论文标题
部分观察到的功能响应数据的强大推断
Robust Inference for Partially Observed Functional Response Data
论文作者
论文摘要
在不同的范围内观察到密集采样曲线的不规则功能数据对建模和推理构成了挑战，并且对超出曲线的敏感性是应用的关注点。由定量超声信号分析中的应用激励，本文研究了一类强大的M估计器，以部分观察到的功能数据，包括功能位置和分位数估计器。估计量的一致性是在部分观察过程的一般条件下建立的。在M估计剂类别的平滑条件下，建立了渐近高斯过程近似值并用于大型样品推断。大型样本近似值证明了自举近似是关于功能响应过程的鲁棒性推断。在模拟和从定量超声分析中对不规则功能数据的分析中证明了该性能。
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.
