Semi-Supervised Dimension Reduction

This project develops sufficient dimension reduction methods that leverage both labeled and unlabeled observations.

Main topics include:

• Principal fitted components
• Semi-supervised covariance estimation
• Sufficient predictors
• High-dimensional regularization

Deconvolution Density Estimation

This project studies nonparametric density estimation for mixed Euclidean and hyperspherical data observed with measurement error.

Main topics include:

• Euclidean measurement error
• Rotational error on hyperspheres
• Deconvolution kernels
• Asymptotic theory