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.
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Stéphane Bouka 1
@article{CRMATH_2019__357_11-12_907_0, author = {St\'ephane Bouka}, 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}, }
Stéphane Bouka. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.11.002/
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