报告一：Testing for the presence of leverage effect
摘 要：In this paper, we propose a test for deciding whether the correlation of a discretely-observed semi-martingale and it quadratic variation (it refers to the leverage effect in the financial econometric) equals zero. The asymptotic setting is based on observations within a long time interval with mesh of the observation grid shrinking to zero. The test is based on forming a sequence of studentized statistics whose distributions are asymptotically normal locally over blocks of shrinking time span, and the collecting the sequence based on the whole data set. The asymptotic behavior of the local studentized statistics is obtained from a similar result in a global setting using the third power variation of the underlying process. We derive the asymptotic distribution of the proposed test statistic under the null hypothesis of zero leverage effect and show that the test has asymptotic power of one against fixed alternatives of processes with non-zero leverage effect. Finally, simulation study verifies the finite sample performance of the test.
报告二：Community detection of sparse networks
报告人: 荆炳义 博士
摘 要：Community detection for networks has been studied intensively in recent years.
However, most studies focus on dense networks with little attention to sparse
networks. In this talk, we will investigate ways to detect communities for sparse
networks. This is work in progress.
报告三：Large dimensional random matrix theory for statistical inferences
摘 要：In probability theory, a random matrix is a matrix-valued random variable. In this talk, I will introduce some random matrix theory which could be used for large dimensional statistical inferences. These include the empirical spectral distributions of sample covariance matrices, the limiting distributions of extreme eigenvalues of sample covariance matrices, exact separation of eigenvalues of sample covariance matrices, CLT for linear spectral statistics of sample covariance matrices and CLT for eigenvalues in a spiked population model.
报告四：Random matrix theory and its applications—Application in Statistics
摘 要：We introduce some statistical inferences based on Random Matrix Theory in high-dimensional frameworks. Two estimation methods of population spectral distribution (PSD) will be discussed, where one is developed from the estimation of moments of a PSD and the other is derived by solving the MP equation on the real line. Moreover, some tests for the covariance matrices will also be detailed, including tests for the identity and sphericity, and tests for the order of a discrete PSD.