报告人：张金廷(新加坡国立大学终身教授，广东财经大学特聘教授)
邀请人：陈蔼祥
时间：2022—2023年下学期第14周—19周每周三上午9:00-11:00
地点：北2—540（大会议室）
报告题目：A simple two-sample test in high-dimensions based on L2-norm
报告提纲：Abstract
Testing the equality of two means is a fundamental inference problem. For high-dimensional data, the Hotelling’s T2-test either performs poorly or becomes inapplicable. Several modifications have been proposed to address this issue. However, most of them are based on asymptotic normality of the null distributions of their test statistics which inevitably requires strong assumptions on the covariance. We study this problem thoroughly and propose an L2-norm based test that works under mild conditions and even when there are fewer observations than the dimension. Specially, to cope with general nonnormality of the null distribution we employ the Welch–Satterthwaite χ2-approximation. We derive a sharp upper bound on the approximation error and use it to justify that χ2-approximation is preferred to normal approximation. Simple ratio-consistent estimators for the parameters in the χ2-approximation are given. Importantly, our test can cope with singularity or near singularity of the covariance which is commonly seen in high dimensions and is the main cause of nonnormality. The power of the proposed test is also investigated. Extensive simulation studies and an application show that our test is at least comparable to and often outperforms several competitors in terms of size control, and the powers are comparable when their sizes are. Supplementary materials for this article are available online.
报告题目：Linear hypothesis testing for weighted functional data with applications
报告提纲：Abstract
In socioeconomic areas, functional observations may be collected with weights, called weighted functional data. In this paper, we deal with a general linear hypothesis testing (GLHT) problem in the framework of functional analysis of variance with weighted functional data. With weights taken into account, we obtain unbiased and consistent estimators of the group mean and covariance functions. For the GLHT problem, we obtain a pointwise F-test statistic and build two global tests, respectively, via integrating the pointwise F-test statistic or taking its supremum over an interval of interest. The asymptotic distributions of test statistics under the null and some local alternatives are derived. Methods for approximating their null distributions are discussed. An application of the proposed methods to density function data is also presented. Intensive simulation studies and two real data examples show that the proposed tests outperform the existing competitors substantially in terms of size control and power.
报告题目：A modified Bartlett test for heteroscedastic one way MANOVA
报告提纲：Abstract
In this paper, we investigate tests of linear hypotheses in heteroscedastic one-way MANOVA via proposing a modified Bartlett (MB) test. The MB test is easy to conduct via using the usual χ2-table. It is shown to be invariant under affine transformations, different choices of the contrast matrix used to define the same hypothesis and different labeling schemes of the mean vectors. Simulation studies and real data applications demonstrate that the MB test performs well and is generally comparable to Krishnamoorthy and Lu’s (J Statist Comput Simul 80(8):873–887, 2010) parametric bootstrap test in terms of size controlling and power.
报告题目：New Tests for equality of several covariance functions for functional data
报告提纲：Abstract
In this article, we propose two new tests for the equality of the covariance functions of several functional populations, namely, a quasi-GPF test and a quasi-Fmax test whose test statistics are obtained via globalizing a pointwise quasi-F-test statistic with integration and taking its supremum over some time interval of interest, respectively. Unlike several existing tests, they are scale-invariant in the sense that their test statistics will not change if we multiply each of the observed functions by any nonzero function of time. We derive the asymptotic random expressions of the two tests under the null hypothesis and show that under some mild conditions, the asymptotic null distribution of the quasi-GPF test is a chi-squared-type mixture whose distribution can be well approximated by a simple-scaled chi-squared distribution. We also propose a random permutation method for approximating the null distributions of the quasi-GPF and Fmax tests. The asymptotic distributions of the two tests under a local alternative are also investigated and the two tests are shown to be root-n consistent. A theoretical power comparison between the quasi-GPF test and the L2-norm-based test proposed in the literature is also given. Simulation studies are presented to demonstrate the finite-sample performance of the new tests against five existing tests. An illustrative example is also presented. Supplementary materials for this article are available online.
报告题目：Forward variable selection for sparse ultra-high dimensional varying coefficient modes
报告提纲：Abstract
In this paper, we propose forward variable selection procedures for feature screening in ultra-high-dimensional generalized varying coefficient models. We employ regression spline to approximate coefficient functions and then maximize the log-likelihood to select an additional relevant covariate sequentially. If we decide we do not significantly improve the log-likelihood any more by selecting any new covariates from our stopping rule, we terminate the forward procedures and give our estimates of relevant covariates. The effect of the size of the current model has been overlooked in stopping rules for sequential procedures for high-dimensional models. Our stopping rule takes into account the size of the current model suitably. Our forward procedures have screening consistency and some other desirable properties under regularity conditions. We also present the results of numerical studies to show their good finite sample performances
报告题目：The study of long-term HIV dynamics using semiparametric nonlinear mixed-effects models
报告提纲：Abstract
Modelling HIV dynamics has played an important role in understanding the pathogenesis of HIV infection in the past several years. Non-linear parametric models, derived from the mechanisms of HIV infection and drug action, have been used to fit short-term clinical data from AIDS clinical trials. However, it is found that the parametric models may not be adequate to fit long-term HIV dynamic data. To preserve the meaningful interpretation of the short-term HIV dynamic models as well as to characterize the long-term dynamics, we introduce a class of semi-parametric non-linear mixed-effects (NLME) models. The models are non-linear in population characteristics (fixed effects) and individual variations (random effects), both of which are modelled semi-parametrically. A basis-based approach is proposed to fit the models, which transforms a general semi-parametric NLME model into a set of standard parametric NLME models, indexed by the bases used. The bases that we employ are natural cubic splines for easy implementation. The resulting standard NLME models are low-dimensional and easy to solve. Statistical inferences that include testing parametric against semi-parametric mixed-effects are investigated. Innovative bootstrap procedures are developed for simulating the empirical distributions of the test statistics. Small-scale simulation and bootstrap studies show that our bootstrap procedures work well. The proposed approach and procedures are applied to long-term HIV dynamic data from an AIDS clinical study. Copyright © 2002 John Wiley & Sons, Ltd
报告人简介：
张金廷教授是新加坡国立大学概率统计系终身教授，博士生、博士后导师。1988年在北京大学取得学士学位，1991年在中国科学院应用数学所取得硕士学位，1999年在美国北卡罗来纳大学教堂山分校获得博士学位，2000年在美国哈佛大学做博士后。张金廷教授先后在美国普林斯顿、罗彻斯特等大学做高级访问学者。张教授培养了十名硕士和七位博士以及八位博士后，其主要学术成果发表在Annals of Statistics（世界统计年刊），JASA（美国统计学会杂志），JRSSB（英国皇家统计学会杂志），Statistics Sinica（统计学报）等统计学国际顶级期刊上，约计50余篇；著有两本英文统计学专著 《函数数据方差分析》《Analysis of Variance for Functional Data》和《丛向数据非参数回归方法》《Nonparametric Regression Methods for Longitudinal Data Analysis》，以及一本学术论文集。现任和曾任多家重要学术期刊的副主编或者编委，并先后六次担任大型国际会议的组织委员。张教授现在的研究领域包括非参数统计，纵向数据分析，函数数据分析，高维数据分析等。
