“十四五”以来，数学与统计学院统计学科研团队围绕复杂高维数据分析、贝叶斯分析等前沿问题开展了卓有成效的研究工作，在统计学国际顶级期刊Journal of the Ameirican Statistical Association、数学国内顶级期刊Science China Mathematics以及统计学国际权威期刊Bayesian Analysis、Statistica Sinica、Journal of Multivariate Analysis、Computational Statistics & Data Analysis、Test、Journal of Statistical Planning and Inference等上发表系列学术论文，受到同行的广泛关注和引用，其中6篇代表性论文如下：
代表性论文一：2021年3月，数学与统计学院统计学科研团队许凯副教授和美国宾州州立大学(The Pennsylvania State University)李润泽教授、同济大学周叶青助理教授、中国人民大学朱利平教授等合作的论文“Testing the effects of high-dimensional covariates via aggregating cumulative covariances”发表在中国数学会(2021年)认定的概率统计类T1期刊Journal of the American Statistical Association上。
论文摘要：In this article, we test for the effects of high-dimensional covariates on the response. In many applications, different components of covariates usually exhibit various levels of variation, which is ubiquitous in high-dimensional data. To simultaneously accommodate such heteroscedasticity and high dimensionality, we propose a novel test based on an aggregation of the marginal cumulative covariances, requiring no prior information on the specific form of regression models. Our proposed test statistic is scale-invariance, tuning-free and convenient to implement. The asymptotic normality of the proposed statistic is established under the null hypothesis. We further study the asymptotic relative efficiency of our proposed test with respect to the state-of-art universal tests in two different settings: one is designed for high-dimensional linear model and the other is introduced in a completely model-free setting. A remarkable finding reveals that, thanks to the scale-invariance property, even under the high-dimensional linear models, our proposed test is asymptotically much more powerful than existing competitors for the covariates with heterogeneous variances while maintaining high efficiency for the homoscedastic ones. Supplementary materials for this article are available online.
代表性论文二：2021年10月，数学与统计学院统计学科研团队许凯副教授、曹明响教授合作的论文“Distance-covariance-based tests for heteroscedasticity in nonlinear regressions”发表在中国数学会(2021年)认定的数学类T1期刊Science China Mathematics上。
论文摘要：We use the distance covariance to introduce novel consistent tests of heteroscedasticity for nonlinear regression models in multidimensional spaces. The proposed tests require no user-defined regularization, are simple to implement based on only pairwise distances between points in the sample and are applicable even if we have non-normal errors and many covariates in the regression model. We establish the asymptotic distributions of the proposed test statistics under the null and alternative hypotheses and a sequence of local alternatives converging to the null at the fastest possible parametric rate. In particular, we focus on whether and how the estimation of the finite-dimensional unknown parameter vector in regression functions will affect the distribution theory. It turns out that the asymptotic null distributions of the suggested test statistics depend on the data generating process, and then a bootstrap scheme and its validity are considered. Simulation studies demonstrate the versatility of our tests in comparison with the score test, the Cramer-von Mises test, the Kolmogorov-Smirnov test and the Zheng-type test. We also use the ultrasonic reference block data set from National Institutes for Standards and Technology to illustrate the practicability of our proposals.
代表性论文三： 2021年3月，数学与统计学院统计学科研团队何道江教授、教师贺磊博士和美国内布拉斯加大学林肯分校(University of Nebraska at Lincoln)孙东初教授合作的论文“Objective Bayesian analysis for the Student-t linear regression”发表在中国数学会(2021年)认定的概率统计类T2期刊Bayesian Analysis上。
论文摘要：In this paper, objective Bayesian analysis for the Student-t linear regression model with unknown degrees of freedom is studied. The reference priors under all the possible group orderings for the parameters in the model are derived. The posterior propriety under each reference prior is validated by considering a larger class of priors. Simulation studies are carried out to investigate the frequentist properties of Bayesian estimators based on the reference priors. Finally, the Bayesian approach is applied to two real data sets.
代表性论文四：2021年10月，数学与统计学院统计学科研团队许凯副教授、何道江教授合作的论文“Omnibus model checks of linear assumptions through distance covariance”发表在中国数学会(2021年)认定的概率统计类T2期刊Statistica Sinica上。
论文摘要：Although the adequacy of linearity is well researched in the statistical literature, few studies examine this topic from the viewpoint of a measure of association. Inspired by the well-known distance covariance (dCov), we propose two omnibus tests for the goodness-of-fit of linearity. Methodologically, our tests do not include any tuning parameters and are conveniently implemented. The theoretical details are of independent interest, mainly because the kernel induced by the dCov is not smooth. We investigate the convergence of our tests under null, fixed, and local alternative hypotheses, and devise a bootstrap scheme to approximate their null distributions, showing that its consistency is justified. Numerical studies demonstrate the effectiveness of our proposed tests relative to that of several existing tests.
代表性论文五：2022年2月，数学与统计学院统计学科研团队许凯副教授和中国人民大学朱利平教授合作的论文“Power analysis of projection-pursuit independence tests”发表在中国数学会(2021年)认定的概率统计类T2期刊Statistica Sinica上。
论文摘要：Three important projection-pursuit correlations, namely, the distance, projection, and multivariate Blum Kiefer Rosenblatt (BKR) correlations, have been proposed in the literature to test for independence between two random vectors in arbitrary dimensions. In this study, we compare the asymptotic power performance of independence tests built upon these three projection-pursuit correlations, in a uniform sense. We show that in the presence of outliers, the projection and multivariate BKR correlation tests are still powerful, whereas the distance correlation test may lose power. We also analyze the minimax optimality of these independence tests. We show that their minimum separation rates are of order n^{-1}, where n stands for the sample size, and that this minimax optimal rate is tight in terms of the projection, distance, and multivariate BKR correlations.
代表性论文六：2022年6月，数学与统计学院统计学科研团队教师王骏博士和北京理工大学田玉斌教授、王典朋预聘助理教授合作的论文“Multidimensional specification test based on non-stationary time series”发表在中国数学会(2021年)认定的概率统计类T2期刊Test上。
论文摘要：In the literature, most works of the specification tests focus on the problem with one-dimensional response or fixed multidimensional responses. In this paper, we develop a new specification test for the parametric models with non-stationary regressor under multidimensional setup, where the dimension of responses may tend to infinity, which fills a gap in the literature. The theoretical results about the asymptotic properties of the proposed test are studied and the optimal rate of the local departure under the alternative hypothesis is also given which ensures the models underpinning by the null and alternative hypotheses can be differentiated. Some simulation studies are done to evaluate the performance of the proposed test with the finite sample. Besides, a real data example based on the US aggregate consumers’ consumption data is employed to illustrate the performance. The results of simulation studies and real data analysis both demonstrate the efficiency of our proposed method.
何道江简介：
何道江，博士，教授，博士生导师，主要从事贝叶斯统计和高维数据分析等方面的研究工作。主持国家自然科学基金、国家社会科学基金、教育部人文社会科学基金、安徽省自然科学基金等项目，在Bayesian Analysis、Statistica Sinica、Test、Journal of Multivariate Analysis、Journal of Statistical Planning and Inference等国际期刊上发表论文30余篇。
曹明响简介：
曹明响，博士，教授，硕士生导师，主要从事高维数据分析等方面的研究工作。主持国家自然科学基金、教育部人文社会科学基金、安徽省自然科学基金、全国统计科学研究项目等项目，在Electronic Journal of Statistics、Journal of Multivariate Analysis、Journal of Statistical Planning and Inference、Science China Mathematics等国际期刊上发表论文20余篇。
许凯简介：
许凯，博士，副教授，硕士生导师。2018年博士毕业于上海财经大学，师从朱利平教授（现任中国人民大学教授）。主要从事复杂非线性相依关系的度量及应用方面的研究工作。主持国家自然科学基金青年项目、面上项目以及安徽省自然科学基金青年项目各1项，在Annals of Statistics、Journal of the American Statistical Association、Biometrika、Statistica Sinica、Journal of Multivariate Analysis、Computational Statistics & Data Analysis、Journal of Statistical Planning and Inference等国际期刊上发表论文30余篇。
贺磊简介：
贺磊，博士，讲师，硕士生导师。2019年博士毕业于上海师范大学，师从岳荣先教授。主要从事贝叶斯分析、试验设计等方面的研究工作。主持国家自然科学基金青年项目和安徽省自然科学基金青年项目各1项，在Bayesian Analysis、Journal of Statistical Planning and Inference、Statistical Papers等国际期刊上发表论文10余篇。兼任中国现场统计研究会试验设计分会理事。
王骏简介：
王骏，博士，讲师。2020年博士毕业于北京理工大学，师从田玉斌教授。主要从事可靠性分析、高维数据分析、变点分析等方面的研究工作。主持安徽省教育厅基金项目1项，在Test、Communications in Statistics-Simulation and Computation、Communications in Statistics-Theory and Methods等国际期刊上发表论文5篇。