Department of Mathematics

Statistics Research Seminar

The Statistics Research Seminar is held from 4:30 pm - 5:30 pm on Tuesday afternoons in Bruner 305.
If you are interested in presenting a talk please contact Dr. Lukun Zheng to schedule a date.


The Spring 2016 seminar schedule is
:

Tuesday, February 23, 2016

Speaker: Dr. Lukun Zheng

Title: One-Way High Dimensional ANOVA

In this talk, we will consider the one way ANOVA in the high dimensional setting. We introduce a new test statistic using the smooth truncation method. The limiting null and alternative distributions of the statistic and the power of the test are analyzed. It is shown that the test is robust to dimensional increase, i.e. the power of the test is just slightly affected by the high dimensional nature of the data. A simulation study is carried out to examine the numerical performance of the test and to compare it with the F test. The results show that the proposed test significantly outperforms the F test in a range of settings.

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Tuesday, February 16, 2016

Speaker: Dr. Lukun Zheng

Title: Markov chains with periodically changing environment and central limit theorem

This talk is a continuation of our last talk. In this talk, I will specifically discuss Markov chains with periodically changing environment. Several central limit theorems will be provided. Several statistical testing procedures will also be introduced.

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Tuesday, February 2, 2016

Speaker: Dr. Lukun Zheng

Title: Statistical inferences about Markov Chains

In this talk, we will firstly review some important concepts and definitions of Markov chain. Then we will introduce MLE for the transition matrix of a finite-state Markov Chain. We will also discuss the statistical testing on 1) if the order of the MC is one; 2) if the transition matrix is a given matrix. Some unpublished new ideas will also be discussed.

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The Fall 2015 seminar schedule is:

Thursday, November 19, 2015

Speaker: Dr. Lukun Zheng

Title: A new diversity estimator induced by birthday problems.

Abstract: The maximum likelihood estimator (MLE) of Gini-Simpson’s diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We propose a new estimator of the GS index and show its unbiasedness. Asymptotic normality of the proposed estimator is established when the number of species in the population is finite and known, finite but unknown, and infinite. Simulations demonstrate advantages of our estimator over the MLE, and a real example for the extinction of dinosaurs endorses the use of our approach.

Keywords. Diversity measure; Gini-Simpson’s index; Birthday problem; U Statistics.

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Thursday, November 12, 2015

Speaker: Dr. David Smith

Title: Improving small sample inference for the GPD via an MCMC adjusted profile likelihood.

Estimation methods for the parameters of the Generalized Pareto distribution have been well studied. While maximum likelihood methods may yield adequate results for estimation and inference in the case for the shape parameter between -.5 to 5 and large sample sizes, very little has been done for cases of small sample sizes. Small sample sizes can occur when fitting the exceedances over a threshold. We study an adjustment made to the signed root of the likelihood ratio statistic and make comparisons of the significance function and profile likelihood-based confidence intervals to the standard method. Considerable improvement is shown for small samples by making the adjustment. The adjustment that we make is easily derived through simulations and do not require complex calculations that are often required to condition on ancillary statistics. Several examples are given to demonstrate the method.

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Thursday, November 5, 2015

Speaker: Dr. Lukun Zheng

He will give a talk on quantile regression. It is widely used in modern statistics, econometrics, and so on. It is a type of regression analysis aiming at the conditional quantiles of a response Y, given the values of the independent variables X=x. We will set up the problem, discuss the advantages and disadvantages, and give some guidelines in applications.

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Thursday, October 29, 2015

Speaker: Dr. Lukun Zheng

Dr. Zheng will continue his talk on support vector machines (SVU). He will mainly focus on soft margin SVU, in which case the data can't be linearly separated. The hinge loss will also be discussed in the application of SVU.

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Thursday, October 22, 2015

Speaker: Dr. Lukun Zheng

He will give a talk on support vector machines(SVU). It is to analyze data and recognize patterns, used for classification and regression analysis. SVU was developed in the area of computer science in 1990s and has been grown in popularity since then. Several important and popular models will be discussed which are applicable to cases with linear or nonlinear class boundaries.

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Thursday, October 8, 2015

Speaker: Dr. Lukun Zheng

He will give a talk on cross-validation. The main purpose of cross-validation is to combine the prediction error and to derive a more accurate model. It is commonly used to measure the predictive performance of a statistical model. Several commonly used cross-validation methods will be introduced. We will also discuss the application of cross-validation on regression and classification problems.

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Thursday, October 1, 2015

Speaker: Dr. Lukun Zheng

He will give a talk on Kernel smoothing methods, which is widely used in many areas of data analysis. It is a generalization of the nearest neighbor regression methods by introducing weights using a kernel function. We will introduce the basic ideas of it, and also give some popular kernel smoothing techniques together with examples for applications.

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Thursday, Sept. 24th, 2015

Speaker: Dr. Lukun Zheng

He will give a talk on Spline functions in data analysis. The idea of spline regression will be introduced with some real life examples. The advantages of spline regression over non-linear polynomial regression models will be discussed. We will also discuss some potential challenges when using Spline methods and some ways to overcome these challenges.