High Dimensional Regression Analysis
The focus is confidence interval construction in high-dimensional sparse linear models. Motivated by applications, the interest is not just on the high-dimensional regression vector, but also on a variety of functionals of the regression vectors, including (1) linear functionals and quadratic functionals of the regression vector; (2) the inner product of two regression vectors; and (3) the estimation accuracy of a given estimator.The following papers tackle the inference problems from two perspectives, (i) how to construct confidence intervals; (ii) what is the necessary sample size to construct adaptive confidence intervals achieving optimal length. From both perspectives, the inference problems in high dimensions exibit significant differeces from those in low dimensions due to the non-convexity structure of sparse linear regression.
- ^{*} Cai, T. T. and Guo, Z. (2017).
Confidence Intervals for High-Dimensional Linear Regression: Minimax Rates and Adaptivity.
The Annals of Statistics, 45(2), 615-646. - ^{*} Cai, T. T. and Guo, Z. (2017).
Accuracy Assessment for High-dimensional Linear Regression.
The Annals of Statistics, to appear.
- Guo, Z., Wang, W., Cai, T. T. and Li, H. (2017).
Optimal Estimation of Genetic Relatedness in High-dimensional Linear Models.
Journal of the American Statistical Association, to appear.
IMS Travel Award, JSM 2017 - ^{*} Cai, T. T. and Guo, Z. (2018).
Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications.
Submitted.
* indicates alphabetical ordering authorship.
High Dimensional Causal Inference / Econometrics
Instrumental variable is an important topic in many fileds. However, the traditional low-dimensional instrumental variable analysis suffers from curse of dimensionality and requires strong assumptions on instrumental variables. The following papers study how to construct confidence intervals for treatment effects and test endogeneity in the presence of invalid instrumental variables and high-dimensional covariates/instrumantal variables. One essenstial novel technique, Two Stage Hard Thresholding, is developed to select valid instruments among a set of candidate instrumenal variables.- Guo, Z., Kang, H., Cai, T. T. and Small, D. S. (2018).
Testing Endogeneity with High Dimensional Covariates.
The Journal of Econometrics, to appear.
- Guo, Z., Kang, H., Cai, T. T. and Small, D. S. (2017).
Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting.
Journal of the Royal Statistical Society: Series B, to appear.
Causal Inference / Econometrics
One key concern of inference for treatment effects and mediation effects is endogeneity, where the treatment or mediator is correlated with unmeasured confounders. To address the endogeneity problem, instrumental variable approach is broadly applied to estimate treatments and mediation effects consistently. The following papers tackle the inference problem for treatment or mediation effects in the non-linear model, including non-linear additive model, logistic model, possion model and zero-inflated count model. The proposed methods have been demonstrated in economics and health studies.- Guo, Z., Small, D. S., Gansky, S. A. and Cheng, J. (2016).
Mediation Analysis for Count and Zero-Inflated Count Data without Sequential Ignorability.
Journal of the Royal Statistical Society: Series C, to appear. - Cheng J., Cheng, N. F., Guo, Z., Gregorich, S., Ismail, A. I. and Gansky, S. A. (2016).
Mediation Analysis for Count and Zero-Inflated Count Data.
Statistical Methods in Medical Research, to appear. - Guo, Z. and Small, D. S. (2014).
Control Function Instrumental Variable Estimation of Nonlinear Causal Effect Models.
Journal of Machine Learning Research, 17(100):1-35, 2016. - Guo, Z., Cheng, J.,Lorch, S. A. and Small, D. S. (2014).
Using an Instrumental Variable to Test for Unmeasured Confounding.
Statistics in Medicine, 33, 3528 - 3546.
Young Investigator Award, Section on Statistics in Epidemiology, JSM 2013
Collaborative Project
- Lowder, E. M., Desmarais, S. L., Guo, Z., Coffey, T. and Van Dorn, R. A. (2016).
Criminal justice outcomes and behavioral health utilization following receipt of SSI/SSDI benefits.
Submitted.
Fractal Analysis
- Guo, Z., Kogan, R., Qiu, H., and Strichartz, R. S.(2014).
Boundary value problems for a family of domains in the Sierpinski gasket.
Illinois Journal of Mathematics, 58, 497 - 519.