Jianfeng Yao

This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the empirical spectral distribution of its symmetrized version converges to the semicircle law, and thus providing the first example of a large correlation matrix deviating from the Marchenko-Pastur law that governs those of Pearson, Kendall, and Spearman. We further establish central limit theorems for linear spectral statistics, which in turn enable the development of Chatterjee's rank correlation-based tests of complete independence among the components.

P-hacking poses challenges to traditional hypothesis testing. In this paper, we propose a robust method for the one-sample significance test that can protect against p-hacking from sample manipulation. Precisely, assuming a sequential arrival of the data whose variance can be time-varying and for which only lower and upper bounds are assumed to exist with possibly unknown values, we use the modern theory of sublinear expectation to build a testing procedure which is robust under such variance uncertainty, and can protect the significance level against potential data manipulation by an experimenter. It is shown that our new method can effectively control the type I error while preserving a satisfactory power, yet a traditional rejection criterion performs poorly under such variance uncertainty. Our theoretical results are well confirmed by a detailed simulation study.

Error cross-sectional dependence is commonly encountered in panel data analysis. We propose a unified test procedure and its power enhancement version for the null hypothesis of cross-sectional independence in large panel data models. The proposed tests show robustness for a wide class of panel model contexts. Specifically, the two procedures are applicable to both heterogeneous and fixed effects panel data models with the presence of weakly exogenous regressors as well as lagged dependent regressors, allowing for a general form of non-normal error distribution. We establish the asymptotic validity of the test procedures under the simultaneous limit scheme where the number of time periods and the number of cross-sectional units go to infinity proportionally using tools from Random Matrix Theory. The derived theories are accompanied by detailed Monte Carlo experiments, which confirm the robustness of the two tests and also suggest the validity of the power enhancement technique. The use of the proposed tests is illustrated with an empirical applications in US house price changes.

In this paper, we study high-dimensional behavior of empirical spectral distributions [ ] for a class of [ ] symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic differential equation driven by fractional Brownian motion with Hurst parameter [ ]. For Wigner-type matrices, we obtain almost sure relative compactness of [ ] in [ ] following the approach in [1]; for Wishart-type matrices, we obtain tightness of [ ] on [ ] by tightness criterions provided in Appendix B. The limit of [ ] as [ ] is also characterized.

This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of q covariance matrices of dimension p×p. Under a limiting scheme where p, q and the sample sizes from the q populations grow to infinity in a proper manner, the proposed test statistics are shown to be asymptotically normal. Simulation results show that finite sample properties of the test procedures are satisfactory under both the null and alternatives. As an application, we derive a test procedure for the Kronecker product covariance specification for transposable data. Empirical analysis of datasets from the Mouse Aging Project and the 1000 Genomes Project (phase 3) is also conducted.