永利赌场

永利赌场
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永利赌场

Songxi Chen Academician of Chinese Academy of Sciences, Professor

Research Areas:Inference for High Dimensional Data; Environmental Modeling and Assessment; Empirical Likelihood; Statistical and Machine Learning; Inference for stochastic processes.

永利赌场 Office: Room 307-A, Welding Building, Tsinghua University


永利赌场 Phone: 010-62784687


Go to Songxi Chen Personal Homepage
职称 Academician of Chinese Academy of Sciences, Professor 地址 Room 307-A, Welding Building, Tsinghua University
电话 010-62784687 邮箱
个人主页 //www.songxichen.com/
Academic History
  • Ph.D. in Statistics, 1993, Australian National University.
  • M.Sc. in Statistics and Operations Research, 1990, Victoria University of Wellington.
  • M.Sc. in Mathematical Statistics, 1988, Beijing Normal University.
  • B.Sc. in Mathematics, 1983, Beijing Normal University.
Employment
  • June 2008 - now: University Chair Professor
  • Founding Director, Center for Statistical Science (2010-2019)
  • Professor, Guanghua School of Management (since 2008)
  • Professor, School of Mathematical Sciences (since 2021)
  • Peking University.
  • July 2006 - Feb. 2017: Full Professor of Statistics, Department of Statistics, Iowa State University.
  • Nov. 2003 - July 2006: Associate Professor, Department of Statistics, Iowa State University.
  • July 2000 - Dec.2003: Associate Professor, National University of Singapore.
  • Jan. 1995 - June 2000: Senior Lecturer/Lecturer, La Trobe University.
  • Nov.1992 - Jan.1995: Statistician, CSIRO Marine Science and Biometrics Unit.
  • July 1983 - Aug. 1985: Lecturer, Beijing Institute of Economics.
Publications
  • [1] Chen, S.X., Smith, P.J., Shafi, M. and Vere-Jones, D. (1990). Some improvements to conventional importance sampling techniques for coded system using Viterbi decoding. Electronics Letters, 26, 802-806.
  • [2] Chen, S.X. (1993). On the coverage accuracy of empirical likelihood confidence regions for linear regression model. Annals of Institute of Statistical Mathematics, 45, 621-637.
  • [3] Chen, S.X. and Hall, P. (1993). Smoothed empirical likelihood confidence intervals for quantiles. Annals of Statistics, 21, 1166-1181.
  • [4] Chen, S.X. and Hall, P. (1994). On the calculation of standard error for quotation in confidence statements. Statistics and Probability Letters, 19 147-151.
  • [5]  Chen, S.X. (1994). Empirical likelihood confidence intervals for linear regression coefficients. Journal of Multivariate Analysis, 49, 24-40.
  • [6] Chen, S.X. (1994) Comparing empirical likelihood and bootstrap hypothesis tests. Journal of Multivariate Analysis, 51, 277-293.
  • [7] Chen, S.X. (1996a) A kernel estimate for density of a biological population using line transect sampling. Royal Statistical Society Ser. C: Applied Statistics 45, 135-150.
  • [8]  Chen, S.X. (1996b) Studying school size effects in line transect sampling using the kernel method. Biometrics 52, 1283-94.
  • [9] Chen, S.X. (1996c) Empirical likelihood confidence intervals for nonparametric density estimation. Biometrika, 83, 329-341.
  • [10] Chen, S.X. and Polacheck, T. (1996) Kernel estimates of mean school size for IWC minke whale data. Report of International Whaling Commission, 46, 341-348.
  • [11] Chen, S.X. (1997). Empirical likelihood based kernel density estimation. Australian Journal of Statistics, 39, 47-56
  • [12] Chen, S.X. (1998). Measurement errors in line transect surveys. Biometrics, 54, 899-908.
  • [13] Brown, B. M. and Chen, S. X. (1998) Combined Empirical Likelihood. Annals of Institute of Statistical Mathematic,50, 697-714.
  • [14] Brown, B. M. and Chen, S. X. (1999) Beta-Bernstein smoothing for regression curves with compact support. Scandinavian Journal of Statistics, 26, 47-59.
  • [15] Chen, S. X. (1999a) Estimation in independent observer line transect surveys for clustered populations. Biometrics 55, No. 3, 754-759.
  • [16] Chen, S. X. and Woolcock, J. (1999) A condition for designing bus-route type access site surveys to estimate recreational fishing effort. Biometrics, 55, No. 3, 799-804.
  • [17] Chen, S. X. (1999b) Beta kernel estimators for density functions. Computational Statistics and Data Analysis, 31, 131-145.
  • [18] Chen, S. X. (2000a) Beta kernel smoothers for regression curves. Statistica Sinica, 10, 73-91.
  • [19] Chen, S. X. (2000b) Animal abundance estimation for independent observer line transect surveys. Special Issue of Environmental and Ecological Statistics: Statistical Ecology and Forest Biometry 7, No. 3, 285-299.
  • [20] Chen, S. X. (2000c) Gamma kernel estimators for density functions. Annals of Institute of Statistical Mathematics,52, 471-480.
  • [21] Chen, S. X. and Lloyd, C. J. (2000). A non-parametric approach to the analysis of two stage mark-recapture experiments. Biometrika, 87, 633-649.
  • [22]  Chen, S. X. and Qin, Yong Song (2000). Empirical Likelihood confidence interval for a local linear smoother.  Biometrika ,87, 946-953.
  • [23] Chen, S. X. and Cowling, A. (2001). Measurement Errors in Line Transect Surveys where Detection varies with Distance and Size.Biometrics,57, 732-742.
  • [24] Chen, S. X. and Qin, Yong Song (2002). Confidence interval based on a local linear smoother. Scandinavian Journal of Statistics, 29, 89-99.
  • [25] Chen, S. X. and Lloyd, C. J. (2002). Estimation of population size based on biased samples using nonparametric binary regression.  Statistica Sinica, 12, 505-518.
  • [26] Chen, S. X.  (2002).  Local linear smoothers using asymmetric kernels. Annals of Institute of Statistical Mathematics, 54, 312-323.
  • [27] Chen, S. X, Yip, P. and Zhou, Y. (2002).  Sequential line transect surveys.  Biometrics, 58, 263-269.
  • [28] Chen, S. X., Hardle, W. and Kleinow, T. (2002). An empirical likelihood goodness-of-fit test for diffusions. Applied quantitative finance, 259--281, Springer, Berlin.
  • [29] Chen, S. X. and Hall, P. (2003).  EFFECTS OF BAGGING AND BIAS CORRECTION ON ESTIMATORS DEFINED BY ESTIMATING EQUATIONS, Statistica Sinica, 13, 97-109.
  • [30] Chen, S. X and Cui, H-J. (2003).  An extended empirical likelihood for generalized linear models. Statistica Sinica, 13, 69-81.
  • [31]  Cui, H-J and Chen, S.X. (2003).  Empirical likelihood confidence regions for parameter in the error-in-variable models, Journal of Multivariate Analysis, 84 (1), 101-115.
  • [32]  Chen, S. X. and Qin, J. (2003) Empirical likelihood based confidence intervals for data with possible zero observations. Statistics and Probability Letters, 65, 29--37.
  • [33] Chen, S. X., Haredle, W. and Li, M. (2003).  An empirical likelihood goodness-of-fit test for time series. Journal of The Royal Statistical Society, Series B, 65, 663-678.
  • [34] Chen, S. X., D. H. Y. Leung and Qin, J. (2003) Information Recovery in a Study with Surrogate Endpoints.  Journal of the American Statistical Association, 98, 1052-1062. 
  • [35] Chen, S. X. and Qin, Y-S. (2003). Coverage accuracy of confidence intervals in nonparametric regression. Acta Math. Appl. Sin. Engl. Ser. 19, 387--396.
  • [36]  Chen, S. X. and Tang, C. (2005).  Nonparametric Estimation of Value at Risk and the Standard Errors for Financial Returns.  Journal of Financial Econometrics, 3, 227-255.
  • [37]  Chen, S.X. and Cui, H. J. (2006) On Bartlett Correction of Empirical Likelihood in the Presence of Nuisance Parameters. Biometrika, 93, 215-220.
  • [38] Chen, S. X. and Qin, J. (2006) An Empirical likelihood Method in Mixture Models with Incomplete Classifications, Statistica Sinica 16, 1101-1115.
  • [39] Chen, S.X. and Cui, H. J. (2007) On the Second Order Properties of Empirical Likelihood for Generalized Estimation Equations. Journal of Econometrics, 141, 492-516.
  • [40] Chen, S.X. and J. Gao (2007) An Adaptive Empirical Likelihood Test for Time Series Models. Journal of Econometrics, 141, 950-972.
  • [41] Chen, S. X. and T. Huang (2007) Nonparametric Estimation of Copula Functions. Canadian Journal of Statistics, 35, 265-282.
  • [42] Chen, S.X.,  J. Gao and Tang, C. Y. (2008)  A test for model specification of diffusion processes, The Annals of Statistics, 36, 167-198.
  • [43] Chen, S.X (2008)  Nonparametric Estimation of Expected Shortfall,  Journal of Financial Econometrics, 6, 87-107.
  • [44] Chen, S. X., Leung, D. Y. H. and J. Qin. (2008)   Improved Semiparametric Estimation Using Surrogate Data, Journal of the Royal Statistical Society, Series B, 803-823.
  • [45] Wang, D.  and S.X. Chen (2009),   Empirical Likelihood for Estimating Equation with Missing Values, The Annals of Statistics, 37, 490-517.
  • [46]  Chen, Song Xi and Chiu Min Wong (2009) Smoothed Block Empirical Likelihood for Quantiles of Weakly Dependent Processes,  Statistica Sinica, 19, 71-82.
  • [47]  Wang, D. and Chen, S. X. (2009): Combining quantitative trait loci analyses and microarray data, an empirical likelihood approach, Computational Statistics and Data Analysis, 53, 1661-1673.
  • [48]  C. Yong Tang and Chen, S. X. (2009), Parameter estimation and bias correction of diffusion processes, Journal of Econometrics, 149, 65-81.
  • [49] Chen, S. X., L. Peng and Y-L, Qin (2009) Effects of Dimensionality on empirical likelihood, Biometrika, , 96, 711–722.
  • [50] Chen, S. X. and I. Van Keilegom (2009) Empirical Likelihood Test for a Class of Regression Models, Bernoulli, 15, 955-976.
  • [51] Chan, N-H, Chen, S.X., Peng, L. and C. L. Yu (2009), Empirical Likelihood Methods Based on Characteristic Functions with Applications to L'evy Processes.  Journal of the American Statistical Association, 104, 1621-1630.
  • [52] Chen, S. X. and I. Van Keilegom (2009) A review on empirical likelihood for regressions (with discussions), Test, 3,415-447.
  • [53] Chen, S. X. and Y-L Qin (2010) A Two Sample Test for Ultra High Dimensional Data with Applications to Gene Sets Testing.  The Annals of Statistics, 38, 808-835.
  • [54] Chen, S. X., C. Y. Tang and V. T. Mule, jr.  (2010) Local post-stratification and diagnostics in Dual System Accuracy and Coverage Evaluation for US Census, Journal of the American Statistical Association, Application and Case Study Section, 105, 105-119.
  • [55] Chen, S. X., Delaigle, A. and Hall, P. (2010) Nonparametric estimation for levy-type processes, Journal of Econometrics,157, 257-271.
  • [56] Chen, S.X., Zhang, L-X. and P-S Zhong (2010) Testing high dimensional covariance matrices, Journal of the American Statistical Association, 105, 810-819.
  • [57] Chen, S. X. and P-S Zhong (2010) ANOVA for longitudinal data with missing values. The Annals of Statistics, 38, 3630-3659.
  • [58] Alzghool, R. , Y-X Lin and S. X. Chen (2010)  Asymptotic Quasi-likelihood Based on Kernel Smoothing for Multivariate Heteroskedastic Models with Correlation, AMERICAN JOURNAL OF MATHEMATICAL AND MANAGEMENT SCIENCES,  30, 147-177.
  • [59] P-S Zhong and S. X. Chen (2011). Tests for High Dimensional Regression Coefficients with Factorial Designs. Journal of the American Statistical Association, 106, 260-274.
  • [60] Chen, S.X. and J. Gao (2011). Simultaneous Specification Test for the Mean and Variance Structures for Nonlinear Time Series Regression.  Econometric Theory, 27, 792–843.
  • [61]  Chen, S. X. and C. Y. Tang (2011). Properties of Census Dual System Population Size Estimators. International Statistical Review, 79， 336-361.
  • [62] J.-Y. Chang and S.X. Chen (2011). On the approximate maximum likelihood estimation for diffusion processes. The Annals of Statistics, 39， 2820-2851.
  • [63]  Chen, S. X. and C. Y. Tang (2011).   Nonparametric Regression with Discrete Covariates and Missing Value.  Statistics and Its Interface, 4， 463-273.
  • [64]  Li, J. and S. X. Chen (2012). Two Sample Tests for High Dimensional Covariance Matrices, The Annals of Statistics, 40, 908-940
  • [65]  Qiu, Y-M and Chen, S. X. (2012). Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation, The Annals of Statistics, 40, 1285-1314.
  • [66] Chen, S. X., Peng, L. and C. L. Yu (2013). Parameter Estimation and Model Testing for Markov Processes via Conditional Characteristic Functions, Bernoulli, 19, 228-251.
  • [67]  Chen, S. X., Tang, C.Y. and J. Qin (2013). Mann-Whitney Test with Adjustments to Pre-treatment Variables for Missing Values and Observational Study, Journal of the Royal Statistical Society, Series B, 75, 81-102.
  • [68] Chen, S. X. and Van Keilegom, I. (2013) Estimation in semiparametric models with missing data.  Annals of the Institute of Statistical Mathematics, 65, 785-805.
  • [69]  P-S Zhong, Chen, S. X. and Minya Xu (2013) Tests alternative to higher criticism for high dimensional means under sparsity and column-wise dependence, The Annals of Statistics, 41, 2820-2851.
  • [70] Chen, S.X. and Z. Xu (2013) On smoothing estimation for seasonal time series with long cycles, Statistics and Its Interface, 6, 435-447.
  • [71]  Chen, S. X and Z. Xu (2014) On the implied volatility for options -- some reasons to smile and more to correct.   Journal of Econometrics, 179, 1-15.
  • [72] J. Chang, Chen, S. X.  and Chen, X. (2015) Empirical likelihood of high dimensional estimating equations with dependent data.  Journal of Econometrics, 185, 283-304.
  • [73] Y. Qiu and S.X. Chen, (2015) Band Width Selection for High Dimensional Covariance Matrix Estimation. Journal of the American Statistical Association, 110, 1160-1174.
  • [74]  Liang, X., T, Zuo, B. Guo, S. Li, H. Zhang, S. Zhang, H. Huang and S. X. Chen. (2015). Assessing Beijing's PM2.5 Pollution: Severity, Weather Impact, APEC and Winter Heating, Proceedings of the Royal Society A, 471, 20150257.
  • [75]  Chen, S.X., Lei, L.-H. and Tu, Y-D (2016). Functional Coefficient Moving Average Models with applications to forecasting Chinese CPI, Statistica Sinica, , 26, 1649-1672.
  • [76] Guo, B. and S.X. Chen (2016).   Tests for High Dimensional Generalized Linear Models. Journal of the Royal Statistical Society, Series B. 78，1079–1102
  • [77] Wang, Y., Tu, Y-D and S. X. Chen (2016) Improving inflation prediction with the quantity theory. Economics Letters, 149, 112-115.
  • [78] Chen, S.X. (2016) Peter Hall's Contribution to the Bootstrap, The Annals of Statistics, 44, No. 5, 1821–1836.
  • [79] Liang, X., Li, S., Zhang, SY, Huang, H. and S.X. Chen (2016). PM2.5 Data Reliability, Consistency and Air Quality Assessment in Five Chinese Cities, Journal of Geophysical Research—Atmosphere, 121(17), 10220–10236.
  • [80] Peng, LH, S.X. Chen and W, Zhou (2016) More Powerful Tests for Sparse High-Dimensional Covariances Matrices, Journal of Multivariate Analysis, 149, 124-143.
  • [81] He, J. and S. X. Chen (2016) Testing Super-Diagonal Structure in High Dimensional Covariance Matrices, Journal of Econometrics, 194, 283-297.
  • [82]  Shuyi Zhang, Bin Guo, Anlan Dong, Jing He, Ziping Xu, Song Xi Chen (2017). Cautionary Tales on Air Quality Improvement in Beijing, Proceedings of the Royal Society A, 473: 20170457.
  • [83] Zuo, T. and S. X. Chen (2017).  Enhancing Estimation for Interest Rate Diffusion Models with Bond Prices. Journal of Business and Economics Statistics, 35:3, 486-498.
  • [84] Y. Qiu, S.X. Chen, D. Nettleton (2018) Detecting Rare and Faint Signals via Thresholding Maximum Likelihood Estimators. The Annals of Statistics, 46， 895-923.  .
  • [85]  Chen, L., Guo, B., Huang, J., He, J., Wang, H., Shuyi Zhang, and S.X. Chen (2018).  Assessing air-quality in Beijing-Tianjing-Hebei region: the method and mixed tales of PM2.5 and O3.  Atmospheric Environment, 193, 290-301.
  • [86] J. He and S. X. Chen (2018) High-Dimensional Two-Sample Covariance Matrix Testing via Super-diagonals, Statistica Sinica, 28，2671-2696.
  • [87]  Li, HB, Wu, JW., Wang, AX, Li, X, Chen, SX, Wang, TQ, Amsalu, E., Gao, Q., Luo, YX, Yang, XH., Wang, W, Guo, J., Guo, YM, Guo, XH. (2018).  Effects of ambient carbon monoxide on daily hospitalizations for cardiovascular disease: a time-stratified case-crossover study of 460,938 cases in Beijing, China from 2013 to 2017,   ENVIRONMENTAL HEALTH, 17:82. 
  • [88] S.X. Chen, J. Li and P.-S. Zhong, (2019) Two-Sample and ANOVA Tests for High Dimensional Means, The Annals of Statistics, 47, 1443-1474.
  • [89] Mao, X., Chen, SX and Wong, R. (2019) Matrix Completion with Covariate Information, Journal of the American Statistical Association, 114, 198-210.
  • [90] Zheng, XY and Chen, SX (2019) Partitioning Structure Learning for Segmented Linear Regression Trees, Advances in Neural Information Processing Systems (NeurIPS), 2019.
  • [91]  Mao, X-J., Wong, R. K-W and Chen, S. X. (2020) Matrix Completion under Low-Rank Missing Mechanism, Statistica Sinica, to appear
  • [92]  Shuyi Zhang, Song Xi Chen, Bin Guo, Hengfang Wang, Wei Lin (2020) Regional Air-Quality Assessment That Adjusts for Meteorological Confounding, Science China Mathematics, 50, 527-558.
  • [93] Xu, Z., Chen, S. X. and Wu, X. (2020) Meteorological Change and Impacts on Air Pollution Results from North China, Journal of Geophysics Research-Atmosphere, 125 (16), e2020JD032423.
  • [94] Zhang, S., Chen, S.X. and L. Lu (2020), Inference for Variance Risk Premium, China Finance Review International, to appear  //doi.org/10.1108/CFRI-04-2020-0044
  • [95] Sun, H., Qiu, Y., Yan, H., Huang, Y., Zhu, Y.,  Gu, J. and Chen, S.X. (2020) Tracking Reproductivity of COVID-19 Epidemic in China with Varying Coefficient SIR Model (with discussion), Journal of Data Science,  18 (3), 455–472.
  • [96] Wan, Y., Xu, M., Huang, H. and Chen, S.X. (2020) A spatio-temporal model for the analysis and prediction of fine particulate matter concentration in Beijing, Enviromentrics, e2648.
  • [97]  Wu, H., Zheng, X., Zhu, J., Lin, W., Zheng, H., Chen, X., Wang, W., Wang, Z., and S. X.  Chen (2020).  Improving PM2.5 forecasts in China suing an initial error transport model, Environmental Science and Technology, 54(17), 10493-10501.
  • [98]  Gu, J., Yan, H., Huang, J., Zhu, Y., Sun, H., Qiu, Y. and S. X. Chen（2020）, Comparing Containment Measures among Nations by Epidemiological Effects of COVID-19. National Science Review, 7 (12), 1847-1851.
  • [99] Wu, H., Lin, W., Kong, L., Tang, X., Wang, W. Wang, ZF and S.X. Chen (2021) A Fast Emission Inversion Scheme Based on Ensemble Optimal Interpolation, Climate and Environmental Research (in Chiese), 26 (2), 191-201.
  • [100]  Zheng, X-Y., Guo, B., He, J. and Chen, S.X. (2021) Effects of COVID-19 Control Measures on Air Quality in North China, Envirionmentrics,2021, e2673.
  • [101]  Chen, S.X. and Zheng, XY (2021) Discussion of ``The timing and effectiveness of implementing mild interventions of COVID-19 in large industrial regions via a synthetic control method", Statistics and Its Interface, 14, 23-24.
  • [102]  Zhang, HM and Chen, S. X. (2021), Concentration Inequalities for Statistical Inference, Communications in Mathematical Research, 37, 1-85.
  • [103]  Chang, J-Y., Chen, S.X., Tang, C-Y. and Wu, T-T (2021) High-dimensional empirical likelihood inference, Biometrika, 108, 127-147.
  • [104] Chen, S.X. and L-H Peng (2021) Distributive statistical inference for massive data, The Annals of Statistics, 2021, Vol. 49, No. 5, 2851–2869.
  • [105]  Zhu, Y.R.，Liang, Y.S. and Chen, S.X. (2021) Assessing Local Emission for Air Pollution via Data Experiments, Atmospheric Environment, 252, 118323.
  • [106] Yan, H., Zhu, YR., Gu, J., Huang, YX., Sun, HX., Zhang, XY., Wang, YT., Qiu, YM. and Chen, S.X. (2021). Better strategies for containing COVID-19 pandemic: a study of 25 countries via a vSIADR model, Proceedings of the Royal Society A, 476: 20200440.
  • [107] Gu, J., Chen, S X., Dong, Q. and Qiu, YM (2021）The effect of population migration and Wuhan lockdown on the control of COVID-19 epidemic based on vSEIdRm model, Statistical Research, Vol.38, No.9.
  • [108]  Huang, YX, Guo, B., Sun, HX, Liu, HJ and S X Chen (2021). Relative Importance of Meteorological Variables on Air Quality and Role of Boundary Layer Height, Atmospheric Environment,267,118737.
  • [109] 王振中, 陈松蹊, 涂云东 (2021). 中国居民消费价格指数的动态结构研究及中美量化比较, 数理统计与管理, 待发表。
  • [110] Li, S., Liu, R., Wang, S., & Chen, S. X. (2021). Radiative effects of particular matters on ozone pollution in six North China cities. Journal of Geophysical Research: Atmospheres, 126, e2021JD035963.
  • [111] 陈松蹊，毛晓军，王聪 （2022）大数据情境下的数据完备化：挑战与对策。 管理世界，2022年第1期。
  • [112] Tong, P. F., Chen, S. X., & Tang, C.Y. (2022). Detecting and evaluating dust-events in North China with ground air quality data. Earth and Space Science, 9, e2021EA001849.
  • [113] Luo,S.S , Zhu,Y.R. & Chen, S.X.(2022). Episode based air quality assessment, Atmospheric Environment,285, 119242.
  • [114] Chen, S.X., Guo, B. and Y.M. Qiu (2023). “Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding.” Journal of Econometrics, 235(2), 1337-1354.
  • [115] Zhu,Y.R., Gu, J., Y.M. Qiu and S.X. Chen (2023). Real-World COVID-19 Vaccine Protection Rates against Infection in the Delta and Omicron Eras. Research. 2023:6;0099. DOI:10.34133/research.0099
  • [116]  Zhu, Y.R., Gu, J., Y.M. Qiu and S.X. Chen (2023). Estimating COVID-19 Vaccine Protection Rates via Dynamic Epidemiological Models--A Study of Ten Countries, The Annals of Applied Statistics, to appear.
  • [117]  Zhang, S.Y., Chen, S.X. and YM Qiu (2023). Mean Tests For High-dimensional Time Series, Statistica Sinica, to appear.
  • [118] Peifeng Tong, Wu Su, He Li, Jialin Ding, Haoxiang Zhan, Song Xi Chen (2023). Distribution Free Domain Generalization, Proceedings of the 40th International Conference on Machine Learning (ICML).
  • [119] Zhang, Y., Chen, S.X. and Bao, L. (2023). Air pollution estimation under air stagnation—A case study of Beijing. Environmetrics, e2819. //doi.org/10.1002/env.2819
  • [120]  Chen, S.X., Y.M. Qiu and Shuyi Zhang (2023) Sharp Optimality for High Dimensional Covariance Testing under Sparse Signals, The Annals of Statistics, to appear.