Nonparametric regression estimation for functional data with correlated errors

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Nonparametric estimation of the average growth curve with general nonstationary error process

International audienceThe nonparametric estimation of the growth curve has been extensively studied in both stationary and some nonstationary particular situations. In this work, we consider the statistical problem of estimating the average growth curve for a fixed design model with nonstationary error process. The nonstationarity considered here is of a general form, and this article may be considered as an extension of previous results. The optimal bandwidth is shown to depend on the singularity of the autocovariance function of the error process along the diagonal. A Monte Carlo study is conducted in order to assess the influence of the number of subjects and the number of observations per subject on the estimation

Plans d'expérience pour l'estimation de la courbe de concentration et de l'AUC

International audienceLe problème dʼintérêt est dʼestimer la fonction de concentration et lʼaire sous la courbe (AUC) à travers lʼestimation des paramètres dʼun modèle de régression linéaire avec un processus dʼerreur autocorrélé. On introduit un estimateur linéaire sans biais simple et non paramétrique de la courbe de concentration et de lʼAUC. On montre que cet estimateur construit à partir dʼun plan dʼéchantillonnage régulier approprié est asymptotiquement optimal

Minimax results for estimating integrals of analytic processes

The problem of predicting integrals of stochastic processes is considered. Linear estimators have been constructed by means of samples at N discrete times for processes having a fixed Hölderian regularity s > 0 in quadratic mean. It is known that the rate of convergence of the mean squared error is of order N-(2s+1). In the class of analytic processes Hp, p ≥ 1, we show that among all estimators, the linear ones are optimal. Moreover, using optimal coefficient estimators derived through the inversion of the covariance matrix, the corresponding maximal error has lower and upper bounds with exponential rates. Optimal simple nonparametric estimators with optimal sampling designs are constructed in H² and H∞ and have also bounds with exponential rates

Optimal sampling designs for nonparametric estimation of spatial averages of random fields

International audienceOptimal designs of sampling spatial locations in estimating spatial averages of randomfields are considered. The random field is assumed to have correlated values according to acovariance function. The quality of estimation is measured by the mean squared error. Simplenonparametric linear estimators along with sampling designs having a limiting densityare considered. For a large class of locally isotropic random fields, we argue for the asymptoticoptimality of simple linear estimators. The convergent rates of the mean squared errorand optimal limiting densities of sampling designs are determined in every dimension. Anexample of simulation is given