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

Asymptotics for the nonparametric estimation of the mean function of a random process

“…. , X n ) is observed in a fixed and balanced design of size p, Cardot and Diack (1998) and Degras and Jallet (2005) have obtained the order O( 1 n ) for the variances of spline estimators as n, p → ∞. Under differentiability conditions on µ and R, Hart and Wehrly (1986) and Degras (2007) have derived exact mean-square rates for kernel and spline estimators.…”

Nonparametric estimation of a trend based upon sampled continuous processes

“…The nonparametric regression literature contains several results on the asymptotic properties of estimators of µ as the sample sizes n and p go to infinity. For instance when D = [0, 1], mean-square convergence rates of kernel and spline estimators can be found in [2,3,6,9]. When D is a compact metric space, [5] gives a universal consistency result as well as the asymptotic normality of all usual regression estimators in the sense of finite dimensional distributions and of the space L 2 (D), with an application to simultaneous confidence intervals.…”