3:00-4:00pm, March 04, 2022, Virtual Statistics Seminar, Webex Meeting Link:
https://gsumeetings.webex.com/gsumeetings/j.php?MTID=ma826129ec840a83218204e4cf7a983ec ,
Dr. Xinyi Li,
Assistant Professor, School of Mathematical and Statistical Sciences, Clemson University,
Spline Smoothing of 3D Solid Models
Abstract:
Over the past two decades, we have seen an exponentially increased amount of point clouds collected in various areas such
as geography, environmental sciences, computer graphics, engineering, economics, and medical imaging. These point clouds
are usually collections of enormous measurements in space defined by an arbitrary coordinates system, and thus they can
also be viewed as a special type of geospatial data. Most existing modeling works focus on reconstructing and modeling
the shape based on the point clouds. However, these point clouds usually contain
other information besides coordinates, such as the brain activity level in neuroimaging and the grade and type of minerals
in the mining industry. Unfortunately, there has been little exploration of the underlying signal and building up a
3D solid model from the point cloud of irregular shapes. To achieve this goal, we propose a class of penalized spline
smoothing methods based on the multivariate spline over the tetrahedral partitions in this paper. The proposed method
can be used to solve the missing data problem, denoise or deblur the point cloud effectively, and provide a multi-resolution
reconstruction of the actual signal. Furthermore, we investigate the theoretical support of the proposed method.
Specifically, we establish the convergence rate and asymptotic normality of the proposed estimator and illustrate
that the convergence rate achieves the optimal nonparametric convergence rate, and the asymptotic normality holds uniformly.
Finally, several simulation examples are conducted to investigate the estimation and prediction performance of the proposed
method and compare it with traditional smoothing methods.
3:00-4:00pm, February 18, 2022, Virtual Statistics Seminar, Webex Meeting Link:
https://gsumeetings.webex.com/gsumeetings/j.php?MTID=m468cb4825270a23007ef366089534d94 ,
Dr. Ting Zhang,
Associate Professor, Department of Statistics, University of Georgia,
High Quantile Regression for Tail Dependent Time Series
Abstract:
Quantile regression serves as a popular and powerful approach for studying the effect of regressors on quantiles of
a response distribution. However, existing results on quantile regression were mainly developed when the quantile
level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the
situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena;
and (ii) the data are no longer independent but collected as a time series that can exhibit serial dependence in both
tail and non-tail regions. To study the asymptotic theory for high quantile regression estimators in the time
series setting, we introduce a previously undescribed tail adversarial stability condition and show that it leads
to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial
dependence in the tail region but are not necessarily strong mixing. Numerical experiments are provided to illustrate
the effect of tail dependence on high quantile regression estimators, where simply ignoring the tail dependence may lead to misleading p-values.
2:00-3:00pm, November 19, 2021, Virtual Colloquium, Webex Meeting Link:
https://gsumeetings.webex.com/gsumeetings/j.php?MTID=mdcc459e78d6e1b68c54f4c484445b641,
Dr. Din Chen,
Professor and Executive Director in Biostatistics,
College of Health Solutions, Arizona State University,
Distinguished Lecture: Integrative Data Harmonization and Statistical Meta-Analysis
Abstract:
Data harmonization and Meta-analysis (MA) is a common statistical approach in evidence-based public health research to
combine meta-data from diverse studies to reach a more reliable and efficient conclusion. It can be performed by either
synthesizing study-level summary statistics (MA-SS) or modeling individual participant-level data (MA-IPD), if available.
However, it remains not fully understood whether the use of MA-IPD indeed gains additional efficiency over MA-SS.
In this talk, we review the classical fixed-effects and random-effects meta-analyses, and further discuss the relative efficiency
between MA-SS and MA-IPD under a general likelihood inference setting. We show theoretically that there is no gain of
efficiency asymptotically by analyzing MA-IPD, provided that the random-effects follow the Gaussian distribution, and maximum likelihood
estimation is used to obtain summary statistics.
Our findings are further confirmed by extensive Monte-Carlo simulation studies and real data analyses.
3:00-4:00pm, November 05, 2021, Virtual Statistics Seminar, Webex Meeting Link:
https://gsumeetings.webex.com/gsumeetings/j.php?MTID=m4dc1b297c92bfaae1d4ee4d1e53d1574 ,
Dr. Yongli Sang,
Department of Mathematics, University of Louisiana at Lafayette,
Depth-based Weighted Jackknife Empirical Likelihood for Non-smooth U-structure Equations
Abstract:
In many applications, parameters of interest are estimated by solving some non-smooth estimating equations with a U-statistic structure.
Jackknife's empirical likelihood (JEL) approach can solve this problem efficiently by reducing the computation complexity of the empirical likelihood (EL)
method. However, like EL, JEL suffers the sensitivity problem to outliers. In this paper, we propose a weighted jackknife empirical likelihood (WJEL)
to tackle the above limitation of JEL. The proposed WJEL tilts the JEL function by assigning smaller weights to outliers.
The asymptotic of the WJEL ratio statistic is derived. It converges in distribution to a multiple of a chi-square random variable.
The multiplying constant depends on the weighting scheme. The self-normalized version of WJEL ratio does not require knowing the constant
and hence yields the standard
chi-square distribution in the limit. The robustness of the proposed method is illustrated by simulation studies and one real data application.