Exact confidence intervals for the Hurst parameter of a fractional Brownian motion

Breton, Jean-Christophe; Nourdin, Ivan; Peccati, Giovanni

doi:10.1214/09-ejs366

Cited by 29 publications

(34 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Estimation of h has paid much attention in the litterature, for instance in the gaussian or Lévy field cases. With this respect, we refer the reader to the recent papers by Brouste et al (2007), Breton et al (2009), Coeurjolly (2008, Lacaux and Loubès (2007) and the references therein.…”

Section: Resultsmentioning

confidence: 99%

On Hölder fields clustering

Cadre

Paris²

2011

TEST

View full text Add to dashboard Cite

In this paper, we study the k-means clustering scheme based on the observations of a phenomenon modelled by a sequence of random fields X 1 , · · · , X n taking values in a Hilbert space. In the k-means algorithm, clustering is performed by computing a Voronoi partition associated with centers that minimize an empirical criterion, called distorsion. The performance of the method is evaluated by comparing a theoretical distorsion of empirically optimal centers to the theoretical optimal distorsion. Our first result states that, provided the underlying distribution satisfies an exponential moment condition, an upper bound for the above performance criterion is O(1/ √ n). Then, motivated by a broad range of applications and computational matters, we use a Hölder property shared by classical random fields in stochastic modelling to construct a numerically simple algorithm that computes empirical centers based on a discretized version of the data. With a judicious choice of the discretization, we are abble to recover the same performance than in the non-discretized case.

show abstract

Section: Resultsmentioning

confidence: 99%

On Hölder fields clustering

Cadre

Paris²

2011

TEST

View full text Add to dashboard Cite

show abstract

“…In addition to their study of convergence in Wiener chaos in [8], which they followed up with sharper results in [9], Nourdin and Peccati have implemented several other applications including: the study of cummulants on Wiener chaos [11], of fluctuations of Hermitian random matrices [12], and, with other authors, other results about the structure of inequalities and convergences on Wiener space, such as [3], [13], [14], [15]. In [16], it was pointed out that if ρ denotes the density of X, then the function…”

Section: Write E [H(x)] − E [H(z)] Using the Solution Of Stein's Equamentioning

confidence: 99%

“…resulting in a convenient formula for the density ρ, which was then exploited to provide new Gaussian lower bound results for certain stochastic models, in [16] for Gaussian fields, and subsequently in [22] for polymer models in Gaussian and non-Gaussian environments, in [18] for stochastic heat equations, in [3] for statistical inference for long-memory stochastic processes, and multivariate extensions of density formulas in [1].…”

Section: Write E [H(x)] − E [H(z)] Using the Solution Of Stein's Equamentioning

confidence: 99%

General Upper and Lower Tail Estimates Using Malliavin Calculus and Stein’s Equations

Eden

Viens

2013

Seminar on Stochastic Analysis, Random Fields and Applications VII

View full text Add to dashboard Cite

Abstract. Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference distribution, and apply it to all reference distributions in the so-called Pearson class. This enables us to give concrete conditions to ensure upper and/or lower bounds on the random variable's tail of various power or exponential types. The Nourdin-Peccati strategy analyzes the relation bewteen Stein's method and the Malliavin calculus, and is adapted to dealing with comparisons to the Gaussian law. By studying the behavior of the solution to general Stein equations in detail, we show that the strategy can be extended to comparisons to a wide class of laws, including all Pearson distributions.Mathematics Subject Classification (2010). Primary 60H07; Secondary 60G15, 60E15.

show abstract

“…Some of the available methods also allow the estimation of the confidence intervals for the Hurst exponent [23,24,33,70], whereas others propose a new and radically different approach to the estimation problem (e.g. [72]).…”

Section: Nowadays This Parameter Is Known As the Hurst Exponent (H)mentioning

confidence: 99%

Bayesian estimation of self-similarity exponent

2011

View full text Add to dashboard Cite

Exact confidence intervals for the Hurst parameter of a fractional Brownian motion

Abstract: In this short note, we show how to use concentration inequalities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion.

Cited by 29 publications

References 13 publications

On Hölder fields clustering

On Hölder fields clustering

General Upper and Lower Tail Estimates Using Malliavin Calculus and Stein’s Equations

Bayesian estimation of self-similarity exponent

Contact Info

Product

Resources

About