Ning Hao
 Associate Professor, Mathematics
 Associate Professor, StatisticsGIDP
 Member of the Graduate Faculty
Contact
 (520) 6212416
 Environment and Natural Res. 2, Rm. S325
 Tucson, AZ 85719
 nhao@arizona.edu
Degrees
 Ph.D. Mathematics
 Stony Brook University, Stony Brook, New York, United States
 Dbar spark theory and Deligne cohomology
 B.S. Mathematics
 Peking University, Beijing, China
Interests
Research
Highdimensional statistical learning; Changepoint detection; Bioinformatics;Geometry and topology.
Teaching
Statistics
Courses
202425 Courses

Independent Study
STAT 599 (Fall 2024)
202324 Courses

Independent Study
MATH 599 (Spring 2024) 
Research
STAT 900 (Spring 2024) 
Statistical Computing
STAT 675 (Spring 2024) 
Thesis
STAT 910 (Spring 2024) 
Intro to Statistical Computing
DATA 375 (Fall 2023) 
Topics In Applied Math
MATH 577 (Fall 2023)
202223 Courses

Theoretical Statistics II
MATH 567B (Spring 2023) 
Dissertation
MATH 920 (Fall 2022) 
Intro to Statistical Computing
DATA 375 (Fall 2022) 
Theoretical Statistics I
MATH 567A (Fall 2022) 
Theoretical Statistics I
STAT 567A (Fall 2022)
202122 Courses

Dissertation
MATH 920 (Spring 2022) 
Intro to Statistical Computing
DATA 375 (Spring 2022) 
Dissertation
MATH 920 (Fall 2021) 
Intro to Statistical Computing
DATA 375 (Fall 2021)
202021 Courses

Dissertation
MATH 920 (Spring 2021) 
Theoretical Statistics II
MATH 567B (Spring 2021) 
Theoretical Statistics II
STAT 567B (Spring 2021) 
Calculus II
MATH 129 (Fall 2020) 
Dissertation
MATH 920 (Fall 2020) 
Theoretical Statistics I
MATH 567A (Fall 2020) 
Theoretical Statistics I
STAT 567A (Fall 2020)
201920 Courses

Independent Study
MATH 599 (Spring 2020)
201819 Courses

Calculus II
MATH 129 (Spring 2019) 
Independent Study
MATH 599 (Spring 2019) 
Intro to Statistical Computing
DATA 375 (Spring 2019) 
Independent Study
MATH 599 (Fall 2018) 
Theoretical Statistics II
MATH 567B (Fall 2018) 
Theoretical Statistics II
STAT 567B (Fall 2018)
201718 Courses

Independent Study
MATH 599 (Spring 2018) 
Theoretical Statistics I
MATH 567A (Spring 2018) 
Theoretical Statistics I
STAT 567A (Spring 2018) 
Independent Study
STAT 599 (Fall 2017) 
Intro Statistical Method
MATH 363 (Fall 2017) 
Theory of Statistics
MATH 466 (Fall 2017)
201617 Courses

Calculus II
MATH 129 (Spring 2017) 
Calculus II
MATH 129 (Fall 2016)
201516 Courses

Intro:Stat+Biostatistics
MATH 263 (Spring 2016) 
Theoretical Statistics I
MATH 567A (Spring 2016) 
Theoretical Statistics I
STAT 567A (Spring 2016)
Scholarly Contributions
Journals/Publications
 Hao, N., Niu, Y., & Xiao, H. (2023). Equivariant Variance Estimation for Multiple Changepoint Model. Electronic Journal of Statistics, 17(2), 38113853. doi:10.1214/23EJS2190
 Wu, R., & Hao, N. (2022). Quadratic Discriminant Analysis by Projection. Journal of Multivariate Analysis.
 Hao, N., Niu, Y., Xiao, F., & Zhang, H. (2020). A super scalable algorithm for segment detection. Statistics in Biosciences. doi:https://doi.org/10.1007/s1256102009278z
 Shin, S. J., Wu, Y., & Hao, N. (2020). A Backward Procedure for Changepoint Detection with Application to Copy Number Variation Detection. Canadian Journal of Statistics, 48(3), 366–385. doi:https://doi.org/10.1002/cjs.11535
 Xiao, F., Luo, X., Hao, N., Niu, Y., Xiao, X., Cai, G., Amos, C. I., & Zhang, H. (2019). An Accurate and Powerful Method for Copy Number Variation Detection. Bioinformatics, 35(17), 28912898. doi:https://doi.org/10.1093/bioinformatics/bty1041
 Hao, N., Feng, Y., & Zhang, H. (2018). Model Selection for High Dimensional Quadratic Regression via Regularization. Journal of the American Statistical Association, 113(522), 615625. doi:https://doi.org/10.1080/01621459.2016.1264956
 Niu, Y., Hao, N., & Dong, B. (2018). A New ReducedRank Linear Discriminant Analysis Method and Its Applications. Statistica Sinica, 28, 189202. doi:https://doi.org/10.5705/ss.202015.0387
 Niu, Y., Hao, N., & Zhang, H. (2018). Interaction Screening by Partial Correlation. Statistics and Its Interface, 11(2), 317325. doi:http://dx.doi.org/10.4310/SII.2018.v11.n2.a9
 Hao, N., & Zhang, H. (2017). A Note on High Dimensional Regression Models with Interactions. The American Statistician, 71(4), 291297. doi:https://doi.org/10.1080/00031305.2016.1264311
 Hao, N., & Zhang, H. (2017). Oracle Pvalues and Variable Screening. Electronic Journal of Statistics, 11, 32513271. doi:doi:10.1214/17EJS1284
 Xiao, F., Niu, Y., Hao, N., Xu, Y., Jin, Z., & Zhang, H. (2017). modSaRa: a computationally efficient R package for CNV identification. Bioinformatics, 33(15), 2384–2385. doi:https://doi.org/10.1093/bioinformatics/btx212
 Niu, Y., Hao, N., & Zhang, H. (2016). Multiple ChangePoint Detection, a Selective Overview. Statistical Science, 31(4), 611623. doi:doi:10.1214/16STS587
 Dong, B., & Hao, N. (2015). Semisupervised high dimensional clustering by tight wavelet frames. SPIE Optical Engineering+ Applications.
 Hao, N., Dong, B., & Fan, J. (2015). Sparsifying the Fisher Linear Discriminant by Rotation. Journal of the Royal Statistical Society: Series B.
 Hao, N., & Zhang, H. H. (2014). Interaction Screening for UltraHigh Dimensional Data. Journal of the American Statistical Association, 109(507), 12851301.More infoIn ultrahigh dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a data set with n observations and p predictors, the augmented design matrix including all linear and order2 terms is of size n × (p (2) + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard machines and software tools for storage and analysis. In theory, the interaction selection consistency is hard to achieve in high dimensional settings. Interaction effects have heavier tails and more complex covariance structures than main effects in a random design, making theoretical analysis difficult. In this article, we propose to tackle these issues by forwardselection based procedures called iFOR, which identify interaction effects in a greedy forward fashion while maintaining the natural hierarchical model structure. Two algorithms, iFORT and iFORM, are studied. Computationally, the iFOR procedures are designed to be simple and fast to implement. No complex optimization tools are needed, since only OLStype calculations are involved; the iFOR algorithms avoid storing and manipulating the whole augmented matrix, so the memory and CPU requirement is minimal; the computational complexity is linear in p for sparse models, hence feasible for p ≫ n. Theoretically, we prove that they possess sure screening property for ultrahigh dimensional settings. Numerical examples are used to demonstrate their finite sample performance.
 Hao, N., Niu, Y. S., & Zhang, H. (2013). Multiple ChangePoint Detection via a Screening and Ranking Algorithm. Statistica Sinica, 23(4), 15531572.More infoLet Y 1, …, Yn be a sequence whose underlying mean is a step function with an unknown number of the steps and unknown change points. The detection of the change points, namely the positions where the mean changes, is an important problem in such fields as engineering, economics, climatology and bioscience. This problem has attracted a lot of attention in statistics, and a variety of solutions have been proposed and implemented. However, there is scant literature on the theoretical properties of those algorithms. Here, we investigate a recently developed algorithm called the Screening and Ranking Algorithm (SaRa). We characterize the theoretical properties of SaRa and show its superiority over other commonly used algorithms. In particular, we develop a false discovery rate approach to the multiple changepoint problem and show a strong sure coverage property for the SaRa.
 Fan, J., Guo, S., & Hao, N. (2012). Variance estimation using refitted crossvalidation in ultrahigh dimensional regression. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 74(1), 3765.More infoAbstract: Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved realized noise and some of the predictors. As a result, the realized noises are actually predicted when extra irrelevant variables are selected, leading to a serious underestimate of the level of noise. We propose a twostage refitted procedure via a data splitting technique, called refitted crossvalidation, to attenuate the influence of irrelevant variables with high spurious correlations. Our asymptotic results show that the resulting procedure performs as well as the oracle estimator, which knows in advance the mean regression function. The simulation studies lend further support to our theoretical claims. The naive twostage estimator and the plugin onestage estimators using the lasso and smoothly clipped absolute deviation are also studied and compared. Their performances can be improved by the refitted crossvalidation method proposed. © 2011 Royal Statistical Society.
Creative Productions
 Hao, N., Niu, Y., Xiao, F., & Zhang, H. (2018. R Package: SSSS. https://publichealth.yale.edu/c2s2/software/SSSS/.
 Shin, S. J., Wu, Y., & Hao, N. (2018. R Package: bwd. https://cran.rproject.org/web/packages/bwd/index.html.
 Xiao, F., Luo, X., Hao, N., Niu, Y., Xiao, X., Cai, G., Amos, C. I., & Zhang, H. (2018. R Package: modSaRa2. https://publichealth.yale.edu/c2s2/software/modSaRa2/.