Journal
ANNALS OF STATISTICS
Volume 44, Issue 5, Pages 2281-2321Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/16-AOS1446
Keywords
Local linear smoothing; asymptotic normality; L-2 convergence; uniform convergence; weighing schemes
Categories
Funding
- NSF [DMS-09-06813]
- Direct For Mathematical & Physical Scien [1228369] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1228369] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1512975] Funding Source: National Science Foundation
Ask authors/readers for more resources
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. Three types of asymptotic properties are investigated in this paper: asymptotic normality, L-2 convergence and uniform convergence. The asymptotic theories are unified on two aspects: (1) the weighing scheme is very general; (2) the magnitude of the number N-i of measurements for the ith subject relative to the sample size n can vary freely. Based on the relative order of Ni to n, functional data are partitioned into three types: non-dense, dense and ultra dense functional data for the OBS and SUBJ schemes. 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available