects
Primary: 60G18: Self-similar processes
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Expectiles robustness local shift sensitivity subordinated Gaussian process fractional Brownian motion

Citation

Coeurjolly, Jean-François; Kortas, Hedi. Expectiles for subordinated Gaussian processes with applications. Electron. J. Statist. 6 (2012), 303--322. doi:10.1214/12-EJS674. https://projecteuclid.org/euclid.ejs/1331216628


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