arXiv subjects

Shouxia Wang

Publications and source records attributed to Shouxia Wang.

3 recordsLinked to original sources

arXiv2025

Two Sample Testing for High-dimensional Functional Data: A Multi-resolution Projection Method

It is of great interest to test the equality of the means in two samples of functional data. Past research has predominantly concentrated on low-dimensional functional data, a focus that may not hold up in high-dimensional scenarios. In this article, we propose a novel two-sample test for the mean functions of high-dimensional functional data, employing a multi-resolution projection (MRP) method. We establish the asymptotic normality of the proposed MRP test statistic and investigate its power performance when the dimension of the functional variables is high. In practice, functional data are observed only at discrete and usually asynchronous points. We further explore the influence of function reconstruction on our test statistic theoretically. Finally, we assess the finite-sample performance of our test through extensive simulation studies and demonstrate its practicality via two real data applications. Specifically, our analysis of global climate data uncovers significant differences in the functional means of climate variables in the years 2020-2069 when comparing intermediate greenhouse gas emission pathways (e.g., RCP4.5) to high greenhouse gas emission pathways (e.g., RCP8.5).

stat.ME↗

arXiv2025

High Dimensional Ensemble Kalman Filter

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution observations of physical models, some key theoretical aspects of the EnKF are open for investigation. This paper proposes several high dimensional EnKF (HD-EnKF) methods equipped with consistent estimators for the important forecast error covariance and Kalman Gain matrices. It then studies the theoretical properties of the EnKF under both fixed and high dimensional state variables, which provides one-step and multiple-step mean square errors of the analysis states to the underlying oracle states offered by the Kalman Filter and gives the much needed insight to the roles played by the forecast error covariance on the accuracy of the EnKF. The accuracy of the data assimilation under the misspecified physical model is also considered. Numerical studies on the Lorenz-96 and the Shallow Water Equation models illustrate that the proposed HD-EnKF algorithms outperform the standard EnKF and widely used inflation methods.

stat.ME↗

arXiv2025

Similarity-Informed Transfer Learning for Multivariate Functional Censored Quantile Regression

To address the challenge of utilizing patient data from other organ transplant centers (source cohorts) to improve survival time estimation and inference for a target center (target cohort) with limited samples and strict data-sharing privacy constraints, we propose the Similarity-Informed Transfer Learning (SITL) method. This approach estimates multivariate functional censored quantile regression by flexibly leveraging information from each source cohort based on its similarity to the target cohort. Furthermore, the method is adaptable to continuously updated real-time data. We establish the asymptotic properties of the estimators obtained using the SITL method, demonstrating improved convergence rates. Additionally, we develop an enhanced approach that combines the SITL method with a resampling technique to construct more accurate confidence intervals for functional coefficients, backed by theoretical guarantees. Extensive simulation studies and an application to kidney transplant data illustrate the significant advantages of the SITL method. Compared to methods that rely solely on the target cohort or indiscriminately pool data across source and target cohorts, the SITL method substantially improves both estimation and inference performance.

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