no. 2
Statistics
Nonparametric recursive density estimation for spatial data
[Estimation nonparamétrique récursive de la densité pour données spatiales]

Présenté par : the Editorial Board

Amiri, Aboubacar1 ; Dabo-Niang, Sophie1, 2 ; Yahaya, Mohamed1, 3
1 Université Lille 3, Laboratoire LEM CNRS 9221, France
2 INRIA-MODAL Team, France
3 FST, Université des Comores, Comoros
Comptes Rendus. Mathématique, Tome 354 (2016) no. 2, pp. 205-210.

Ce papier traite de l'estimation de la densité spatiale dans le cas récursif. Nous étudions les propiétés asymptotiques d'une nouvelle version de l'estimateur de Parzen–Rozenblatt. Nous établissons les convergences en moyenne quadratique et presque sûre de cet estimateur ; des vitesses de convergence sont données.

This paper deals with non-parametric density estimation for spatial data. We study the asymptotic properties of a new recursive version of the Parzen–Rozenblatt estimator. The mean square error and an almost sure convergence result with rate of such estimator are derived.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.10.010
Amiri, Aboubacar 1 ; Dabo-Niang, Sophie 1, 2 ; Yahaya, Mohamed 1, 3

1 Université Lille 3, Laboratoire LEM CNRS 9221, France
2 INRIA-MODAL Team, France
3 FST, Université des Comores, Comoros 
@article{CRMATH_2016__354_2_205_0,
     author = {Amiri, Aboubacar and Dabo-Niang, Sophie and Yahaya, Mohamed},
     title = {Nonparametric recursive density estimation for spatial data},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {205--210},
     publisher = {Elsevier},
     volume = {354},
     number = {2},
     year = {2016},
     doi = {10.1016/j.crma.2015.10.010},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2015.10.010/}
}
TY  - JOUR
AU  - Amiri, Aboubacar
AU  - Dabo-Niang, Sophie
AU  - Yahaya, Mohamed
TI  - Nonparametric recursive density estimation for spatial data
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 205
EP  - 210
VL  - 354
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2015.10.010/
DO  - 10.1016/j.crma.2015.10.010
LA  - en
ID  - CRMATH_2016__354_2_205_0
ER  - 
%0 Journal Article
%A Amiri, Aboubacar
%A Dabo-Niang, Sophie
%A Yahaya, Mohamed
%T Nonparametric recursive density estimation for spatial data
%J Comptes Rendus. Mathématique
%D 2016
%P 205-210
%V 354
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2015.10.010/
%R 10.1016/j.crma.2015.10.010
%G en
%F CRMATH_2016__354_2_205_0
Amiri, Aboubacar; Dabo-Niang, Sophie; Yahaya, Mohamed. Nonparametric recursive density estimation for spatial data. Comptes Rendus. Mathématique, Tome 354 (2016) no. 2, pp. 205-210. doi : 10.1016/j.crma.2015.10.010. http://www.numdam.org/articles/10.1016/j.crma.2015.10.010/

[1] Amiri, A. Sur une famille paramétrique d'estimateurs séquentiels de la densité pour un processus fortement mélangeant, C. R. Acad. Sci. Paris, Sér. I, Volume 347 (2009), pp. 309-314

[2] Baek, J.; Liang, H.-Y. Asymptotic normality of recursive density estimates under some dependence assumptions, Metrika, Volume 60 (2004), pp. 155-166

[3] Biau, G.; Cadre, B. Nonparametric spatial prediction, Stat. Inference Stoch. Process., Volume 7 (2004), pp. 327-349

[4] Blanke, D.; Bosq, D. Inference and Prediction in Large Dimensions, Wiley Series in Probability and Statistics, Dunod, 2007

[5] Carbon, M.; Tran, L.-T.; Wu, B. Kernel density estimation for random fields: the L1 theory, J. Nonparametr. Stat., Volume 6 (1997), pp. 157-170

[6] Carbon, M.; Tran, L.-T.; Wu, B. Kernel density estimation for random fields, Stat. Probab. Lett., Volume 36 (1997), pp. 115-125

[7] Chiles, J.-P.; Delfiner, P. Statistics for Spatial Data, Wiley, New York, 1999

[8] Conley, T. GMM estimation with cross sectional dependence, J. Econom., Volume 92 (1999), pp. 1-45

[9] Cressie, N.-A.-C. Statistics for Spatial Data, Wiley Series in Probability and Mathematical Statistics, Wiley-Interscience, New York, 1991

[10] Dabo-Niang, S.; Yao, A.-F. Kernel regression estimation for continuous spatial processes, Math. Methods Stat., Volume 16 (2007), pp. 298-317

[11] Davies, H.-I.; Wegman, E.-J. Remarks on some recursive estimators of a probability density, Ann. Stat., Volume 7 (1979), pp. 316-327

[12] Deheuvels, P. Sur une famille d'estimateurs de la densité d'une variable aléatoire, C. R. Acad. Sci. Paris, Volume 276 (1974), pp. 1013-1015

[13] Isogai, E. A Berry–Esseen-type bound for recursive estimators of a density and its derivatives, J. Stat. Plan. Inference, Volume 40 (1994), pp. 1-4

[14] Masry, E. Recursive probability density estimation for weakly dependent stationary processes, IEEE Trans. Inf. Theory, Volume 32 (1986), pp. 254-267

[15] Mezhoud, K.-A. et al. Recursive kernel estimation of the density under η-dependence, J. Korean Stat. Soc. (2014), pp. 1-12

[16] Mugisha, R.-X.; Samanta, M. On the class of estimates of the probability function and mode based on random number of observations, Calcutta Stat. Assoc. Bull., Volume 117 (1981), pp. 23-40

[17] Robinson, P.-M. Asymptotic theory for nonparametric regression with spatial data, J. Econom., Volume 165 (2011), pp. 5-19

[18] Stout, W.-F., Academic Press, New York (1974), pp. 120-121

[19] Tran, L.-T. Kernel density estimation on random fields, J. Multivar. Anal., Volume 34 (1990), pp. 37-53

[20] Wagner, T.; Wolverton, C. Recursive estimates of probability density, IEEE Trans. Syst. Sci. Cybern., Volume 5 (1969), pp. 307-308

[21] Yamato, H. Sequential estimation of a continuous probability density function and mode, Bull. Math. Stat., Volume 14 (1972), pp. 1-12

Cité par Sources :