We first establish, through a Berry–Esseen-type bound, the asymptotic normality of a local linear estimate of the regression function in a fixed design setting when the errors are stationary isotropic spatial random fields. On the other hand, we investigate the weak convergence of an empirical estimate of the variance of these errors in a general α-mixing setting.
Nous établissons tout d'abord, à travers une borne de type Berry–Esseen, la normalité asymptotique d'un estimateur localement linéaire de la fonction de régression dans le cadre d'un design déterministe, lorsque les erreurs sont des champs aléatoires spatiaux isotropiques stationnaires. Nous établissons ensuite la convergence faible d'un estimateur de la variance de ces erreurs dans un cadre spatial α-mélangeant.
Accepted:
Published online:
@article{CRMATH_2019__357_11-12_907_0, author = {Bouka, St\'ephane}, title = {Estimation of the trend function and auto-covariance for spatial models}, journal = {Comptes Rendus. Math\'ematique}, pages = {907--911}, publisher = {Elsevier}, volume = {357}, number = {11-12}, year = {2019}, doi = {10.1016/j.crma.2019.11.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2019.11.002/} }
TY - JOUR AU - Bouka, Stéphane TI - Estimation of the trend function and auto-covariance for spatial models JO - Comptes Rendus. Mathématique PY - 2019 SP - 907 EP - 911 VL - 357 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2019.11.002/ DO - 10.1016/j.crma.2019.11.002 LA - en ID - CRMATH_2019__357_11-12_907_0 ER -
%0 Journal Article %A Bouka, Stéphane %T Estimation of the trend function and auto-covariance for spatial models %J Comptes Rendus. Mathématique %D 2019 %P 907-911 %V 357 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2019.11.002/ %R 10.1016/j.crma.2019.11.002 %G en %F CRMATH_2019__357_11-12_907_0
Bouka, Stéphane. Estimation of the trend function and auto-covariance for spatial models. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 907-911. doi : 10.1016/j.crma.2019.11.002. http://archive.numdam.org/articles/10.1016/j.crma.2019.11.002/
[1] Nonparametric spatial prediction, Stat. Inference Stoch. Process., Volume 7 (2004), pp. 327-349
[2] Non-parametric level set estimation for spatial data, Adv. Appl. Stat., Volume 46 (2015), pp. 119-158
[3] Statistics for Spatial Data, Wiley, New York, 1993
[4] Kernel regression estimation for continuous spatial processes, Math. Methods Stat., Volume 1 (2007), pp. 298-317
[5] On local linear regression for strongly mixing random fields, J. Multivar. Anal., Volume 156 (2017), pp. 103-115
[6] Smoothing parameter selection methods for nonparametric with spatially correlated errors, Can. J. Stat., Volume 33 (2005), pp. 279-295
[7] Moment inequalities for spatial processes, Stat. Probab. Lett., Volume 78 (2008), pp. 687-697
[8] Minimax testing composite null hypotheses in the discrete regression scheme, Math. Methods Stat., Volume 10 (2001), pp. 375-394
[9] Kernel density estimation on random fields, J. Multivar. Anal., Volume 34 (1990), pp. 37-53
[10] Estimation of the trend function for spatio-temporal models, J. Nonparametr. Stat., Volume 22 (2009), pp. 567-588
Cited by Sources: