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Activity Number: 132 - Functional Data and Time Series
Type: Contributed
Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #304611
Title: Robust M-Estimation for Partially Observed Functional Data
Author(s): Yeonjoo Park* and Xiaohui Chen and Douglas Simpson
Companies: University of Texas at San Antonio and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
Keywords: Bootstrap; Functional central limit theorem; Irregular functional data; M-estimates of location; Robustness; Trend inference

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. To derive asymptotic properties under 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 in application to data from quantitative ultrasound analysis.

Authors who are presenting talks have a * after their name.

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