复杂结构数据分析，包括函数型数据、高维数据、流形与非欧结构数据等；

机器学习的统计学方法与理论，以及与微分方程（ODE/PDE）相关的的统计学习与推断；

函数型数据、高维数据以及微分动力系统在生物医学研究、人类基因组学、神经影像学、金融和经济学、工程学等领域的应用。

PACE：涵盖本课题组与合作者在函数型数据与纵向数据分析领域提出的多种模型与方法的各类常用算法： fdapace on CRAN (R package) 和 PACE in Matlab。

Yang, Y., Yao, F.*, and Zhao, P. (2023)  Online smooth backfitting for generalized additive models. (supplementary material). Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2023.2182213.

Xu, L., Yao, F., Yao, Q., and Zhang, H. (2023).  Non-asymptotic guarantees for robust statistical learning under infinite variance assumption. Journal of Machine Learning Research, 24(92), 1−46, https://jmlr.org/papers/volume24/22-0034/22-0034.pdf.

Xue, K.#, Yang, J.#, and Yao, F.* (2023)  Optimal linear discrinimant analysis for high-dimensional functional data (supplementary material). Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2022.2164288.

Hu, X., and Yao, F.* (2022)  Dynamic principal component analysis in high dimensions (supplementary material). Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2022.2115917.

Zhou, H., Yao, F.*, and Zhang, H. (2022)  Functional linear regression for discretely observed data: from ideal to reality (supplementary material). Biometrika, published online, https://doi.org/10.1093/biomet/asac053.

Zhou, Y., Koustaal, M., Yu, D., Kong D., and Yao, F.* (2022)  Nonparametric principal subspace regression. Journal of Machine Learning Research, 23(237), 1-28, https://jmlr.org/papers/volume23/20-963/20-963.pdf.

Shao, L.#, Lin Z.#, and Yao, F.* (2022)  Intrinsic Riemannian functional data analysis for sparse longitudinal observations (supplementary material). The Annals of Statistics, 50(3), 1696-1721, https://doi.org/10.1214/22-AOS2172.

Yang, Y., and Yao, F.* (2022)  Online estimation for functional data (supplementary material). Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2021.2002158.

Chen, H., Ren, H., Yao, F.*, and Zou, C. (2021)  Data-driven selection of the number of change-points via error rate control (supplementary material). Journal of the American StatisticalAssociation, published online, https://doi.org/10.1080/01621459.2021.1999820.

Lin, Z., and Yao, F.* (2021). Functional regression on manifold with contamination (supplementary material). Biometrika, 108(2), 167-181.

Xue, K., and Yao, F.* (2020). Distribution and correlation free two-sample test of high-dimensional means. The Annals of Statistics, 48, 1304-1328.

Lin, Z., and Yao, F.* (2019).  Intrinsic Riemannian functional data analysis.The Annals of Statistics, 47, 3533-3577.

Koudstaal, M., and Yao, F.* (2018). From mutiple Gaussian Sequences to functional data and beyond: a Stein estimation approach (supplementarymaterial). Journal of the Royal Statistical Society,Series B, 80, 319-342.

Lin, Z., Müller, H. G., and Yao, F.*(2018). Mixture inner product spaces and their application to functional data analysis.The Annals of Statistics, 45, 370-400.

Dai, X., Müller, H. G., and Yao, F.* (2017). Optimal Bayes classifiers for functional data and density ratios (supplementary material).Biometrika, 104, 545-560 .

Kong D.#, Xue, K.#, Yao, F.*, and Zhang, H. H. (2016). Partially functional linear regression in high dimensions (supplementary material). Biometrika, 103, 147-159.

Yao, F.*, Wu, Y., and Zou, J. (2016). Probability enhanced effective dimension reduction for classifying sparse functional data (Rejoinderto comments). Test, 25, 1-22, 52-58.

Yao, F.*, Lei, E., and Wu, Y. (2015). Effective dimension reduction for sparse functional data. Biometrika, 102, 421-437.

Zhu, H., Yao, F.*, and Zhang, H. H. (2014). Structured functional additive regression in reproducing kernel Hilbert spaces. Journal of the Royal Statistical Society, Series B, 76, 581-603.

Müller, H. G., Wu, Y., and Yao, F.* (2013). Continuously additive models for nonlinear functional regression. Biometrika, 100, 607-622.

Acar, E., Craiu, R. V., and Yao, F.* (2011). Dependence calibration in conditional copulas: a nonparametric approach (web appendix). Biometrics,67, 445-453.

Yao, F.*, Fu, Y., and Lee, T. C. M. (2011). Functional mixture regression (web appendix). Biostatistics, 12, 341-353.

Müller, H. G., and Yao, F. (2010). Additive modeling of functional gradients.Biometrika, 97, 791-805.

Müller, H. G., and Yao, F. (2010). Empirical dynamics for longitudinal data. The Annals of Statistics, 38, 3458-3486.

Yao, F., and Müller, H. G. (2010). Functional quadratic regression. Biometrika, 97, 49-64.

Lai, R. C. S., Lee, T. C. M., Wong,R. K. W., and  Yao, F. (2010). Nonparametric ceptrum estimation via optimalrisk smoothing. IEEE Transactions on Signal Processing, 58, 1507-1514.

Hall, P., Müller, H. G., and Yao, F. (2009). Estimation of functional derivatives.The Annals of Statistics,37, 3307-3329.

Müller, H. G., and Yao, F. (2008). Functional additive models. Journal of American Statistical Association, 103, 1534-1544.

Hall, P., Müller, H. G., and Yao, F. (2008). Modeling sparse generalized longitudinal observations with latent Gaussian processes. Journal of the Royal Statistical Society, Series B, 70, 703-723.

Yao, F., and Lee, T. C. M. (2007). Spectral density estimation using sharpened periodograms. IEEE Transactions on Signal Processing,55, 4711-4716.

Yao, F. (2007). Functional principal component analysis for longitudinal and survival data. Statistica Sinica, 17, 965-983.

Yao. F. (2007). Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data. Journal of Multivariate Analysis, 98, 40-56.

Müller, H. G., Stadtmüller, U., and Yao, F. (2006). Functional variance processes.Journal of American Statistical Association,101, 1007-1018.

Yao, F.*, and Lee, T. C. M. (2006). Penalized spline models for functional principal component analysis. Journal of the Royal Statistical Society, Series B, 68, 3-25.

Yao, F., Müller, H. G., and Wang, J. L. (2005). Functional linear regression analysis for longitudinal data. The Annals of Statistics, 33,2873-2903.

Yao, F., Müller, H. G., and Wang, J. L. (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100, 577-590.

Yao, F., Müller, H. G., Clifford, A. J., Dueker, S. R., Follett, J., Lin, Y., Buchholz, B. A., and Vogel, J. S.(2003). Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics, 59, 676-685.