Robust Inference for Partially Observed Functional Response Data

Irregular functional data, in which densely sampled curves are observed over different ranges, pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in quantitative ultrasound signal analysis, this study investigates a class of robust M-estimators for partially observed functional data, including functional location and quantile esti-mators. The consistency of the estimators is established under general conditions on the partial observation process. Under smoothness conditions on the class of M -estimators, asymptotic Gaussian process approximations are established and used for large-sample inference. The large-sample approximations justify using a boot-strap approximation for robust inferences about the functional response process. The performance of the proposed estimators is demonstrated by means of simu-lations and an analysis of irregular functional data from quantitative ultrasound analysis.