2013年实验室学术活动

报告题目: Universality of the largest eigenvalue of sample covariance matrices
报 告 人: Prof.Wang Zhou,National University of Singapore

时间地点: 2013年10月24日上午10:30 S709
摘  要: In this talk, I will discuss the universality of the largest eigenvalue of a class of large dimensional real or complex sample covariance matrices.


报告题目: Functional integration and index theory
报 告 人: Prof. Jean-Michel Bismut,University Paris-Sud, France

时间地点: 2013年10月11日下午4:00 S703
摘  要: In the first part of the talk, I will explain the connections between the heat equation proof of the index theorem for Dirac operators, and the localization formulas of Duistermaat-Heckman. In particular, I will show how to pass from integration with respect to the Brownian measure on the loop space of a Riemannian manifold to integration of differential forms on this loop space. In the above situation, the geometry of the loop space is associated with its L2-Riemannian metric. In a second part of the talk, I will show how replacing the L2-metric by a H1-metric determines a new measure on the loop space, which corresponds to a geometric Langevin process, whose generator is a hypoelliptic operator on the total space of the tangent bundle. I will naturally explain how the above suggests the possibility of deforming the elliptic Dirac operator to a family of hypoelliptic Dirac operators.


报告题目: Limit problems for the evolutional models oftwodimensional Young diagrams
报 告 人: Prof. Bin Xie(谢宾) ,Shishu University, Japan

时间地点: 2013年9月18日上午10:00 S1013
摘  要: In this talk, we will introducesome limit problems for a dynamics of two-dimensional Young diagrams. The dynamics of two-dimensional Young diagrams is naturally associated with the grand-canonical ensembles determined from two types of statistics called uniform and restricted uniform statistics.Under some proper scaling, we will discuss the hydrodynamic limit and the fluctuation problem for both uniform and restricted uniform statistics of the evolutional Young diagrams. For the fluctuation problemof our model, the limits are characterized by two linear stochastic partial differential equations, whose invariant measures are identical to the fluctuation limits in the static situations. This talk is based on a joint work with T. Funaki et al.


报告题目: Least squares estimation of threshold models: a practical two-stage procedure(159)
报 告 人: Dr. Dong Li,Hong Kong University of Science and Technology, HK

时间地点: 2013年9月6日下午4:00 S712
摘  要: Threshold models have attracted too much attention and been widely used in econometrics, economics and finance for modeling nonlinear phenomena. Its success is partially due to its simplicity in terms of both model-fitting and model-interpretation. A popular approach to fit a threshold model is the conditional least squares method. However, as modeling data with threshold type of models the computational costs become substantial. This paper proposes a novel method, two-stage grid-search procedure, to quickly search the least squares estimate of the threshold parameter in threshold models. Compared with the standard grid-search procedure used in literature, our new method extremely reduces computational costs, which only requires least-squares operations of order O(\sqrt{n}). Its validity is also verified theoretically. The performance of our procedure is evaluated via Monte Carlo simulation studies in finite samples.


报告题目: Stochastic Calculus for G-Brownian Motion on Manifolds(158)
报 告 人: Prof. Z. Qian,University of Oxford

时间地点: 2013年9月6日下午2:30 S712
摘  要: In this talk I outline how to define Stratonovich's integration for G-Brownian motion via the rough path analysis, and apply the theory in constructing a class of G-Brownian motion on manifolds. We then identify a class of fully nonlinear equations and obtain stochastic representation (in viscosity sense) for their solutions. This talk is based on a joint work with Geng Xi and Danyun Yang at the Oxford-Man Institute in Quantitative Finance, Oxford.


报告题目: Poissonian loop ensemble in discrete space(157)
报 告 人: 常寅山 博士,Université Paris-Sud (巴黎11大)

时间地点: 2013年7月30日上午9:30 S712
摘  要: As an analogue and a generalization of the Brownian loops, the Markovian loops are introduced and studied mainly by Le Jan. Given a Markov semi-group, Le Jan defines a sigma finite measure on the space of loops when the bridge measure is well-defined. The Poissonian loop ensemble (or loop soup) is the Poisson random measure driven by the Markovian loop measure. The loop model has many relations with other objects in probability, e.g. random interlacement, Gaussian free field, branching process with immigration, uniform spanning tree, permenantal fields, etc.

In this talk, we will mainly present the basic properties and interesting results based on the work of Le Jan, Sznitman, Lemaire, Lupu, … We will restrict ourselves on Markovian loops on discrete space. To be more precise, we will talk about the compatibility of the loop soup, the occupation field, the loop clusters together with a few relations with other fields.


报告题目: Consistent Cross-Validation for Tuning Parameter Selection in High-Dimensional Variable Selection(156)
报 告 人: Yang Feng, Assistant Professor Department of Statistics, Columbia University, USA

时间地点: 2013年7月22日上午10:00 S708
摘  要: Asymptotic behavior of tuning parameter selection in the standard cross-validation methods is investigated for the high-dimensional variable selection. It is shown that the shrinkage problem with LASSO penalty is not always the true reason for the over-selection phenomenon in cross-validation based tuning parameter selection. After identifying the potential problems with the standard cross-validation methods, we propose a new procedure, Consistent Cross-Validation (CCV), for selecting the optimal tuning parameter. CCV is shown to enjoy the model selection consistency. Extensive simulations and real data analysis support the theoretical results and demonstrate that CCV also works well in terms of prediction.


报告题目: Stochastic variational principles and FBsde's on Lie groups(155)
报 告 人: Prof. Ane Bela Cruzeiro, Grupo de Física Matemática da Universidade de Lisboa, Portugal

时间地点: 2013年7月19日下午2:30 S712
摘  要: We prove a Euler-Poincaré reduction theorem for stochastic processes taking values in a Lie group and show examples of its application, notably to the derivation of Navier-Stokes equations. We also show the relations of such processes with forward-backward stochastic systems. This is joint work with Marc Arnaudon (Bordeaux) and Xin Chen (Lisbon).


报告题目: Functional Linear Mixed-Effects Model in Characterizing Population Trend and Variability of Circadian Rhythm using Actigraphy Data(154)
报 告 人: Jimin Ding, Assistant Professor, Washington University in St. Louis

时间地点: 2013年7月18日下午3:30 S712
摘  要: We propose a functional linear mixed-effects model to investigate correlated functional curves with application to the actigraphy data collected from a study of sleep disorders. The study has been conducted in the Medical School of Washington University in Saint Louis, which contains actigraphy data over a week for each subject. An actigraph is a watch-like device attached to the wrist or leg that contains accelerometers to measure movements minute-by-minute throughout the day of each day it is worn. The resulting data are densely measured activity levels over 24-hour period for several days for each patient. We view them as curves over time clustered by subjects and model these data using the functional linear mixed-effects model to incorporates multiple ixed-effects and random-effects functions of arbitrary form. The proposed model is: a generalization of 1) functional linear models by including random-effects functions; 2) linear mixed-effects models to the functional space. We develop a new method to iteratively estimate the population trends and decompose the functional variation from between- and within- subject. The individual profile prediction are adaptively shrunk toward the population average. We apply the proposed functional linear mixed-effects model to investigate the relationship between the clinical covariates and activities of the patients, discover the major variation directions, describe the circadian rhythm and reveal some interesting insights into patient's activity patterns.


报告题目: Bayesian analysis in partially identified models(153)
报 告 人: Yuan Liao, Assistant Professor,Department of Mathematics, University of Maryland

时间地点: 2013年7月15日下午4:30 S708
摘  要: One of the fundamental questions for Bayesian analysis is how much prior information can be updated by the data. In many applications of econometrics and survival analysis, the available information from the data is not strong enough to identify the parameter of interest. Instead, the parameter is only ``partially identified" on a non-singleton set. While the prior information is often washed away by the data as sample size diverges in traditional models, it is no longer the case in partially identified models. Instead, the shape of the posterior is determined by the prior even asymptotically, and the classical Bernsten von Mises theorem does not hold. I will discuss many applied examples to motivate partially identified models, and introduce some recent asymptotic results on the posterior distributions. I will also construct Bayesian credible intervals in the new framework, and both the Bayesian and frequentist coverage probabilities are investigated and compared.


报告题目: The Clark Formula of Generalized Levy Functionals(152)
报 告 人: Prof. Yuh-Jia Lee (李育嘉),National University of Kaohsiung, Taiwan

时间地点: 2013年7月15日下午4:00 S709
摘  要:


报告题目: The Asymptotic Expansion of Forward Equations of Singularly Perturbed Diffusion (151)
报 告 人: Prof. Tzuu-Shuh Chiang (姜祖恕),Institute of Mathematics Academia Sinica, Taiwan

时间地点: 2013年7月15日下午3:00 S709
摘  要:


报告题目: The Kolmogorov Filter(150)
报 告 人: Prof. Hui Zou, University of Minnesota

时间地点: 2013年7月11日下午4:00 S709
摘  要: Variable screening techniques have been proposed to mitigate the impact of high dimensionality in classification problems, including t-test marginal screening (Fan & Fan, 2008) and maximum marginal likelihood screening (Fan & Song, 2010). However, these methods rely on strong modelling assumptions that are easily violated in real applications. To circumvent the parametric modelling assumptions, we propose a new variable screening technique for binary classification based on the Kolmogorov–Smirnov statistic.We prove that this so-called Kolmogorov filter enjoys the sure screening property under much weakened model assumptions. We supplement our theoretical study by a simulation study.


报告题目: Imprinting Test of Disease -Associated SNPs under mixture model
报 告 人: 郭建华 教授,东北师范大学数学与统计学院、 应用统计教育部重点实验室

时间地点: 2013年6月27日上午10:00 S709
摘  要: Genomic imprinting represents a known aspect of the etiology of schizophrenia, a serious and common neuropsychiatric disease. This study delineates the significance of imprinting on the relationships between schizophrenia-associated single-nucleotide polymorphisms (SNP) of the GABRB2 gene for the subunit of receptors and the quantitative trait of GABRB2 mRNA expression. The imprinting phenomenon depicts differential expression levels of the allele depending on its parental origin. When the parental origin is unknown, the expression level has a finite normal mixture distribution. A random sample on expression levels from a population is naturally divided into three sub-samples according to the number of minor alleles an individual possesses. This understanding leads to a likelihood ratio test (LRT) for the presence of the imprinting. Due to non-regularity of the finite mixture model, the classical asymptotic conclusions on likelihood-based inferences are inapplicable. In this paper, we first prove the maximum likelihood estimator of the mixing distribution is consistent in the current setting. We find the LRT statistic has an elegant null limiting distribution. Simulation studies confirm the limiting distribution provides precise approximations to the finite sample distributions in various parameter settings. The LRT is applied to expression data sets on the schizophrenia susceptibility gene GABRB2. Our analyses provide evidences of imprintings on a number of isoform expressions of its receptor subunit protein encoded by the GABRB2 gene.


报告题目: 非平稳时间序列的理论及应用
报 告 人: 高集体 教授,Monosh University, Australia

时间地点: 2013年6月21日下午2:00 S703
简  介:


报告题目: 分位数回归模型的若干研究
报 告 人: 朱仲义 教授,复旦大学统计系

时间地点: 2013年6月25日下午4:00 S712
摘  要: 在这个讲座中,我们将首先介绍分位数回归模型的一般特性,其次在三个方面介绍我们最近的研究成果:1.对分位数回归模型,我们提出了一种统一的变量选择方法,此方法能够选择变量,同时能够区分常系数和变系数;2.对自变量带有测量误差的分位数回归模型,我们利用校正得分函数的方法,提出了相合估计方法,并且在理论和数值模拟上证实了方法的有效性;3. 基于CSUM方法,对分位数回归模型我们提出了一种变点的检验和估计方法。通过理论和模拟分析,新方法优于其他方法。


报告题目: Flexible Modeling of Medical Cost Data
报 告 人: Lei Liu(刘磊), PhD,Associate Professor,Department of Preventive Medicine Northwestern University,USA

时间地点: 2013年6月25日下午4:00 S712
摘  要: Medical cost data are often skewed to the right and heteroscedastic, having a nonlinear relation with covariates. To tackle these issues, we consider an extension to generalized linear models by assuming nonlinear covariate effects in the mean function and allowing the variance to be an unknown but smooth function of the mean. We make no further assumption on the distributional form. The unknown functions are described by penalized splines, and the estimation is carried out using nonparametric quasi-likelihood. Simulation studies show the flexibility and advantages of our approach. We apply the model to the annual medical costs of heart failure patients in the clinical data repository (CDR) at the University of Virginia Hospital System. We also discuss how to adopt this modeling framework in correlated medical costs data.


报告题目: A rotational approach to high dimensional classification
报 告 人: Ning Hao, Associate Professor,Department of Mathematics, the University of Arizona, USA

时间地点: 2013年6月13日下午3:30 S712
摘  要: Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To efficiently use them, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications and rotations of data are required to create the needed sparsity. In this talk, we propose a surprisingly simple rotation to create the required sparsity. The proposed rotate-and-solve procedure can be combined with any existing classifiers, and is robust against the sparse level of the true model. We show that this rotation does create the sparsity needed for high dimensional classifications. The methodological power is demonstrated by a number of simulation and real data examples and the improvements of our method over some popular high dimensional classification rules are clearly shown.


报告题目: Machine Learning and Its Application in Variable Annuity Hedging
报 告 人: Guojun Gan博士,Director, VA Hedging Research & Development Manulife Financial, Toronto, Ontario, Canada

时间地点: 2013年6月13日上午10:00 S709
简  介:


报告题目: A generalization of Fourier series expansion and its involvements in mathematics
报 告 人: Prof.Tao QIAN,University of Macau

时间地点: 2013年4月27日下午4:00 S1013
简  介: Rational orthogonal expansions can be considered as generalizations of Fourier series expansion. We introduce the so called Adaptive Fourier Decomposition (AFD) and its relations to a number of mathematical subjects, including best n-rational approximation, Beurling-Lax backward shift operator invariant subspaces, phase and amplitude retrieval problems, etc.


报告题目: Scalable Spectral Algorithms for Community Detection in Directed Networks
报 告 人: Tao Shi, Associate Professor,Department of Statistics, Department of Computer Science and Engineering,The Ohio State University

时间地点: 2013年4月17日下午2:00 S712
简  介: Community detection has been one of the central problems in network studies and directed network is particular challenging due to asymmetry among its links. In this talk, we discuss incorporating the direction of links reveals new perspective on communities regarding to two different roles, source and terminal. Intriguingly, such communities appear to be connected with unique spectral property of the graph Laplacian of the adjacency matrix and we exploit this connection by using regularized SVD methods. We propose harvesting algorithms, coupled with regularized SVDs, that are linearly scalable for efficient identification of communities in huge directed networks. The algorithm showed great performance and scalability on benchmark networks in simulations and successfully recovered communities in real social networks applications (with ~2 million nodes and ~50 million edges). This is a joint work with Sungmin Kim (OSU).


报告题目: 统计质量控制图简介及某些热点研究问题
报 告 人: 王兆军 教授,南开大学

时间地点: 2013年3月15日下午4:00 S712
简  介: 主要介绍统计质量控制图的一些基本概念和近十年的三个热点研究问题:关于profilde,healthcare数据的监控以及高维复杂数据的在线监控。


报告题目: Semi-parametric Models for Longitudinal Count Responses with Overdispersion and Structural Zeros
报 告 人: Wan Tang,Associate Professor , University of Rochester Dept of Biostatistics and Computational Biology

时间地点: 2013年3月11日上午10:00 S709
简  介: Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson loglinear regression. Ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. In this talk, we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a new semi-parametric modeling approach to address the limitations of these methods. We illustrate our approach with both simulated and real study data.


报告题目: Semiparametric Estimation in Linear Dynamic Panel Data Models
报 告 人: Prof.Liqun Wang, Department of Statistics, University of Manitoba, Canada

时间地点: 2013年3月8日下午4:00 S712
简  介: Repeated measures data are common in many research areas. In statistics, the mainstream research adopts nonlinear mixed-effects models to describe the response variables through some other covariates. In contrast, in econometrics dynamic models are mainly used to predict the response through its own past values. It is interesting to see the connections and differences between these two approaches. We study the second-order least squares estimator for the autoregressive panel data models. This method requires only the specification of the first two conditional moments of the unobserved effects given the process initial observation, and does not require any other distributional assumptions. The data generating process can be either stationary or nonstationary. The proposed estimator is consistent and asymptotically normal for large N and finite T under fairly general regularity conditions. Moreover, we show that our estimator reaches an optimal semiparametric efficiency bound. Monte Carlo simulation studies show that the proposed estimator performs satisfactorily in finite sample situations compared to the usual first-differenced generalized method of moment (GMM) and the random effects pseudo maximum likelihood (PML) estimators.


报告题目: Semiparametric Estimation in Linear Dynamic Panel Data Models
报 告 人: Prof.Liqun Wang,Department of Statistics, University of Manitoba, Canada

时间地点: 2013年3月5日下午4:00 S712
简  介: Repeated measures data are common in many research areas. In statistics, the mainstream research adopts nonlinear mixed-effects models to describe the response variables through some other covariates. In contrast, in econometrics dynamic models are mainly used to predict the response through its own past values. It is interesting to see the connections and differences between these two approaches.We study the second-order least squares estimator for the autoregressive panel data models. This method requires only the specification of the first two conditional moments of the unobserved effects given the process initial observation, and does not require any other distributional assumptions. The data generating process can be either stationary or nonstationary. The proposed estimator is consistent and asymptotically normal for large N and finite T under fairly general regularity conditions. Moreover, we show that our estimator reaches an optimal semiparametric efficiency bound. Monte Carlo simulation studies show that the proposed estimator performs satisfactorily in finite sample situations compared to the usual first-differenced generalized method of moment (GMM) and the random effects pseudo maximum likelihood (PML) estimators.


报告题目: Large deviation principles for generalized Feynman-Kac functionals and $L^p$-independence of spectral radius
报 告 人: Prof. Kuzuhiro Kuwae, Kumamoto University

时间地点: 2013年2月20日下午4:00 S703
简  介: I will talk about the large deviation principles of occupation distribution for generalized Feynman-Kac functionals are presented in the framework of symmetric Markov processes having doubly Feller or strong Feller property under mild conditions on measures. As a consequence, we expose the $L^p$-independence of spectral radius of our generalized Feynman-Kac functionals. The result extends the works on LDPs by Takeda, Takeda-Tawara and Tawara. This is a joint work with D. Kim and Y. Tawara, which is a continuation of the previous joint work with De Leva and Kim published in JFA. If I have a time, we mention the Fukushima's decomposition in the strict sense for functions locally in the domain of Dirichlet form having energy measure of Dynkin class without assuming no inside killing.


报告题目: A generalized beta copula with applications in modeling multivariate long-tailed data
报 告 人: Prof. Zhengjun Zhang,University of Wisconsin,USA

时间地点: 2013年1月9日下午2:00 S703
简  介: This work proposes a new copula class that we call the MGB2 copula. The new copula originates from extracting the dependence function of the multivariate GB2 distribution (MGB2) whose marginals follow the univariate generalized beta distribution of the second kind (GB2). The MGB2 copula can capture non-elliptical and asymmetric dependencies among marginal coordinates and provides a simple formulation for multidimensional applications. The new class features positive tail dependence in the upper tail and tail independence in the lower tail. Furthermore, it includes some well-known copula classes, such as the Gaussian copula, as special or limiting cases. The validation of the MGB2 copula can be assessed by a graphical tool of the so-called “conditional plots”. To illustrate the usefulness of the MGB2 copula in practice, we build a trivariate model to analyze a data set that contains rich information on bodily injury liability claims closed within two-week period in years 1987, 1992, and 1997. Reparametrized log-F (EGB2) distributions are chosen to accommodate the right-skewness and the long-tailedness of the outcome variables,while continuous predictors are fitted by non-linear curves in the marginal regression models. The pairwise dependence structures exhibited motivate the application of the MGB2 copula. For comparison purposes we also consider the alternative Gumbel copula and t copula for the adaption of the upper tail dependence. The quantitative and graphical assessment for goodness-of-fit demonstrates the comparative advantage of the MGB2 copula over the other two copulas, which practically establishes the necessity for the development of this new copula class.


 

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