Yi-Cheng Li

MINIMAX AND ADAPTIVE COVARIANCE FUNCTION ESTIMATION IN FUNCTIONAL DATA ANALYSIS

Exact Asymptotic Efficiency under zCDP: Diameter-Constrained Information Geometry

Protecting individual privacy has become a central and urgent concern in modern data analysis, given the vast quantities of data now generated and processed. In this paper, we develop a systematic theory of exact asymptotic efficiency for regular parametric estimation under central zero-concentrated differential privac...

Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy

A novel differentially private van Trees inequality is developed that connects Fisher information with the $\rho$-zCDP constraint and may be useful for other private estimation problems and construct carefully designed prior distributions to obtain matching minimax lower bounds.

The Cost of Discretization in Functional Linear Regression: Minimax Rates and Adaptation

We study scalar-on-function linear regression when each covariate curve is observed only through finitely many noisy point evaluations. Our goal is to characterize the minimax estimation and prediction risks as joint functions of the number of trajectories $n$ and the within-trajectory resolution $m$. Working in a fixe...