The Statistics Seminar has talks on a variety of topics. For more information contact Yongli Sang.
During the Spring 2019 semester we will meet on Friday from 10:00-11:00 in Maxim Doucet Hall room 209.
22 February 2019
Jackknife Empirical Likelihood Approach for K-sample Tests via Energy Distance
Abstract: Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the equality of K (K at least 2) distributions in this talk. By applying the jackknife empirical likelihood approach, the standard limiting chi-square distribution with degree freedom of K-1 is established and is used to determine critical value and p-value of the test. Simulation studies show that our method is competitive to existing methods in terms of power of the tests in most cases. The proposed method is illustrated in an application on a real data set.
14 March 2019 (THURSDAY in room 208)
Fourier transform and project methods in kernel entropy estimation for linear processes
University of Mississippi
Abstract: Entropy is widely applied in the fields of information theory, statistical classification, pattern recognition and so on since it is a measure of uncertainty in a probability distribution. The quadratic functional plays an important role in the study of quadratic Renyi entropy and the Shannon entropy. It is a challenging problem to study the estimation of the quadratic functional and the corresponding entropies for dependent case. In this talk, we consider the estimation of the quadratic functional for linear processes. With a Fourier transform on the kernel function and the projection method, it is shown that, the kernel estimator has similar asymptotical properties as the i.i.d. case studied in Gine and Nickl (2008) if the linear process (X_n: n \in N) has the defined short range dependence. We also provide an application to L_2^2 divergence and the extension to multivariate linear processes. The simulation study for linear processes with Gaussian and \alpha-stable innovations confirms the theoretical results. As an illustration, we estimate the L_2^2 divergences among the density functions of average annual river flows for four rivers and obtain promising results. This is a joint work with Yongli Sang and Fangjun Xu.
During the Fall 2018 semester we will meet on Friday from 11:00-12:00 in Maxim Doucet room 212.
31 August 2018
Fiducial Inference with Applications
Abstract: Fiducial distribution for a parameter is essentially the posterior distribution with no a prior distribution on parameters. In this talk, we shall describe Fisher's method of finding a fiducial distribution for a parameter and fiducial inference through examples involving well-known distributions such as the normal and related distributions. We then describe the approach for finding fiducial distributions for the parameters of a location-scale family and illustrate the approach for the Weibull distribution. In particular, we shall see fiducial methods for finding confidence intervals, prediction intervals, prediction limits for the mean of a future sample. All the methods will be illustrated using some practical examples.
7 September 2018
Fiducial Inference with Applications, part 2
Abstract: In the second part of this seminar series, we shall develop fiducial distributions for gamma parameters and show some applications. We then provide fiducial solutions for correlation analysis in a multivariate normal setup. For discrete distributions, we outline two different approaches of finding fiducial distributions, and illustrate the methods for the binomial, Poisson and hypergeometric distributions. Advantages our fiducial approach over other large sample approaches will be illustrated through some applications. Finally, fiducial inference for a mixture distribution will be described.
14 September 2018
Jackknife Empirical Likelihood for Gini Correlations
Abstract: The Gini correlation plays an important role in measuring dependence of random variables with heavy tailed distributions, whose properties are a mixture of Pearson's and Spearman's correlations. Due to the structure of this dependence measure, there are two Gini correlations between each pair of random variables, which are not equal in general. Both the Gini correlation and the equality of the two Gini correlations play important roles in Economics. In the literature, there are limited papers focusing on the inference of the Gini correlations and their equality testing. We have developed the jackknife empirical likelihood (JEL) approach for the single Gini correlation, for testing the equality of the two Gini correlations, and for the Gini correlations' differences of two independent samples. The standard limiting chi-square distributions of those jackknife empirical likelihood ratio statistics are established and used to construct confidence intervals, rejection regions, and to calculate $p$-values of the tests.
21 September 2018
The Ultimate Antithesis of Asymptotic Theory: Estimation with a Sample of Size 1
Abstract: Many statistical results depend heavily on the asymptotic theory which provides us a guidance by using a 'large sample' approach. This is also the foundation of several widely used tools like the Central Limit Theorem or the Laws of Large Numbers. In this seminar talk we will explore the total opposite of the asymptotic theory that deals with statistical inferences with a single observation. We are going to review some interesting existing results, and discuss about potential open problems.
28 September 2018
Correlation and regression analyses involving circular variables
Abstract: Bivariate data involving circular variables arise in many areas of research. Some examples are: wind directions at 6 am and at noon at an observatory station, dihedral angles in the protein folding problem, positions of homologous genes in two circular RNAs, phase angles between two living tissues, amount of rain fall and wind direction, and orientation of bird’s nest and direction of creek flow. In this talk, I will present correlation and regression analyses of bivariate data involving one or both circular variables.
19 October 2018
Highest posterior mass prediction intervals for binomial and poisson distributions
Abstract: The problems of constructing prediction intervals(PIs) for the binomial and Poisson distributions are considered. New highest posterior mass (HPM) PIs based on fiducial approach are proposed. Other fiducial PIs, an exact PI and approximate PIs are reviewed and compared with the HPM-PIs. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are less conservative than other fiducial PIs and comparable with the approximate one based on the joint sampling approach for the binomial case. For the Poisson case, the HPM-PIs are better than the other PIs in terms of coverage probabilities and precision. The methods are illustrated using some practical examples.
26 October 2018
Confidence intervals for the mean and a percentile based on zero-inflated lognormal data
Md Sazib Hasan
Abstract: The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include zeros, a simple confidence interval (CI) that is obtained by modifying Tian’s [Inferences on the mean of zero-inflated lognormal data: the generalized variable approach. Stat Med. 2005;24:3223—3232] generalized CI, is proposed. A fiducial upper confidence limit (UCL) and a closed-form approximate UCL for an upper percentile are developed. Our simulation studies indicate that the proposed methods are very satisfactory in terms of coverage probability and precision, and better than existing methods for maintaining balanced tail error rates. The proposed CI and the UCL are simple and easy to calculate. All the methods considered are illustrated using samples of data involving airborne chlorine concentrations and data on diagnostic test costs.
During the Spring 2018 semester we will meet on Fridays from 2:00-3:50 in Maxim Doucet Hall room 211.
23 February 2018
An Introduction to Circular Statistics
Abstract: In many diverse scientific fields, the measurements are directions. Examples are directions of flight of a bird in Biology, of wind in Meteorology, of protein folding in Bioinformatics, of knee flexion in Medicine, etc. In this first talk of a series on Circular Statistics, I will start with those unique features and challenges dealing with circular data, then discuss some summary measures in Circular Statistics.
9 March 2018
Probability Models for Circular Data
Abstract: In this talk, I will first go over some of the methods that one can construct a circular probability distribution and summarize some common distributions used in Circular Statistics. Then, I will discuss some properties of the asymmetric generalized von Mises (AGvM) distribution proposed in Kim and SenGupta (2013). A real data example will be provided to illustrate the practical utility of the AGvM distribution.
16 March 2018
Inferences for a Skew-Normal Distribution
Abstract: A three parameter Skew-Normal distribution (SND), which is an interesting generalization of the usual two parameter normal distribution, is getting a lot of attention lately due to its flexibility to accommodate both positively skewed as well as negatively skewed shapes, apart from the symmetric shape, to model various types of datasets. Though a lot of work has been done to characterize SND, and deriving many of its distributional properties, relatively less efforts have been devoted to inferences on the model parameters due to some intrinsic complexities. In this talk we will focus on estimation of the location parameter along with some other interesting results.
23 March 2018
Hierarchical Bayesian Models for Continuous and Positively Skewed Data From Small Areas
University of Houston
Abstract:The log-transformation is widely used to deal with skewed data, however it could be problematic due to the back transformation. In this talk, I will present hierarchical Bayesian models for continuous and positively skewed random variable without logarithmic transformation using three distributions: exponential, gamma and generalized gamma. In these models, a second order Taylor series Laplace approximation is used to ease computational difficulties due to complex forms of the posterior and conditional posterior distributions. The utility of the proposed models will be illustrated using the generalized gamma model applied to small area estimations in the Nepal census data.
13 April 2018
Memory properties of transformations of linear processes
Abstract: We study the memory properties of transformations of linear processes. Dittmann and Granger (2002) studied the polynomial transformations of Gaussian FARIMA(0,d,0) processes by applying the orthonormality of the Hermite polynomials under the measure for the standard normal distribution. Nevertheless, the orthogonality does not hold for transformations of non-Gaussian linear processes. Instead, we use the decomposition developed by Ho and Hsing (1996, 1997) to study the memory properties of nonlinear transformations of linear processes, which include the FARIMA(p,d,q) processes, and obtain consistent results as in the Gaussian case. In particular, for stationary processes, the transformations of short-memory time series still have short-memory and the transformation of long-memory time series may have different weaker memory parameters which depend on the power rank of the transformation. On the other hand, the memory properties of transformations of non-stationary time series may not depend on the power ranks of the transformations. This study has application in econometrics and financial data analysis when the time series observations have non-Gaussian heavy tails.
20 April 2018
Abstract: R Markdown provides an authoring framework for data science and statistics. You can use a single R Markdown file to save and execute code, generate high quality reports that can be shared with an audience. R Markdown support multiple languages including R, Python, and SQL, as well as dozens of static and dynamic output formats including HTML, PDF, MS Word, Beamer, HTML5 slides, Tufte-style handouts, books, dashboards, shiny applications, scientific articles, websites, and more.