Estimating jump intensity and detecting jump instants in the context of <i>p</i> derivatives

Denis Bosq

doi:10.1016/j.crma.2016.03.016

Statistics

Estimating jump intensity and detecting jump instants in the context of p derivatives
[Estimation de l'intensité et des instants de sauts pour des processus à p dérivées]

Présenté par : Paul Deheuvels

Denis Bosq ¹

¹ LSTA, Université Pierre-et-Marie-Curie (Paris-6), France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 729-734.

Résumé
Abstract

Dans cet article, nous considérons le processus $ARMA D^{(p)} (q, r)$ , où $D = D [0, 1]$ est l'espace des fonctions càdlàg et où la p^e dérivée a un saut éventuel. Nous envisageons de détecter l'intensité et la position des sauts. Des résultats asymptotiques sont obtenus.

In this paper we consider the $ARMA D^{(p)} (q, r)$ process where $D [0, 1]$ is the space of the càdlàg function and the p-th derivative has a possible jump. One envisages to detect the intensity and position of the jumps in the context of p derivatives. Asymptotic results are derived.

Reçu le : 2016-02-03
Accepté le : 2016-03-31
Publié le : 2016-05-05

DOI : 10.1016/j.crma.2016.03.016

Affiliations des auteurs :

Denis Bosq ¹

¹ LSTA, Université Pierre-et-Marie-Curie (Paris-6), France

@article{CRMATH_2016__354_7_729_0,
     author = {Denis Bosq},
     title = {Estimating jump intensity and detecting jump instants in the context of \protect\emph{p} derivatives},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {729--734},
     publisher = {Elsevier},
     volume = {354},
     number = {7},
     year = {2016},
     doi = {10.1016/j.crma.2016.03.016},
     language = {en},
}

TY  - JOUR
AU  - Denis Bosq
TI  - Estimating jump intensity and detecting jump instants in the context of p derivatives
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 729
EP  - 734
VL  - 354
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crma.2016.03.016
LA  - en
ID  - CRMATH_2016__354_7_729_0
ER  -

%0 Journal Article
%A Denis Bosq
%T Estimating jump intensity and detecting jump instants in the context of p derivatives
%J Comptes Rendus. Mathématique
%D 2016
%P 729-734
%V 354
%N 7
%I Elsevier
%R 10.1016/j.crma.2016.03.016
%G en
%F CRMATH_2016__354_7_729_0

Denis Bosq. Estimating jump intensity and detecting jump instants in the context of p derivatives. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 729-734. doi : 10.1016/j.crma.2016.03.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.03.016/

Bibliographie
Cité par

[1] P. Billingsley Convergence of Probability Measures, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons Inc., New York, 1999

[2] D. Blanke; D. Bosq Exponential bounds for intensity of jumps, Math. Methods Statist., Volume 23 (2014) no. 4, pp. 239-255

[3] D. Blanke; D. Bosq Detecting and estimating intensity of jumps for discretely observed processes, J. Multivariate Anal., Volume 146 (2016), pp. 119-137

[4] D. Blanke; C. Vial Estimating the order of mean-square derivatives with quadratic variations, Stat. Inference Stoch. Process., Volume 14 (2011) no. 1, pp. 85-99

[5] D. Blanke; C. Vial Global smoothness estimation of a Gaussian process from general sequence designs, Electron. J. Stat., Volume 8 (2014) no. 1, pp. 1152-1187

[6] D. Bosq Estimating and detecting jumps. Applications to $D [0, 1]$ -valued linear processes (M. Hallin; D.M. Mason; D. Pfeifer; J.G. Steinebach, eds.), Mathematical Statistics and Limit Theorems. Festschrift in Honour of Paul Deheuvels, Springer, 2015, p. 4166

[7] D. Cates; A. Gelb Detecting derivative discontinuity locations in piecewise continuous functions from Fourier spectral data, Numer. Algorithms, Volume 46 (2007) no. 1, pp. 59-84

[8] U. Çetin; I. Sheynzon A simple model for market booms and crashes, Math. Financ. Econ., Volume 8 (2014) no. 3, pp. 291-319

[9] R. Dmowska; B.V. Kostrov A shearing crack in a semi-space under plane strain conditions, Arch. Mech. (Arch. Mech. Stos.), Volume 25 (1973), pp. 421-440

[10] L. Horváth; P. Kokoszka Inference for Functional Data with Applications, Springer Series in Statistics, Springer, New York, 2012

[11] J.-H. Joo; P. Qiu Jump detection in a regression curve and its derivative, Technometrics, Volume 51 (2009) no. 3, pp. 289-305

[12] O. Scherzer Denoising with higher order derivatives of bounded variation and an application to parameter estimation, Computing, Volume 60 (1998) no. 1, pp. 1-27

[13] F. Takahashi Asymptotic behavior of large solutions to H-systems with perturbations, Nonlinear Anal., Volume 58 (2004) no. 3–4, pp. 459-475

[14] N.M. Tanushev Superpositions and higher order Gaussian beams, Commun. Math. Sci., Volume 6 (2008) no. 2, pp. 449-475

Cité par Sources :

Commentaires - Politique