Tony Cai

Education

PhD, Cornell University, 1996

Career and Recent Professional Awards

The 2008 COPSS Presidents' Award, Committee of Presidents of Statistical Societies
Medallion Lecturer, Institute of Mathematical Statistics, 2009
Fellow of the Institute of Mathematical Statistics (IMS).

Academic Positions Held

Wharton: 2000present (named Dorothy Silberberg Professor, 2007).
Previous appointment: Purdue University

For more information, go to My Personal Page

Tony Cai and Zijian Guo (2016), Confidence Intervals for HighDimensional Linear Regression: Minimax Rates and Adaptivity , The Annals of Statistics, to appear.

Tony Cai and Xin Lu Tan (2016), Optimal Estimation of a Quadratic Functional and Detection of Simultaneous Signals, Statistica Sinica, to appear.

Tony Cai, Yonina C. Eldar, Xiaodong Li (2016), Global Testing against Sparse Alternatives in TimeFrequency Analysis, The Annals of Statistics, to appear.

Tony Cai and Anru Zhang (2016), Inference for Highdimensional Differential Correlation Matrices, Journal of Multivariate Analysis, 143, pp. 107126.

Tony Cai and WenXin Zhou (2016), Matrix Completion via MaxNorm Constrained Optimization, Electronic Journal of Statistics, 10, pp. 14931525. 10.1214/16EJS1147

Tony Cai and Anru Zhang (2016), Minimax RateOptimal Estimation of HighDimensional Covariance Matrices with Incomplete Data, Journal of Multivariate Analysis, to appear.

Zijian Guo, Hyunseung Kang, Tony Cai, Dylan Small (Draft), Testing endogeneity with possibly invalid instruments and high dimensional covariates.

Tony Cai, Tengyuan Liang, Alexander Rakhlin (2016), Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix , The Annals of Statistics, (to appear).

Hyunseung Kang, Anru Zhang, Tony Cai, Dylan Small (2016), Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization, Journal of the American Statistical Association, 111, pp. 132144.

Zijian Guo, Wanjie Wang, Tony Cai, Hongzhe Li (Under Review), Optimal estimation of coheritability in highdimensional linear models.

Past Courses

STAT111 INTRODUCTORY STATISTICS

Introduction to concepts in probability. Basic statistical inference procedures of estimation, confidence intervals and hypothesis testing directed towards applications in science and medicine. The use of the JMP statistical package.

STAT430 PROBABILITY

Discrete and continuous sample spaces and probability; random variables, distributions, independence; expectation and generating functions; Markov chains and recurrence theory.

STAT431 STATISTICAL INFERENCE

Graphical displays; one and twosample confidence intervals; one and twosample hypothesis tests; one and twoway ANOVA; simple and multiple linear leastsquares regression; nonlinear regression; variable selection; logistic regression; categorical data analysis; goodnessoffit tests. A methodology course. This course does not have business applications but has significant overlap with STAT 101 and 102.

STAT510 PROBABILITY

Elements of matrix algebra. Discrete and continuous random variables and their distributions. Moments and moment generating functions. Joint distributions. Functions and transformations of random variables. Law of large numbers and the central limit theorem. Point estimation: sufficiency, maximum likelihood, minimum variance. Confidence intervals.

STAT915 NONPARAMETRIC INFERENCE

Statistical inference when the functional form of the distribution is not specified. Nonparametric function estimation, density estimation, survival analysis, contingency tables, association, and efficiency.

STAT972 ADV TOPICS IN MATH STAT

A continuation of STAT 970.

STAT991 SEM IN ADV APPL OF STAT

This seminar will be taken by doctoral candidates after the completion of most of their coursework. Topics vary from year to year and are chosen from advance probability, statistical inference, robust methods, and decision theory with principal emphasis on applications.

Medallion Lecturer, Institute of Mathematical Statistics, 2009 The COPSS Presidents’ Award, Committee of Presidents of Statistical Societies, 2008 Fellow, Institute of Mathematical Statistics, 2006