Properties of Design-Based Functional Principal Components Analysis

Abstract

This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA' estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.

Revised version for J. of Statistical Planning and Inference (January 2009)

References in corpus (1)

• Common functional principal components

Cited by in corpus (10)

• Multivariate varying coefficient model for functional responses
• Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
• Using complex surveys to estimate the $L_1$-median of a functional variable: application to electricity load curves
• Calibration and partial calibration on principal components when the number of auxiliary variables is large
• Highly Irregular Functional Generalized Linear Regression with Electronic Health Records
• Model-assisted estimation through random forests in finite population sampling
• A note on the consistency of the Narain-Horvitz-Thompson estimator
• Determinantal Sampling Designs
• Rotation Sampling for Functional Data
• Preserving the distribution function in surveys in case of imputation for zero inflated data