Mean estimation with data missing at random for functional covariables

FERRATY, F.; SUED, M.; VIEU, P.

STATISTICS

TAYLOR & FRANCIS LTD

Lugar: Londres; Año: 2011

0233-1888

In a missing-data setting, we want to estimate the mean of a scalar outcome, based on a sample in which anexplanatory variable is observed for every subject while responses are missing by happenstance for some ofthem.We consider two kinds of estimates of the mean response when the explanatory variable is functional.One is based on the average of the predicted values and the second one is a functional adaptation of theHorvitz–Thompson estimator.We show that the infinite dimensionality of the problem does not affect therates of convergence by stating that the estimates are root-n consistent, under missing at random (MAR)assumption. These asymptotic features are completed by simulated experiments illustrating the easinessof implementation and the good behaviour on finite sample sizes of the method. This is the first paperemphasizing that the insensitiveness of averaged estimates, well known in multivariate non-parametricstatistics, remains true for an infinite-dimensional covariable. In this sense, this work opens the way forvarious other results of this kind in functional data analysis.