Name: Hu Qirui
Title: Assistant Professor
Research direction: Functional data, nonparametric statistics, time series, change point analysis, differential privacy
Professor courses: Statistics, Machine Learning, Statistical Theory and Methods
E - mail：huqirui@mail.shufe.edu.cn
Research Field
My current research field is statistical inference theory for complex data types, with a focus on data-driven cross applications. Specifically, it is generally a fusion of one or more of the following directions:
Perform corresponding statistical inference on the basic components of functional data (such as mean, covariance, functional principal components, etc.) and models constructed based on functional data (under the $L ^ 2 $or $L ^ \ infty $metric). At present, the focus is on combining non parametric methods with Gaussian strong approximation techniques to establish a consistent inference theory from sparse to dense sampling scenarios, such as constructing simultaneous confidence bands, testing stationarity, testing separability, etc.
Prediction, change point analysis, and imprecise testing of time series and spatial series. The current focus is on the issue of change point testing and detection for functional time series (stationary/non-stationary), such as testing for abrupt, gradual, irregular jumps, and sequential change point testing.
Non parametric problems on complex regions: Functional data and non parametric regression on special regions (2D/3D irregular domains, spheres, etc.); Application of 2D images and 3D point cloud data; And statistical inference on general manifolds. At present, we hope to develop more statistical theoretical properties in areas such as binary, ternary, and spherical splines.
The inference problem of nonlinear statistics under the central/local differential privacy framework, such as constructing confidence intervals or simultaneous confidence sequences. The current goal is to design suitable differential privacy mechanisms for common nonlinear statistics in highly heterogeneous scenarios such as distributed, federated learning, decentralized learning, etc., and provide feasible inference programs.
In addition, many knowledgeable and friendly peers have introduced me to other rich and interesting subfields of statistics; I am still in the early stages of these directions. If you are interested in my research, think it can be used for your work, or are willing to provide interesting questions for me to learn and participate in collaboration, please feel free to contact me via email. I welcome any form of collaboration (theoretical, applied).
If you wish to study or conduct research with me under my guidance, we hope that you are proficient in theories such as probability theory and stochastic processes (the more mathematical knowledge you have, the better); The application direction hopes that you are proficient in at least one programming language (R or C++), and preferably have experience in data collection and data cleaning.
Educational Background
2016.9-2020.6 Beijing Normal University, School of Statistics, Bachelor of Statistics
2020.9-2025.6Tsinghua University, Department of Statistics and Data Science, Ph.D. in Statistics
Work Experience
From July 2022 to present, Assistant Professor, Department of Mathematical Statistics, School of Statistics and Data Science, Shanghai University of Finance and Economics
Research Achievement
⋆indicates corresponding author, (α,β) indicates contributed equally
Publication (Updated on 2025.9.1):
Peer-reviewed journal:
[1] Hu, Q. and Yang, L. (2025+). Statistical inference for functional data over multi-dimensional domain. Statistica Sinica, DOI: 10.5705/ss.202024.0344.
[2] Cai, L. and Hu, Q.⋆(2025+). Simultaneous inference for the distribution of FPC scores of functional data. Statistica Sinica, DOI: 10.5705/ss.202023.0246.
[3] Hu, Q. (2025). Testing relevant hypotheses in functional variance function via self-normalization. Scandinavian Journal of Statistics, 52(3), 1301–1329.
[4] Hu, Q. and Li, J. (2025). Simultaneous inference for covariance function of next-generation functional data. Electronic Journal of Statistics, 19 (2) 3188 - 3232.
[5] Cai, L. and Hu, Q.⋆(2025). From sparse to dense functional data: phase transitions from a simultaneous inference perspective. Statistics and Computing, 35, 146.
[6] Cai, L. and Hu, Q.⋆(2025). Global inference and test of eigen-systems of image data over complicated domain. Journal of Computational and Graphical Statistics, 34(2), 729–745.
[7] Hu, Q. (2024). Change point test and detection of functional variance function with stationary error. Journal of Multivariate Analysis, 202, 105311. IMS Hannan Graduate Student Travel Award 2024.
[8] Cai, L. and Hu, Q.⋆(2024). Simultaneous inference and uniform test for eigen[1]systems of functional data. Computational Statistics and Data Analysis,192, 107900.
[9] Hu, Q. and Li, J. (2024). Statistical inference for mean function of longitudinal imaging data over complicated domains. Statistica Sinica, 34, 955-982.
[10] Tian, Z., Wu, P., Yang, Z., Cai, D., and Hu, Q.⋆(2023). Robust nonparametric estimation of average treatment effects: a propensity score-based varying coefficient approach. Stat 12, e637.
[11] Li, J.,Hu, Q.⋆ and Zhang, F.(2022). Multi-step-ahead prediction interval for locally stationary time series with application to air pollutants concentration data. Stat, 11, e411. ISI Jan Tinbergen Awards 2021.
[12] Xu, N., Wu, P., Ma, G., Hu, Q., Hu, X., Wu, R., Wang, Y. Xu, H., Chen, L. and Zhang, P. (2022). In-flight spectral response function retrieval of a multi-spectral radiometer based on the functional data analysis technique. IEEE Transactions on Geoscience and Remote Sensing, 60, 1-10.
[13] Wu, P., Hu, Q., Tong, X. and Wu, M.(2020). Learning causal effect using machine learning with application to china’s typhoon. Acta Mathematicae Applicatae Sinica, English Series, 36, 702-713.
Peer-reviewed conference:
1] Liu,Y., Hu, Q., Ding, L and Kong, L (2023). Online local differential private quantile inference via self-normalization. Proceedings of the 40th International Conference on Machine Learning (ICML 2023).
[2] Liu, Y.(α,β), Hu, Q.(α,β) and Kong, L. (2024). Tuning-free estimation and inference of cumulative distribution function under local differential privacy. Proceedings of the 41th International Conference on Machine Learning (ICML 2024).
[3] Ding, L., Hu, Y., Denier, N., Shi, E., Zhang, J., Hu, Q., Hughes, D., Kong, L. and Jiang, B. (2024). Probing social bias in labor market text generation by chatgpt: a masked language model approach. Advances in Neural Information Processing Systems (NeurIPS 2024).
Manuscripts under review or revision:
[1] Cai, L. and Hu, Q.⋆(2025+). Simultaneous inference for long-run covariance function of functional time series. Computational Statistics and Data Analysis. Revision Invited.
[2] Sun, S., Cai, L. and Hu, Q.⋆(2025+). Statistical inference for mean function of partially observed functional time series. Biometrics. Revision Invited.
[3] Bai, L.(α,β), Hu, Q.(α,β) and Wu, W. (2025+). Inference for structural changes in nonstationary functional time series with partial measurement error. Submitted.
[4] Cai, L. and Hu, Q.⋆(2025+). From sparse to dense functional time series: phase transitions of detecting structural breaks and beyond. Submitted. arxiv.org/abs/2412.20858
[5] Cai, L. and Hu, Q.⋆(2025+). Unified theory of testing relevant hypothesis in functional time series. Submitted. arxiv.org/abs/2508.18624
[6] Cai, L., Hu, Q.⋆, Sun, J. and Wu, S. (2025+). Time-uniform and asymptotic confidence sequence of quantile under local differential privacy. Submitted.
[7] Cai, L., Hu, Q.⋆ and Wu, S. (2025+). Privacy-aware data integration for enhanced quantile inference. Submitted.
[8] Cai, L., Hu, Q.⋆ and Wu, S. (2025+). Federated learning of quantile inference under local differential privacy. Submitted.
[9] Cai, L, Sun, S. and Hu, Q.⋆(2025+). Simultaneous inference for partially observed functional data. Submitted.
[10] Hu, Q. and Liu, Y. (2025+). Censoring with plausible deniability: asymmetric local privacy for multi-category CDF estimation. Submitted.
[11] Liu, Y.(α,β), Hu, Q.(α,β) and Kong, L. (2025+). Advancing quantile estimation under local differential privacy: non-asymptotic bounds and algorithmic
performance. Submitted.
[12] Xu, M., Cai, L. and Hu, Q.⋆(2025+). Uniform inference for principal components of functional time series with applications to financial data. Submitted.
Pantent:
[1] Simultaneous confidence surface acquisition and systems for spatial regions, Li,J., Hu, Q. and Yang, L. (2024,Set,17). CN113934980B.
Rewards
IMS Hannan Graduate Student Travel Award, April, 2024.
ISI Jan Tinbergen Awards, Division A - First Prize, May 2021
Social work
Anonymous reviewers, including Annals of statistics(2), Statistica Sinica(3) ，Stochastic Environmental Research and Risk Assessment(1)，Stat(1) Waiting for journals, conferences such as ICML (2025), NeurIPS (2024, 2025), ICLR (2025), AISTATS (2025, 2026), etc.
