**Probability & Statistics Seminar**

**Seminars for Spring 2024**

9:00am – 9:50am

**Dr Paramahansa Pramanik**

University of South Alabama

**On Estimation of Function-on-function Regression Kernels with Brownian Berkson Errors.**

In this paper, we introduce a new methodology to determine an optimal kernel of function-on-function regression in the presence of a stochastic differential equation with Berkson error. We assume that the response variable, unobserved true predictor, the best available observed measure of the true predictor, and the regression kernels are functions of space and time, and the regressor dynamics follow a stochastic differential equation. First, we construct an objective function as a time-dependent Mean Square Error (MSE) and then minimize it with respect to regression coefficients subject to stochastic Berkson error dynamics. A Feynman-type path integral control approach is used to determine a Wick-rotated Schrodinger-type equation that has the complete information of the system. Using first-order conditions for these kernels give us a closed-form solution.

9:00am – 9:50am

**Dr. Xiang Huang**

Vanderbilt University

**Testing and estimating treatment effect in the presence of delayed onset of the effect for cancer immunotherapies **

The standard log-rank test has been extended by adopting various weight functions. Cancer vaccine or immunotherapy trials have shown a delayed onset of effect for the experimental therapy. This is manifested as a delayed separation of the survival curves. We propose new weighted log-rank tests to account for such delay. We implement a numerical evaluation of the Schoenfeld approximation (NESA) for the mean of the test statistic. The NESA enables us to assess the power and to calculate the sample size for detecting such delayed treatment effect and also for a more general specification of the non-proportional hazards in a trial. Extensive simulation studies are conducted to compare the performance of the proposed tests with the standard log-rank test and to assess their robustness to model mis-specifications. Our tests outperform the Gρ,γ class in general and have performance close to the optimal test. We demonstrate our methods on two cancer immunotherapy trials.

9:00am – 9:50am

**Dr Huybrechts Bindele**

University of South Alabama

**Rank-based Estimating Equation with non-ignorable missing responses via empirical likelihood**

In this talk, we will consider a general regression model with responses missing not at random. We will consider a rank-based estimating equation of the regression parameter from which a rank-based estimator will be derived. Based on its asymptotic normality property, a consistent sandwich estimator of the corresponding asymptotic covariance matrix is developed. In order to overcome the under coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different missing mechanisms will be considered, and the simulation results will show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A real data example will be provided to illustrate our methods.

See Previous Seminars

**Previous Statistics Seminars**

9:00am – 9:50am

**Dr. Kalimuthu Krishnamoorthy**

University of Louisiana

**Fiducial Inference with Applications**

Fiducial distribution for a parameter is essentially the posterior distribution with no a prior distribution on the parameter. 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 binomial. We then describe the approach for finding fiducial distributions for the parameters of a location-scale family. In particular, we shall see fiducial methods for finding confidence intervals, prediction intervals and prediction limits for the mean of a future sample. Application to analysis of zero-inflated lognormal data will also be discussed. All the methods will be illustrated using some practical examples.

9:00am – 9:50am

**Dr. Ngartelbaye Guerngar (Serge)**

University of North Alabama

**Phase transition for Fractional Stochastic Partial Differential Equations in Bounded Domains **

Stochastic partial differential equations (SPDEs) are partial differential equations (PDEs) with a random component. They have many applications in many areas of science and engineering. In this talk, I will discuss an interesting property of the solution of an SPDE driven by a Gaussian noise in a bounded domain. This is based on my joint work with E. Nane (Auburn University) and M. Foondun (University of Strathclyde).

9:00am – 9:50am

**Mr. Thierry Taning Longla**

PhD Student and Data analyst, Yildiz Technical University (Turkey)

**Investigating the robustness of wireless sensor networks**

Human designs are susceptible to being corrupted by errors or failures. Many social and natural systems have strange abilities to resist failures and maintain basic functions even when some of their components fail. Robustness is a key question in many disciplines, such as biology, economics, and security, just to mention a few. The evolution of telecommunications nowadays has made the world a small village. The arrival of 5G and 6G has boosted the digitization and proliferation of the Internet of Things, with sensors as key elements. Depending on the environment where sensors are deployed, these networks are subject to several constraints, necessitating the design of robust systems for them. In this project, a robustness analysis of complex networks, particularly sensor networks, was done. Sensor devices here are viewed as vertices, the wireless link between the nodes as edges, and the information exchange between the nodes as weights. We did an investigation of the effect of node removal in complex networks. To quantify or assess the level of robustness of wireless sensor networks, we used the inverse percolation and the Laplacian matrix fielder value. We interpret the results of our experiments. and proposed some topologies to be used in building robust sensor networks. Python programming language was used for simulations and computations. In addition, we use network software such as Pajek and yED for visualization and analysis.

9:00am – 9:50am

**Dr. Qingyang Zhang**

University of Arkansas

**On relationships between Chatterjee’s and Spearman’s correlation coefficients **

In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this talk, we will study the probabilistic relationships between Chatterjee’s correlation and the widely used Spearman’s correlation. We will show that, under independence, the two sample-based correlations are asymptotically joint normal and asymptotically independent. For dependent variables, we will establish some extremal cases featuring large differences between these two metrics. Motivated by these findings, a new independence test is proposed by combining Chatterjee’s and Spearman’s correlations into a maximal strength measure of variable association. We will use both simulated data and a real-world dataset to show the good sensitivity of the new test to different correlation patterns.

9:00am – 9:50am

**Dr. Melik Masarifoglu**

Senior Data Analyst at NMQ Digitals (Turkey)

**Predictive Analytics for E-Commerce Sales**

Consider a hotel chain that wants to predict how many customers will stay in a certain location this weekend so they can ensure they have enough staff and resources to handle . Steward Health Care, the largest for-profit private hospital operator in the United States (38 hospitals). They predicted hospital volume. Why? They found out that during peaks in patient volume, the hospital is often understaffed, and during valleys in patient volume, the hospital is often overstaffed. This is highly inefficient, and typically leads to hospitals incurring extremely high expenses for on-call staff and overtime pay . With predictive analytics, they saved 2 million dollars (just eight of the 38 hospitals in Steward’s network). Energy Companies predict energy consumption to manage capacity planning. This talk is about such applications of predictive analytics.

9:00am – 9:50am

**Wilfried Youmbi**

Department of Economics at the University of Western Ontario

**Nonparametric Analysis of Random Coalitional Multi-Utility Models **

In this paper, we study a method for testing the rational behavior of a population of consumers when observed choice data reveal a non-transitive preference relation. To this end, we develop a stochastic version of the coalitional multi-utility (CMU) model developed in Aguiar et al. (2022). The motivating application is to test the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational consumers with complete, but not necessarily transitive, preference relations. We test a necessary and sufficient condition that does not rely on any restriction on unobserved heterogeneity or the number of goods. We provide an empirical characterization of this novel stochastic choice model and show that this characterization can be tested statistically. We also show how to evaluate the welfare implications of an observed price change. This work is a generalization of Kitamura & Stoye (2018)’s work on the nonparametric test of random utility models (RUM) for finite choice sets to situations where preferences are not transitive. We apply the new test to the UK Family Expenditure Survey (FES) and find evidence against RUM, while the random CMU model is not rejected in the dataset.

11:00am – 12:00pm

**Dr. Theophile Bougna Lonla**

World Bank Economist

**Poverty and transport modeling: Perspectives offered by Big Data and Machine Learning**

Data and good models are at the forefront of all efficient decision-making processes, especially for poverty alleviation and transport planning. Technological advancement and the recent developments in ‘Big Data’ and machine learning provide useful information and methods that are nice complements to data collected through conventional methods and traditional models. The identification of key challenges and the current knowledge gaps in poverty and transport modeling are explored. Practical examples of how machine learning and big data are combined with statistical and economic models to tackle poverty and transport challenges. Promising areas for future opportunities and research, including new data collection, data analytics, and application development to support and inform policymakers’ decisions are also discussed.

11:00am – 12:00pm

**Chathurika Abeykoon**

University of Mississippi

**The Double Descent Behavior In Two Layer Neural Network For Binary Classification**

Recent studies observed a surprising concept about test error called the double descent phenomenon where the increasing model complexity decreases the test error first and then the error increases and decreases again. To observe this, we worked on a two-layer neural network model with a ReLU activation function designed for binary classification under supervised learning. Our aim was to observe and find the mathematical concept behind the double descent behavior of the test error in the model for varying over-parameterization and under-parameterization ratios. We have been able to derive a closed-form solution for the test error of the model and a theorem to find the parameters with optimal empirical loss when model complexity increases. We proved the existence of the double descent phenomenon in our model for square loss function using the theorems derived.

11:00am – 12:00pm

**Dr. Jeremy Clark**

University of Mississippi

**On two-dimensional Brownian motion singularly tilted through a point potential**

A well-known but interesting characteristic of two-dimensional Brownian motion is that it will (almost surely) never return exactly to the origin even though it will reenter any given small neighborhood of the origin infinitely many times. I will discuss a two-dimensional diffusion process closely connected to Brownian motion

that has just enough drift towards the origin to enable it to return there. This opens up the possibility of formulating a theory of its local time, a characterization of the time spent in the vicinity of the origin. The transition probabilities for this diffusion process are defined through an integration kernel that has arisen in recent articles on the two-dimensional stochastic heat equation. The work that I will present is in collaboration with Barkat Mian.

11:00am – 12:00pm

**Dr. Xin Dang**

University of Mississippi

**Feature screening for ultrahigh-dimensional classification via Gini distance correlation**

Gini distance correlation (GDC) was recently proposed to measure dependence between a categorical variable and numerical random vector. In this talk, we utilize the GDC to establish a feature screening for ultrahigh-dimensional classification where the response variable is categorical. It can be used for screening individual features as well as grouped features. The proposed procedure possesses several appealing properties. It is model-free. No model specification is needed. It holds the sure independence screening property and the ranking consistency property. The proposed screening method can deal with the case that the response has divergent number of categories. Simulation and real data applications are presented to compare performance of the proposed screening procedure.

11:00am – 12:00pm

**Mathias Muia Nthiani & Mous-Abou**

University of Mississippi

**A point on discrete vs continuous state-space markov chains/A comparison of estimation techniques for copula-based Markov chains**

In this talk a Bernoulli Markov chain based on the Mardia copula family is considered. We obtain estimators for the parameters in the structure of the Markov chain and provide their confidence intervals. Moreover, for Markov chains generated by symmetric copulas with uniform marginals we provide new estimators and confidence intervals for copula parameters by considering several families of copulas introduced in Longla(2023). A simulation study is provided with a comparison to other known estimators such as the MLE and that of Longla and Peligrad (2021). We then make a comparison of discrete versus continuous state-space Markov chains.

11:00am – 12:00pm

**Dr. Olivier Menoukeu Pamen**

University of Liverpool, UK

**A uniqueness and smoothness result for multidimensional SDE’s on the plane with nondecreasing coefficient**

In this talk, we discuss the path by path uniqueness for multidimensional stochastic differentialequations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, ver-ifies a spacial linear growth condition and is componentwise nondeacreasing. We first show theresult for bounded and measurable drift. Our proofs rely on a local time-space representation ofBrownian sheet and a type of law of the iterated logarithm for the Brownian sheet. The result inthe unbounded case then follows by using the Gronwall’s lemma on the plane. Under boundednessof the solution, we also prove that the obtained solution is Malliavin smooth.This talk is based on a joint work with A. M. Bogso and M. Dieye.

11:00am – 12:00pm

**Dr. Martial Longla**

University of Mississippi

**Exchangeable copulas and m-dependent copulas**

I will talk about a new set of copulas that I have been dealing with. I obtained these copulas while searching for conditions to have a Markov chain that is exchangeable. In the process, I was dragged into m-dependent Markov chains, and ended up providing a characterization of some families of copulas that I call m-dependent copulas, idempotent copulas and exchangeable copulas. Exchangeable copulas remind me of De Finetti’s theorem. The large sample theory of parameter estimators has been done for these families under The assumption that the Data has uniform marginal distribution.

**Louis Aimé FONO**

Research Group in Applied Mathematics for Social Science

University of Douala-Cameroon

**On Some Probability Distributions of Customer Sensitivity for Premium Renewal in Non-life Insurance**

Every year, non- life insurers face the recursing problem of adjusting premium. This problem comes from the trade-off between the need of increasing the global revenue of the company and the need of retention of the existing customers of the portfolio. Traditional pricing methods (General Linear Model or Credibility Theory) solve this problem by a static approach and they do not take into account the customer sensitivity and/or the prices offered by competing companies. Elena et al. [1] formalized and solved the pricing renewal problem of a non-life insurance company by using a dynamic approach based on reinforcement learning (Markov Decision Problem). The insurer has a portfolio of costumers and therefore a total turnover (initial state). At the time of contract renewal, the insurer (agent) offers a renewal premium to the first insured (we say that the agent takes action). Whether or not the insured accepts the renewal premium, his decision leads the company to a new state (new income and new retention). Then, taking into account the new situation of the company, the insurer repeats sequentially the same action to all the others insureds in the portfolio.

This paper extends and improves the model of Elena et al. in various circumstances. More precisely, we propose some families of probability distributions that take into consideration sensitivity of insurers to the new premiums. We rewrite the Elena et al.’s model by replacing regression probability by the obtained probability distributions and we obtain our new pricing models. We find the best strategy for insurer to set renewal price through reinforcement learning algorithms. The implementation of the newly obtained reinforcement models on a portfolio of contracts by using backward SARSA( ) learning agent yields better results than those obtained by Elena and al. [1]. Keywords: Pricing renewal in Non-life insurance; Reinforcement learning; Customer sensitivity; Customer renewal probabilities.

References

[1] Elena K. and Garcia J., Maestre R. and Fernandez F. (2019) Reinforcement learning for pricing strategy optimization in the insurance industry, Engineering Applications of Artificial Intelligence, 80 (C) 8-19. https://doi.org/10.1016/j.engappai.2019.01.010

[2] Ngnié F.C. Mbama E.B., Fotso S. and Fono L.A. (2021) On the study of premium renewal problem in non-life insurance based on two families of customer renewal probability through reinforcement learning. Online Astin Colloquia.

**Xinyuan Chen**

Assistant Professor of Statistics

Mississippi State University

**A Bayesian Machine Learning Approach for Estimating Heterogeneous Survivor Causal Effects: Applications to a Critical Care Trial**

Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development of tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for specific subgroups of participants, therefore requiring the principal stratification framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate models for the potential outcomes and latent strata membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home, but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and source of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field. We also demonstrated through a simulation study that our proposed Bayesian machine learning approach outperforms other parametric methods in reducing the estimation bias in both the average causal effect and heterogeneous causal effects for always-survivors.

**Ngongo Isidore Seraphin**

ENS, Universite de Yaounde 1, Cameroun.

**Inference for nonstationary time series of counts with application to change-point problems**

We consider an integer-valued time series Y = (Yt)t∈Z where the model after a time k∗ is Poisson

autoregressive with the conditional mean that depends on a parameter θ∗ ∈ Θ ⊂ Rd. The structure of the

process before k∗ is unknown; it could be any other integer-valued time series, that is, the process Y could

be nonstationary. It is established that the maximum likelihood estimator of θ∗ computed on the nonstationary

observations is consistent and asymptotically normal. Subsequently, we carry out the sequential

change-point detection in a large class of Poisson autoregressive models. We propose a monitoring scheme

for detecting change in the model. The procedure is based on an updated estimator, which is computed

without the historical observations. The asymptotic behavior of the detector is studied, in particular, the

above results of inference in a nonstationary setting are applied to prove the consistency of the proposed

procedure. A simulation study as well as a real data application are provided.

Keywords: Time series of counts, Poisson autoregression, likelihood estimation, change-point, sequential

detection, weak convergence.

**Huybrechts Bindele**

University of South Alabama

**Robust estimation and selection for single-index regression model**

In this talk, we will consider a single-index regression model, from which we will discuss a robust estimation procedure for the model parameters and an efficient variable selection of relevant predictors. The proposed approach known as the penalized generalized signed-rank procedure will be introduced. Asymptotic properties of the resulting estimators will be discussed under mild regularity conditions. Extensive Monte Carlo simulation experiments will be carried out to study the finite sample performance of the proposed approach. The simulation results will demonstrate that the proposed approach dominates many of the existing ones in terms of robustness in estimation and efficiency of variable selection. Finally, a real data example will be discussed to illustrate the method.

**Magda Peligrad**

University of Cincinnati

**The CLT for stationary Markov chains with trivial tail sigma field**

In this talk we consider stationary Markov chains with trivial two-sided tail sigma field and present the tools leading to the following result: Any additive functional of such a Markov chain satisfies the central limit theorem provided the variance of partial sums divided by n is bounded.

The method is based on martingale decomposition using a new idea involving conditioning with respect to both the past and the future of the chain. No assumption of irreducibility or aperiodicity is needed.

Hume 321 at 4:30 PM

**Jialin Zhang**

Mississippi State University

**Unfolding Entropic Statistics**

This talk is organized into three parts.

1) Entropy estimation in Turing’s perspective is described. Given an iid sample from a countable alphabet under a probability distribution, Turing’s formula (introduced by Good (1953), hence also known as the Good-Turing formula) is a mind-bending non-parametric estimator of total probability associated with letters of the alphabet that are NOT represented in the sample. Some interesting facts and thoughts about entropy estimators are introduced.

2) Turing’s formula brought about a new characterization of probability distributions on general countable alphabets that provides a new way to do statistics on alphabets, where the usual statistical concepts associated with random variables (on the real line) no longer exist. The new perspective, in turn, inspires some thoughts on the characterization of probability distribution when the underlying sample space is unclear. An application example of authorship attribution is provided at the end.

3) Shannon’s entropy is only finitely defined for distributions with fast decaying tails on a countable alphabet. The unboundedness of Shannon’s entropy over thick-tailed distributions on an alphabet prevents its potential utility from being fully realized. Zhang (2020) proposed generalized Shannon’s entropy (GSE), which is finitely defined everywhere. Some interesting results about GSE and a new test of independence inspired by GSE are introduced. The new test does not require the knowledge of cardinality, and it is consistent and would detect any form of dependence structure in the general alternative space given a sufficiently large sample.

**Martial Longla**

University of Mississippi

**Sometimes, Disorder Helps** (pdf)

**Timothy Fortune**

University of Mississippi

**Local Limit Theorem for Linear Random Fields** (pdf)

**Dongsheng Wu**

University of Alabama-Huntsville

**Weak Convergence of Martingales and its Application to Nonlinear Cointegrating Model** (pdf)

**Xin Dang**

University of Mississippi

**Gini Distance Correlation and Feature Selection ** (pdf)

**Qian Zhou**

Mississippi State University

**Model Misspecification in Statistical Analysis ** (pdf)

**Tung-Lung Wu**

Mississippi State University

**Tests for High-Dimensional Covariance Matrices Using Random Matrix Projection ** (pdf)

**Dao Nguyen**

University of California-Berkeley

**Iterated Filtering and Iterated Smoothing Algorithms** (pdf)

**David Mason**

University of Delaware

**Bootstrapping the Student t‐Statistic** (pdf)

**Yichuan Zhao**

Georgia State University

**Jackknife Empirical Likelihood Methods for the Gini Index** (pdf)

**Junying Zhang**

Taiyuan University of Technology, Taiyuan, P. R. China

**Marginal Empirical Likelihood Independence Screening in Sparse Ultrahigh Dimensional Additive Models** (pdf)

**Yimin Xiao**

Michigan State University

**On the Excursion Probabilities of Gaussian Random Fields** (pdf)

**Charles Katholi**

University of Alabama at Birmingham

**Estimating Proportions by Group Testing: A Frequentist Approach** (pdf)

**Cuilan Gao**

St. Jude Children’s Research Hospital

**Evaluate Agreement of Differential Expression for Translational Cross-Species Genomics** (pdf)

**Yang Cheng**

Mississippi State University

**Orbit Uncertainty Propagation Using Sparse Grid-Based Method** (pdf)

**Meng Zhao**

Mississippi State University

**Local Linear Regression with Censored Data** (pdf)

**Pradeep Singh**

Southeast Missouri State University

**A Modified Approach in Statistical Significance for Genome Wide Studies** (pdf)

**Ebenezer Olusegun George**

University of Memphis

**On the Exchangeable Multinomial Distribution** (pdf)

**Deo Kumar Srivastava**

St. Jude Children’s Research Hospital

**Robust Multiple Regression based on Winsorization and Bootstrap Methods** (pdf)

**Paul Schliekelman**

University of Georgia

**Integrating Genome-wide Expression Information into Genome Scans for Complex Traits** (pdf)

**Justin Shows**

Mississippi State University

**Sparse Estimation and Inference for Censored Median Regression** (pdf)

**Hanzhe Zheng**

Merck Research Laboratories

**Adaptive Design in Clinical Trials** (pdf)

**Stan Pounds**

St. Jude Children’s Research Hospital

**Reference Alignment of SNP Microarray Signals for Copy Number Analysis of Tumors** (pdf)

**Russell Stocker**

Mississippi State University

**Optimal Goodness-of-Fit Tests** (pdf)

**Gauri Sankar Datta**

University of Georgia

**Bayesian approach to survey sampling** (pdf)

**Dawn Wilkins**

University of Mississippi

**Supervised and Unsupervised Learning with Microarray Data** (pdf)

**Hemant K. Tiwari**

University of Alabama at Birmingham

**Issues & Challenges in Genetic Analysis of Complex Disorders** (pdf)

**Ajit Sadana**

University of Mississippi

**A Fractal Analysis of Binding and Dissociation Kinetics of Glucose and Related Analytes on Biosensor Surfaces** (pdf)

**Jane L. Harvill**

Mississippi State University

**Modeling and Prediction for Nonlinear Time Series** (pdf)

**Fenghai Duan**

Yale School of Public Healthy

**Probe-level Correction in Analysis of Affymetrix Data** (pdf)

**J. Sunil Rao**

Case Western Reserve University

**Spike and slab variable selection: frequentist and Bayesian strategies (in DNA microarray data analysis)** (pdf)

**Warren May**

University of Mississippi Medical Center

**On Being a Statistician in a Medical Center Environment** (pdf)

**Malay Ghosh**

University of Florida

**Hierarchical Bayesian Neural Networks: An Application to Prostate Cancer Study** (pdf)

**Pranab K. Sen**

University of North Carolina at Chapel Hill

**Constrained Inference in Statistical Practice** (pdf)

**Ebenezer Olusegun George**

University of Memphis

**Statistical Methods for Analyzing Clustered Discrete Data: Applications to Teratology Studies** (pdf)

**Haimeng Zhang**

Concordia College

**Estimating Survival Functions In Koziol-Green Models** (pdf)

**Deo Kumar Srivastava**

St. Jude Children’s Hospital

**Impact of Censoring in Survival Analysis** (pdf)

**Z. Govindarajulu**

University of Kentucky

** Robustness of Small Sample Size Re-estimation Procedures** (pdf)

**Xueqin Wang**

University of Mississippi

**Asymptotics of the Theil-Sen Estimator in Simple Linear Regression Model With a Random Covariate** (pdf)

**Xueqin Wang**

University of Mississippi

**Unbiasedness of the Theil-Sen Estimator** (pdf)

**Patrick D. Gerard**

Mississippi State University

**Estimating Polulation Density in Line Transect Sampling Using Kernel Methods** (pdf)