Longitudinal data with nonstationary errors: a nonparametric three-stage approach

Abstract

Additive model, cochlear implant, kernel smoothing, longitudinal data, random effects, three-stage procedure, 62G07, 62P10, 62F12,

Non-parametric estimation of the average growth curve with a general non-stationary error process

“…This include, as a special case, processes with stationary autocovariance function such as the Ornstein-Uhlenbeck process, and some specific nonstationary class of parametric autocovariance structure considered by Ferreira et al [3] and expanded by Núñez-Antón et al [9] to unbalanced data.…”

“…Although repeated measurements can naturally arise in practical situations, they can make the estimators of the curve f asymptotically consistent (see Hart and Wehrly, [7], and the comments of Härdle, [6]). Other models that take into account the individual effects are considered by Boularan et al [2] and Núñez-Antón et al [9], known respectively as two-and three-stage additive models, with specific parametric non-stationary covariance structure.…”

Semi‐parametric Analysis of Covariance Under Dependence Conditions Within Each Group

“…Basically, two ways have been explored in the literature: one based on linear (or, more generally, parametric) regression models, and another based on non‐parametric regression models. See the books by Seber (1977) and Jones (1993) for the parametric case, and the papers of Munk & Dette (1998), Dette & Neumeyer (2001), Vilar‐Fernández & González‐Manteiga (2004) and Núñez‐Antón, Rodríguez‐Poo & Vieu (1999) for the non‐parametric case, together with the references therein. For the books and papers mentioned, the last one in each case corresponds to the situation of longitudinal data.…”

“…The interest in covariance analysis is closely related to its applications to real data, some of which appear in Seber (1977), Vilar‐Fernández & González‐Manteiga (2004), Jones (1993) and Núñez‐Antón et al (1999) in fields such as agriculture, economics, medicine and audiology, respectively. Despite the variety of real situations related to covariance analysis covered by the parametric and non‐parametric models studied in the statistical literature, there are still many practical situations in which these models seem inadequate.…”

Convergence de l'estimateur spline cubique de lissage dans un modèle de régression longitudinale avec erreur de type processus

“…Leur convergence, connue dans le cas de données comportant un bruit indépendant et identiquement distribué (iid) (Craven et Wahba [4], Ragozin [7]), est étudiée ici dans un modèle plus général de données longitudinales où le bruit est un processus aléatoire (situation courante en pratique, par exemple en présence de corrélation et/ou d'hétéroscédasticité dans les données). Notre travail est à rapprocher de celui de Cardot et Diack [3] pour les splines hybrides, et plus généralement, de celui de Cardot [2] pour l'analyse en composantes principales lissée, de Boularan et al [1] et de Nuñez-Anton et al [6] pour les estimateurs à noyaux. Nous donnons ici les vitesses de convergence des estimateurs splines cubiques de lissage pour les critères d'erreur quadratique moyenne MDSE et MISE.…”