Estimating the order of mean-square derivatives with quadratic variations

Blanke, Delphine; Vial, Céline

doi:10.1007/s11203-011-9055-1

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…In Blanke and Vial (2011), an exponential bound is obtained for P( r 0 = r 0 ) in the equidistant case, implying that, almost surely for n large enough, r 0 is equal to r 0 . Here, we generalize this result to regular sequence designs but also, we complete it with the average behavior of r 0 .…”

Section: Asymptotic Resultsmentioning

confidence: 99%

“…Our methodology is based on an estimator of r 0 , say r 0 , derived from quadratic variations of divided differences of X and consequently, generalize the estimator studied by Blanke and Vial (2011) for the equidistant case. In a second step, we proceed to the estimation of β 0 , with an estimator β 0 which can be viewed as a simplification of that studied, in the case r 0 = 0, by Kent and Wood (1997).…”

Section: Introductionmentioning

confidence: 99%

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Global smoothness estimation of a Gaussian process from general sequence designs

Blanke¹,

Vial²

2014

Electron. J. Statist.

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We consider a real Gaussian process X having a global unknown smoothness (r0, β0), r0 ∈ N 0 and β0 ∈]0, 1[, with X (r 0 ) (the mean-square derivative of X if r0 ≥ 1) supposed to be locally stationary with index β0. From the behavior of quadratic variations built on divided differences of X, we derive an estimator of (r0, β0) based on -not necessarily equally spacedobservations of X. Various numerical studies of these estimators exhibit their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.

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Section: Asymptotic Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global smoothness estimation of a Gaussian process from general sequence designs

Blanke¹,

Vial²

2014

Electron. J. Statist.

Self Cite

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show abstract

“…Several examples of processes satisfy our condition (H2). See, for instance, Berman (1974), Blanke and Vial (2011), , and the references therein. Let us here mention few of them.…”

Section: Supplementary Materialsmentioning

confidence: 99%

Adaptive optimal estimation of irregular mean and covariance functions

Golovkine¹,

Klutchnikoff²,

Patilea³

2021

Preprint

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We propose straightforward nonparametric estimators for the mean and the covariance functions of functional data. Our setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity, and are measured with error at discrete design points. The measurement error could be heteroscedastic. The design points could be either randomly drawn or common for all curves. The definition of our nonparametric estimators depends on the local regularity of the stochastic process generating the functional data. We first propose a simple estimator of this local regularity which takes strength from the replication and regularization features of functional data. Next, we use the "smoothing first, then estimate" approach for the mean and the covariance functions. The new nonparametric estimators achieve optimal rates of convergence. They can be applied with both sparsely or densely sampled curves, are easy to calculate and to update, and perform well in simulations. Simulations built upon a real data example on household power consumption illustrate the effectiveness of the new approach.

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Estimating jump intensity and detecting jump instants in the context of p derivatives

Bosq

2016

Comptes Rendus. Mathématique

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Estimating the order of mean-square derivatives with quadratic variations

Abstract: Inference for Gaussian processes, Locally stationary process, Quadratic variations, Interpolation, 62M, 60G15, 60G17,

Cited by 4 publications

References 15 publications

Global smoothness estimation of a Gaussian process from general sequence designs

Global smoothness estimation of a Gaussian process from general sequence designs

Adaptive optimal estimation of irregular mean and covariance functions

Estimating jump intensity and detecting jump instants in the context of p derivatives

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