Complex-structured data analysis, including functional, high-dimensional, manifold and non-Euclidean data objects;

Incorporating machine learning methods and theory, ordinary/partial differential equations with statistical modeling and inference;

Applications involving functional, high-dimensional and differential dynamics in biomedical studies, human genetics, neuroimaging, finance and economics, engineering etc.

PACE is a versatile collection of various models and methods for functional/longitudinal data analysis and dynamics modeling, and is available in R (fdapace on CRAN) and Matlab (PACE in Matlab).

Tan, J.#, Zhang, G.#, Wang, X., Huang, H., and Yao, F. (2024) Green's matching: an efficient approach to parameter estimation in complex dynamic systems. (supplementary material). Journal of the Royal Statistical Society, Series B, accepted.

Chen, Z.#, Yang, Y.#, and Yao, F.* (2023) Dynamic matrix recovery. (supplementary material). Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2023.2297468.

Luo, S.#, Yang, Y.#, Shi, C.#, Yao, F., Ye, J., and Zhu, H. (2023) Policy Evaluation for Temporal and/or Spatial Dependent Experiments (supplementary material).Journal of the Royal Statistical Society, Series B, published online, https://doi.org/10.1093/jrsssb/qkad136.

Ma, T., Yao, F. and Zhou, Z. (2023) Network-level traffic flow prediction: functional time series vs. functional neural network approach. Annals of Applied Statistics, published online, https://doi.org/10.1214/23-AOAS1795.

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, Volume 110, Issue 2, Pages 381–393, 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, 118:543, 1630-1644, https://doi.org/10.1080/01621459.2021.2002158.

Liang, D., Huang, H., Guan, Y., and Yao, F.* (2022)  Test of weak separability for spatially stationary functional field (supplementary material).Journal of the American Statistical Association, published online, https://doi.org/10.1080/01621459.2021.2002156.

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 Statistical Association, 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.