Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data
The estimation of a regression function by kernel method for longitudinal or functional data is considered. In the context of longitudinal data analysis, a random function typically represents a subject that is often observed at a small number of time points, while in the studies of functional data the random realization is usually measured on a dense grid. However, essentially the same methods can be applied to both sampling plans, as well as in a number of settings lying between them. In this paper general results are derived for the asymptotic distributions of real-valued functions with arguments which are functionals formed by weighted averages of longitudinal or functional data. Asymptotic distributions for the estimators of the mean and covariance functions obtained from noisy observations with the presence of within-subject correlation are studied. These asymptotic normality results are comparable to those standard rates obtained from independent data, which is illustrated in a simulation study. Besides, this paper discusses the conditions associated with sampling plans, which are required for the validity of local properties of kernel-based estimators for longitudinal or functional data.
Volume (Year): 98 (2007)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ramsay, James O. & Ramsey, James B., 2002. "Functional data analysis of the dynamics of the monthly index of nondurable goods production," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 327-344, March.
- Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
- Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:40-56. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.