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Seminar 21 May @ 4 pm

     Functional limit theorems for financial markets with long-range dependence Date :  Friday, 21 May 2021 Time:   4-5 pm Speaker:   Professor  Yuliya Mishura (Kyiv National University, Ukraine) Abstract: We start with an additive stochastic sequence that is based on the sequence of independent identically distributed (iid) random variables and has the coefficients that allow for dependency on the past. Then we formulate the conditions of the weak convergence to some limit process in terms of coefficients and characteristic function of  any  basic  random variable. We adapt the general conditions to the case where the limit process is Gaussian. Then we move onto the multiplicative scheme in order to get a positive limit process (with the probability 1) that can be used for modelling of some asset prices from financial markets. Hence, we assume that all multipliers in the prelimit multiplicative scheme are positive, and therefore impose additional restrictions on the coefficients. In t
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Seminar 6 May @ 10 am

    Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Kendall's Rank Correlation Matrices and its Applications Date :  Thursday, 6 May 2021 Time:   10 -11 am Speaker:  Associate Professor Zeng Li  ( Southern University of Science and Technology) . Abstract: In this talk we will talk about the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall’s rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further propose three nonparametric procedures for high dimensional

Seminar 29 April @ 10 am

   Estimating a Change Point in a Sequence of Very High-Dimensional Covariance Matrices Date :  Thursday, 29 April 2021 Time:   10 -11 am Speaker: Dr Qing Yang  ( University of Science and Technology of China ) . Abstract: This paper considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step we use the components after dimension reduction to determine the position of the change point. Theoretical properties are developed for both steps and numerical studies are conducted to support the new methodology. Zoom Link:  Please contact Yanrong Yang ( yanrong.yang@anu.edu.au ) to obtain the zoom link for this seminar.

Seminar 30 April @ 9am

  How framelets enhance graph neural networks Date:  Friday, 30 April 2021 Time:   9-10am Speaker:   Dr  Yu Guang Wang (Max Planck Institute for Mathematics in the Sciences,  Leipzig, Germany) Abstract:  This work presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreove

Seminar 8 April @ 10 am

  Projected Estimation for Large-dimensional Matrix Factor Models Date:  Thursday, 8 April 2021 Time:   10am AEST, Canberra.  Speaker: Professor Xinbing Kong  ( Nanjing Audit University ) . Abstract:   In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that of a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the

Seminar 1 April @ 2 pm

  Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Kendall's Rank Correlation Matrices and its Applications Date:  Thursday, 1 April 2021 Time:   2 -3pm Speaker:  Assoc. Professor Zeng Li   ( Southern University of Science and Technology ) . Abstract:  I n this talk we will talk about the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall’s rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further propose three nonparametric procedures for high dimensional ind

Seminar 26 March @ 3pm

  Estimation, diagnostics, and extensions of nonparametric Hawkes processes.   Date:  Friday, 26 March 2021 Time:   3-4pm Speaker:  Assoc. Professor Jiancang Zhuang   (The Institute of Statistical Mathematics Japan and Department of Statistical Sciences, the Graduate University for Advanced Studies) . Abstract:   The Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This talk discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models. For illustration, I use the kernel function as the basic smoothing tool and the earthquake data and crime data as two application examples, to show how a Hawkes model is formulated from scratch. Zoom Link:  https://macquarie.zoom.us/j/84842498866?pwd=TTIySVRCNUZOT2hNbW1nZFpHNEJE

Seminar 25 March @10am

Statistical inference for high dimensional principal components Date: 25 March 2021, Thursday Time: 10am AEDT Speaker: Dr Xiucai Ding (University of California, Davis) Abstract: In this talk, I will present some recent results on the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we derive the joint distribution of the extreme eigenvalues and the generalized components of the associated eigenvectors, i.e., the projections of the eigenvectors onto arbitrary given direction, assuming that the dimension and sample size are comparably large. In general, the joint distribution is given in terms of linear combinations of finitely many Gaussian and Chi-square variables, with parameters depending on the projection direction and the spikes. We also apply the results to various high dimensional statistical hypothesis testing problems

Seminar 19 March @ 3pm

  Order Selection with Confidence for Mixture Models Date:  Friday 19 March 2021 Time:  3pm Speaker:  Dr Hien Nguyen ( La Trobe University) Abstract: Finite mixture models are distribution models that are defined by convex combinations of a finite number of elements (components) from some base distribution class, where the number of elements dictates the complexity of the mixture model. Given that data arise from a class of finite mixture models, where the number of components is unknown, an important problem that arises is choice of the number of components that one should use to model the data. We present a hypothesis test-based algorithm to selecting the number of components of a mixture model that yields a lower bound on the number of components, with confidence. We demonstrate that in special circumstances, the approach also yields a method that consistently selects the correct number of components, and we demonstrate the effectiveness of the approach via a study of the class prob

Seminar 11 March @ 10am

Random FPUT Lattices   Date: Thursday 11 March 2021 Time: 10am Speaker:   Professor J. Douglas Wright (Drexel University) Abstract: We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is both strong and almost sure, but the rate of convergence is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm. This work is joint with Drexel PhD student, Josh McGinnis. Zoom Link:  https://macquarie.zoom.us/j/83753405912?pwd=VU96LzJqbnhVODQwMnhhTS9VNEc5Zz09