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

We study the nonparametric estimation of the mean function of a random process indexed by a compact metric space. We elaborate on the asymptotic variance and prove asymptotic normality for a general class of linear estimators. An application to simultaneous confidence intervals is proposed and investigated by simulation.

[1]  Xuming He,et al.  Conditional growth charts , 2006 .

[2]  D. M. Allen,et al.  Analysis of growth and dose response curves. , 1969, Biometrics.

[3]  C. Diack,et al.  Convergence en moyenne quadratique de l'estimateur de la régression par splines hybrides , 1998 .

[4]  M. Hutchinson,et al.  ON SPLINE SMOOTHING WITH AUTOCORRELATED ERRORS , 1989 .

[5]  Alfred O. Hero,et al.  Simultaneous confidence intervals for image reconstruction problems , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[6]  Convergence de l'estimateur spline cubique de lissage dans un modèle de régression longitudinale avec erreur de type processus , 2005 .

[7]  Adrian Bowman,et al.  On the use of nonparametric regression for model checking , 1989 .

[8]  C. Loader,et al.  Simultaneous Confidence Bands for Linear Regression and Smoothing , 1994 .

[9]  Jay H. Beder.  A Sieve Estimator for the Mean of a Gaussian Process , 1987 .

[10]  Jian Huang,et al.  Estimation of the mean function with panel count data using monotone polynomial splines , 2007 .

[11]  Wei Biao Wu,et al.  Inference of trends in time series , 2007 .

[12]  Samuel Kotz,et al.  Multivariate T-Distributions and Their Applications , 2004 .

[13]  David Degras.  Contribution à l'étude de la régression non paramétrique et à l'estimation de la moyenne d'un processus à temps continu , 2007 .

[14]  Fang Yao,et al.  Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data , 2007 .

[15]  J. Hart,et al.  Kernel Regression Estimation Using Repeated Measurements Data , 1986 .

[16]  S. Lagakos,et al.  Nonparametric estimation of the mean function of a stochastic process with missing observations , 2007, Lifetime data analysis.