Weighing Schemes for Functional Data

• Activity Number: 485
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xiaoke Zhang* and Jane-Ling Wang
• Companies: University of Delaware and University of California at Davis
• Keywords: Local linear smoothing ; Asymptotic normality ; L2 convergence ; Uniform convergence ; Weighing schemes

Abstract

Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling plan, be it dense, sparse, or neither. These two weighing schemes are compared both theoretically and numerically. We also propose a new class of weighing schemes in terms of a mixture of the OBS and SUBJ weights, of which theoretical and numerical performances are examined and compared.