no. 4
Statistiques
Dimension reduction in spatial regression with kernel SAVE method
[Réduction de la dimension en régression spatiale avec la méthode SAVE à noyau]
Affossogbe, Mètolidji Moquilas Raymond1 ; Nkiet, Guy Martial2  ; Ogouyandjou, Carlos1
1 Institut de Mathématiques et de Sciences Physiques,Porto Novo, Bénin
2 Université des Sciences et Techniques de Masuku, Franceville, Gabon
Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 475-479.

Nous considérons la version lisse de la méthode SAVE pour prendre en compte des observations spatialement dépendantes émanant d’un champ aléatoire fortement mélangeant. Nous proposons des estimateurs à noyau pour la matrice d’intérêt et l’espace de rédution de la dimension, et montrons leur convergence.

We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the interest matrix and the effective dimension reduction (EDR) space, and show their consistency.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.187
Affossogbe, Mètolidji Moquilas Raymond 1 ; Nkiet, Guy Martial 2 ; Ogouyandjou, Carlos 1

1 Institut de Mathématiques et de Sciences Physiques,Porto Novo, Bénin
2 Université des Sciences et Techniques de Masuku, Franceville, Gabon 
@article{CRMATH_2021__359_4_475_0,
     author = {Affossogbe, M\`etolidji Moquilas Raymond and Nkiet, Guy Martial and Ogouyandjou, Carlos},
     title = {Dimension reduction in spatial regression with kernel {SAVE} method},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {475--479},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {4},
     year = {2021},
     doi = {10.5802/crmath.187},
     zbl = {07362167},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.187/}
}
TY  - JOUR
AU  - Affossogbe, Mètolidji Moquilas Raymond
AU  - Nkiet, Guy Martial
AU  - Ogouyandjou, Carlos
TI  - Dimension reduction in spatial regression with kernel SAVE method
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 475
EP  - 479
VL  - 359
IS  - 4
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.187/
DO  - 10.5802/crmath.187
LA  - en
ID  - CRMATH_2021__359_4_475_0
ER  - 
%0 Journal Article
%A Affossogbe, Mètolidji Moquilas Raymond
%A Nkiet, Guy Martial
%A Ogouyandjou, Carlos
%T Dimension reduction in spatial regression with kernel SAVE method
%J Comptes Rendus. Mathématique
%D 2021
%P 475-479
%V 359
%N 4
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.187/
%R 10.5802/crmath.187
%G en
%F CRMATH_2021__359_4_475_0
Affossogbe, Mètolidji Moquilas Raymond; Nkiet, Guy Martial; Ogouyandjou, Carlos. Dimension reduction in spatial regression with kernel SAVE method. Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 475-479. doi : 10.5802/crmath.187. http://www.numdam.org/articles/10.5802/crmath.187/

[1] Attouch, M. K.; Gheriballah, A.; Laksaci, A. Robust nonparametric estimation for functional spatial regression, Recent Advances in Functional Data Analysis and Related Topics (Contributions to Statistics), Physica-Verlag, 2011, pp. 27-31 | DOI

[2] Carbon, Michel; Francq, Christian; Tran, Lanh Tat Kernel regression estimation for random fields, J. Stat. Plann. Inference, Volume 137 (2007) no. 3, pp. 778-798 | DOI | MR | Zbl

[3] Carbon, Michel; Tran, Lanh Tat; Wu, Berlin Kernel density estimation for random fields, Stat. Probab. Lett., Volume 36 (1997) no. 2, pp. 115-125 | DOI | Zbl

[4] Cook, R. D.; Weisberg, S. Discussion of a paper by K. C. Li, J. Am. Stat. Assoc., Volume 86 (1991), pp. 328-332

[5] Ferré, Louis; Yao, Anne-Françoise Functional Sliced Inverse Regression analysis, Statistics, Volume 37 (2003) no. 6, pp. 475-488 | DOI | MR

[6] Hallin, Marc; Lu, Zudi; Tran, Lanh Tat Local linear spatial regression, Ann. Stat., Volume 32 (2004) no. 6, pp. 2469-2500 | MR | Zbl

[7] Li, Jiexiang; Tran, Lanh Tat Nonparametric estimation of conditional expectation, J. Stat. Plann. Inference, Volume 139 (2009) no. 2, pp. 164-175 | MR | Zbl

[8] Li, Ker-Chau Sliced inverse regression for dimension reduction, J. Am. Stat. Assoc., Volume 86 (1991) no. 414, pp. 316-342 | MR | Zbl

[9] Loubes, J. M.; Yao, Anne-Françoise Kernel Inverse Regression for spatial random fields, Int. J. Appl. Math. Stat., Volume 32 (2013), pp. 1-26

[10] Lu, Zudi; Chen, Xing Spatial kernel regression estimation : weak consistency, Stat. Probab. Lett., Volume 68 (2004) no. 2, pp. 125-136 | MR | Zbl

[11] Menezes, Raquel; García-Soidán, Pilar; Ferreira, Célia Nonparametric spatial prediction under stochastic sampling design, J. Nonparametric Stat., Volume 22 (2010) no. 3, pp. 363-377 | DOI | MR | Zbl

[12] Tran, Lanh Tat Kernel density estimation on random fields, J. Multivariate Anal., Volume 34 (1990) no. 1, pp. 37-53 | DOI | MR | Zbl

[13] Zhu, Li-Xing; Fang, Kai-Tai Asymptotics for kernel estimate of sliced inverse regression, Ann. Stat., Volume 24 (1996) no. 3, pp. 1053-1068 | MR | Zbl

[14] Zhu, Liping; Zhu, Li-Xing On kernel method for sliced average variance estimation, J. Multivariate Anal., Volume 98 (2007) no. 5, pp. 970-991 | MR | Zbl

Cité par Sources :