Robust M-estimation for Partially Observed Functional Data
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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 many applications. This paper investigates a class of robust M-estimators for partially observed functional data, modeling irregular structure using a missing data framework. We derive asymptotic normality of functional M-estimator under the proposed framework and show root-n rates of convergence. Furthermore, we propose a class of functional trend tests to find significant directions in the trend of location. For the implementation of the inferential test, we adopt a joint bootstrap approach. The performance is demonstrated in simulations and application to data from quantitative ultrasound analysis.
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