6533b86ffe1ef96bd12cdc94

RESEARCH PRODUCT

Properties of Design-Based Functional Principal Components Analysis.

Hervé CardotMohamed ChaouchCamelia GogaCatherine Labruère

subject

Statistics and ProbabilityContext (language use)Mathematics - Statistics TheoryStatistics Theory (math.ST)Perturbation theory01 natural sciencesVariance estimationHorvitz–Thompson estimatorSurvey sampling010104 statistics & probabilityLinearization[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]0502 economics and businessStatisticsConsistent estimatorFOS: Mathematicsvon Mises expansionApplied mathematicsHorvitz-Thompson estimator[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsComputingMilieux_MISCELLANEOUS050205 econometrics MathematicsEigenfunctionsInfluence functionApplied Mathematics05 social sciencesMathematical statisticsEstimator[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Covariance operatorCovariance16. Peace & justice[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]Delta methodModel-assisted estimationStatistics Probability and Uncertainty

description

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.

yearjournalcountryeditionlanguage
2010-01-01
https://hal.archives-ouvertes.fr/hal-00558588