Search Results - "Tony Cai, T."

OPTIMAL RATES OF CONVERGENCE FOR NOISY SPARSE PHASE RETRIEVAL VIA THRESHOLDED WIRTINGER FLOW by Cai, T. Tony, Li, Xiaodong, Ma, Zongming

“…This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal x ϵ ℝp from noisy quadratic measurements yj = (a′jx)² + εj, j = 1 , …”
Get full text

Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models by Ma, Rong, Tony Cai, T., Li, Hongzhe

“…High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this article, global testing and large-scale multiple testing…”
Get full text

SPARSE PCA: OPTIMAL RATES AND ADAPTIVE ESTIMATION by Cai, T. Tony, Ma, Zongming, Wu, Yihong

“…Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax…”
Get full text

Transfer learning for high‐dimensional linear regression: Prediction, estimation and minimax optimality by Li, Sai, Cai, T. Tony, Li, Hongzhe

“…This paper considers estimation and prediction of a high‐dimensional linear regression in the setting of transfer learning where, in addition to observations…”
Get full text

Two‐sample test of high dimensional means under dependence by Tony Cai, T, Liu, Weidong, Xia, Yin

“…The paper considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. We…”
Get full text

Minimax and Adaptive Prediction for Functional Linear Regression by Cai, T. Tony, Yuan, Ming

“…This article considers minimax and adaptive prediction with functional predictors in the framework of functional linear model and reproducing kernel Hilbert…”
Get full text

The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy by Cai, T. Tony, Wang, Yichen, Zhang, Linjun

“…Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the…”
Get full text

Semisupervised inference for explained variance in high dimensional linear regression and its applications by Tony Cai, T., Guo, Zijian

“…Summary The paper considers statistical inference for the explained variance βTΣβ under the high dimensional linear model Y=Xβ+ε in the semisupervised setting,…”
Get full text

LIMITING LAWS FOR DIVERGENT SPIKED EIGENVALUES AND LARGEST NONSPIKED EIGENVALUE OF SAMPLE COVARIANCE MATRICES by Cai, T. Tony, Han, Xiao, Pan, Guangming

“…We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance…”
Get full text

LIMITING LAWS OF COHERENCE OF RANDOM MATRICES WITH APPLICATIONS TO TESTING COVARIANCE STRUCTURE AND CONSTRUCTION OF COMPRESSED SENSING MATRICES by Cai, T. Tony, Jiang, Tiefeng

“…Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important…”
Get full text

High dimensional linear discriminant analysis: optimality, adaptive algorithm and missing data by Cai, T. Tony, Zhang, Linjun

“…The paper develops optimality theory for linear discriminant analysis in the high dimensional setting. A data-driven and tuning-free classification rule, which…”
Get full text

Confidence intervals for causal effects with invalid instruments by using two-stage hard thresholding with voting by Guo, Zijian, Kang, Hyunseung, Cai, T. Tony, Small, Dylan S.

“…A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable…”
Get full text

Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer by Li, Sai, Zhang, Linjun, Cai, T. Tony, Li, Hongzhe

“…Transfer learning provides a powerful tool for incorporating data from related studies into a target study of interest. In epidemiology and medical studies,…”
Get full text

Prediction in Functional Linear Regression by Cai, T. Tony, Hall, Peter

“…There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case…”
Get full text

Optimal Permutation Recovery in Permuted Monotone Matrix Model by Ma, Rong, Tony Cai, T., Li, Hongzhe

“…Motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies, we consider a permuted monotone matrix model , where the rows…”
Get full text

ESTIMATING SPARSE PRECISION MATRIX: OPTIMAL RATES OF CONVERGENCE AND ADAPTIVE ESTIMATION by Cai, T. Tony, Liu, Weidong, Zhou, Harrison H.

“…Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of…”
Get full text

Optimal statistical inference for individualized treatment effects in high‐dimensional models by Cai, Tianxi, Tony Cai, T., Guo, Zijian

“…The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a…”
Get full text

Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms by Tony Cai, T., Ma, Rong

“…Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone…”
Get full text

OPTIMAL RATES OF CONVERGENCE FOR SPARSE COVARIANCE MATRIX ESTIMATION by Cai, T. Tony, Zhou, Harrison H.

“…This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman…”
Get full text

Heteroskedastic PCA: Algorithm, optimality, and applications by Zhang, Anru R., Cai, T. Tony, Wu, Yihong

“…A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA,…”
Get full text