Discussion of Paper "Estimating the mean and covariance structure nonparametrically when the data are curves" by John A. Rice and B. W. Silverman (1991)


Jia-Tong Jiang
2010-05-07  12:30 - 14:30
Room 405, Mathematics Research Center Building (ori. New Math. Bldg.)

This paper developed methods for the analysis of a collection of curves which are stochastically modelled as independent realizations of a random function with an unknown mean and covariance structure. They propose the use of penalized roughness approach to estimate the mean function non-parametrically under the assumption that it is smooth and suggested a form of cross-validation for choosing the smoothing parameter. In the estimation of the covariance structure, they are primarily concerned with models in which the first few eigenfunctions are smooth and the eigenvalues decay rapidly, they proposed smooth nonparametric estimates of the eigenfunctions and a suitable method of cross-validation to determine the amount of smoothing.