Park Yeonjoo, Chen Xiaohui, Simpson Douglas G
University of Texas at San Antonio.
University of Illinois at Urbana-Champaign.
Stat Sin. 2022 Oct;32(4):2265-2293. doi: 10.5705/ss.202020.0358.
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 paper investigates a class of robust M-estimators for partially observed functional data including functional location and quantile estimators. 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 a bootstrap approximation for robust inferences about the functional response process. The performance is demonstrated in simulations and in the analysis of irregular functional data from quantitative ultrasound analysis.
在不同范围内观测到密集采样曲线的不规则函数数据，给建模和推断带来了挑战，并且对异常曲线的敏感性是应用中的一个关注点。受定量超声信号分析应用的启发，本文研究了一类用于部分观测函数数据的稳健M估计量，包括函数位置估计量和分位数估计量。在部分观测过程的一般条件下建立了估计量的一致性。在M估计量类的光滑条件下，建立了渐近高斯过程近似，并将其用于大样本推断。大样本近似证明了对函数响应过程进行稳健推断的自助法近似的合理性。通过模拟以及对来自定量超声分析的不规则函数数据的分析，展示了该方法的性能。
