• • Bing Li and Jun Song (2017)

    Nonlinear sufficient dimension reduction for functional data

    The Annals of Statistics, 45, 1059--1095.

    We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where both the predictor and the response may be random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads to construction of two functional spaces: the first representing the functional data, assumed to be a Hilbert space, and the second characterizing nonlinearity, assumed to be a reproducing kernel Hilbert space. A particularly attractive feature of our construction is that the two spaces are nested, in the sense that the kernel for the second space is determined by the inner product of the first. We propose two estimators for this general dimension reduction problem, and establish the consistency and convergence rate for one of them. These asymptotic results are flexible enough to accommodate both fully and partially observed functional data. We investigate the performances of our estimators by simulations, and applied them to data sets about speech recognition and handwritten symbols.      
  • • Bing Li and Jun Song (2017+)

    Dimension reduction for functional data based on weak conditional moments


  • • Holly Holt, Gabriel Villar, Weiyi Cheng, Jun Song, and Christina Grozinger (2017+)

    Molecular, physiological and behavioral responses of honey bee (Apis mellifera) drones to infection with microsporidian parasites


  • Jun Song and Bing Li (2018+)

    Kernel Functional Principal Component Analysis.

  • Jun Song, Naomi S. Altman, and Kalyan Das (2018+)

    Self-modeling Nonlinear Poisson regression model.

  • Jun Song, Bing Li, and Hannu Oja (2018+)

    On functional Spearman's correlation and the related canonical correlation analysis.

  • Jun Song and Won Chang (2018+)

    Calibration of High-dimensional Spatial Data via nonlinear sufficient dimension reduction.