Department of Statistics
University of Delaware
A Systematic Study on Weighing Schemes for Functional Data
Nonparametric estimation of mean and covariance functions is fundamental in functional data analysis and plenty of methods have been developed and intensively studied. Although not always emphasized, each method usually adopts a pre-specified weighing scheme in the estimation procedure, i.e., a strategy of allocating weights to observations. In this talk, we systematically explore the effect of weighing schemes on the local linear smoothers for both mean and covariance functions. For each estimator, we first establish its unified asymptotic properties under a general weighing scheme. Then we focus on two special but commonly used schemes, the equal-weight-per-observation (OBS) scheme, and the equal-weight-per-subject (SUBJ) scheme, and provide a comprehensive comparison of their asymptotic properties and numerical performances. Finally, to improve both OBS and SUBJ estimators, we propose two new weighing schemes, one is based on the mixture of the OBS and SUBJ weights, and the other is optimal in terms of L2 convergence.
Refreshments at 3:45 pm in Snedecor 2101.