A non-smoothing framework for inference on functional means

Abstract

This talk introduces a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. Motivated by the right-continuity of these curves, we develop a non-smoothing approach that involves weaker conditions than existing conditions imposed when using smoothing to estimate functional means under a fixed dense design. Notably, our procedure allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. Under this non-smoothing framework, we devise an empirical likelihood method to construct confidence bands for the functional means. Our method utilizes the known optimality of empirical likelihood. It also respects range and monotonicity constraints on occupation time curves.  A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.

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