Probability and Statistics Seminar, Spring 2007
Date
Speaker
Title
Friday, January 26, 2007  2:00 p.m - 3:00 p.m., MP3311 Charles Champ, Georgia Southern Univ

Some Notes on the Reliability of Measurement
Friday, February 2, 2007 2:00 p.m - 3:00 p.m., MP3311 Martin Dunbar, Georgia Southern Univ Performance Analysis of CUSUM Charts
Friday, March 2, 2007 2:00 p.m - 3:00 p.m., MP3311 Broderick Oluyede, Georgia Southern Univ ON DEPENDENCE AND ASYMPTOTIC COMPARISONS FOR TESTS OF
ASSOCIATION
Friday, April 6, 2007 2:00 p.m - 3:00 p.m., MP3311 Mavis Pararai, Georgia Southern Univ MEASUREMENT ERRORS IN THE GENERALIZED POISSON-POISSON REGRESSION MODEL
Friday, April 13, 2007 2:00 p.m - 3:00 p.m., MP3311 Hani Samawi, Georgia Southern Univ Optimal Sign Test for One Sample Bivariate Location Model Using an Alternative Bivariate Ranked Set Sample

1. Friday, January 26, 2007, 2:00 p.m. - 3:00 p.m.  Room: MP 3311.

Speaker: Charles W. Champ, Georgia Southern University


Title: Some Notes on the Reliability of Measurement

Abstract: Modelling the reliability of a measurement is discussed. A
measure of reliability found in the literature is what is referred to as the
intraclass correlation coefficient of reliability. This measure is actually
the square of the correlation between the actual and observed measurement
on an individual. Some examples are given to illustrate the consequences of
unreliable measurements.

2. Friday, February 2, 2007 2:00 p.m - 3:00 p.m., Room: MP3311

Speaker:  Martin Dunbar, Georgia Southern University

Title:  Performance Analysis of CUSUM Charts
 
Abstract:  The integral equation and Markov chain methods for analyzing the performances of one- and two-sided CUSUM charts with known in-control process parameters are discussed.  These methods provide us with ways to approximate the run length distribution of the chart.  Since parameters of the run length distribution are commonly used measures of the performance of a control chart, it is important to choose an accurate approximation method. We develop some new Markov chain approximations using methods similar to the methods for approximating a solution to integral equations used to describe the run length distribution.

3. Friday, March 2, 2007 2:00 p.m - 3:00 p.m., Room: MP3311

Speaker:  Broderick Oluyede, Georgia Southern University

Title:  ON DEPENDENCE AND ASYMPTOTIC COMPARISONS FOR TESTS OF
ASSOCIATION

Abstract: 
In this note, the theory of large deviations is used in certain power
comparisons in ordinal contingency tables, based on the fact that under
an alternative the distribution of the test statistic(s) can be approximated by
a Gaussian distribution.  Four test statistics namely sum of log-likelihood
ratio statistics, sum of chi-square statistics, the modified chi-square
statistic and the sum of chi-bar-squared statistics for testing independence against
positive dependence notions stronger than quadrant dependence are compared
with respect to size and power via extensive computer simulations.  The
estimated sizes of the modified chi-square statistic and the sum of
log-likelihood ratio test statistic for the partitioned table are in close
agreement with their corresponding nominal levels.  However, the estimated
sizes of the sum of the chi-square statistics and the chi-bar-squared
statistic overstates the nominal test levels.  For samples as small as ten,
the modified chi-square test statistic performed better than the other test
statistics.
 
Key Words and Phrases:  Marginal distribution, Likelihood ratio test,
Positive dependence, Power of a test.
 
AMS 1985 Subject Classification: Primary 62H05, Secondary 62H17

4. Friday, April 6, 2007 2:00 p.m - 3:00 p.m., Room: MP3311

Speaker:  Mavis Pararai, Georgia Southern University

Title:  MEASUREMENT ERRORS IN THE GENERALIZED POISSON-POISSON REGRESSION MODEL

Abstract: Count data regression models have been widely used in statistics to model
 response variables that are assumed to have been correctly reported. This
 assumption might be violated as some counts might be misreported. The
 generalized Poisson-Poisson mixture regression (GPPMR) model is developed
to
 model counts that are accurately reported, underreported and overreported.
 The GPPMR model is applied to two data sets: (1) National Pregnancy and
 Health Survey (NPHS) Data and (2) School Crime Supplement Data. The GPPMR
 model is compared to the Negative Binomial-Poisson mixture regression
 (NBPMR) model. The two models seem to perform equally the same with the
 Negative Binomial-Poisson mixture regression model performing better than
 the GPPMR model. Finally, a simulation study is conducted to investigate
the
 properties of the maximum likelihood estimates of the parameters of the
 GPPMR model.
 
 4. Friday, April 13, 2007 2:00 p.m - 3:00 p.m., Room: MP3311

Speaker:  Hani Samawi, Georgia Southern University

Title:  Optimal Sign Test for One Sample Bivariate Location Model Using an Alternative Bivariate Ranked Set Sample

Abstract:

 The aim of this paper is to find optimal alternatives bivariate ranked set sample for one sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for bivariate sign test are the alternative designs with quantifying order statistics with labels  when the set size r is odd and  when the set size r is even. The asymptotic distribution and Pitman efficiencies of those designs are derived. Simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with Bootstrap algorithm for P-value estimation is used.
Probability and Statistics Seminar, Fall 2006
Date
Speaker
Title
Friday, September 1, 2006  2:00 p.m - 3:00 p.m., MP3311 Hani Samawi, Georgia Southern Univ

Bivariate sign test for one-sample bivariate location model using ranked set sampling, I
Friday, September 8, 2006  2:00 p.m - 3:00 p.m., MP3311 Hani Samawi, Georgia Southern Univ

Bivariate sign test for one-sample bivariate location model using ranked set sampling, II
Friday, September 15, 2006  2:00 p.m - 3:00 p.m., MP3311 Hani Samawi, Georgia Southern Univ

Bivariate sign test for one-sample bivariate location model using ranked set sampling, III
Friday, September 15, 2006  2:00 p.m - 3:00 p.m., MP3311 Stephen W. Looney,

Medical College of Georgia

A Two-Sample Method for Analyzing Combined Samples of Correlated and Uncorrelated Data

1. Friday, September 1st, 8th and 15th, 2006, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Hani Samawi, Georgia Southern University

Title:  Bivariate sign test for one-sample bivariate location model using ranked set sampling

This article introduces a bivariate sign test for the one-sample bivariate location model using a bivariate ranked set sample (BVRSS). We show that the proposed test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the noncentrality parameter are derived. The asymptotic distribution of the vector of sample median as an estimator of the locations of the bivariate model is introduced. Theoretical and numerical comparisons of the asymptotic efficiency of the BVRSS sign test with respect to the BVSRS sign test are also given. 

2. Friday, November 10, 2006, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Stephen W. Looney, Medical College of Georgia

Title:  A Two-Sample Method for Analyzing Combined Samples of Correlated and Uncorrelated Data

Either by design, carelessness, or accident, the data in a study may consist of a combination of correlated and uncorrelated data.  When comparing two means, the data may consist of one sub-sample in which the observations for Treatment 1 and Treatment 2 are independent of each other, and another sub-sample which consists of paired observations taken under both treatments.  In this presentation, a new method is presented for analyzing such data. The proposed method is based on asymptotic results and is evaluated using simulation. The simulation results indicate that the proposed method can provide substantial improvement in Type I error rate and power when compared with existing methods.


Probability and Statistics Seminar, Spring 2006
Date
Speaker
Title
Friday, February 3, 2006  2:00 p.m - 3:00 p.m., MP3311 Charles Champ, Georgia Southern Univ MEWMA Charts Useful in Monitoring for a Shift in the Covariance Matrix, I
Friday, February 10, 2006  2:00 p.m - 3:00 p.m.,  MP3311 Charles Champ, Georgia Southern Univ MEWMA Charts Useful in Monitoring for a Shift in the Covariance Matrix, II
Friday, April 28, 2006  2:00 p.m - 3:00 p.m., MP3311 Bryan Griffin, Department of Curriculum, Foundations, &
Reading, Georgia Southern Univ		 Logistic regression with correlated data: Comparison of marginal
and  random-effect models

1. Friday, February 3, 2006, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Charles Champ, Georgia Southern Univeristy.

Title:  MEWMA Charts Useful in Monitoring for a Shift in the Covariance Matrix, I

Abstract: The commonly recommended charts for monitoring the mean vector are affected by a shift in the covariance matrix. As in the univariate case,
a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector.
One such chart is the chart that plots the generalized sample variance |S| verses the sample number. We propose two multivariate exponentially weighted
moving average (MEWMA) charts based on the matrix E of MEWMA sample covariance matrices. The first of these charts plots the statistic |\Simga-1E| verses
the sample number. The |S| chart is a special case. The plotted statistic of the second chart is the likehood ratio (LR) statistic with S replaced by E with the
chart based on the LR statistic as a special case. Simulation is used to determine the run length properites of the charts. A design method is given for determining
the near optimal chart for monitoring the covariance matrix under the multivariate normal model. Sample size recommendations are given based on the average run
length of the chart. To illustrate their use, each of the charts is applied to an example. Some comparisons are made with other charts found in the literature for
monitoring for a change in the covariance matrix.
 

2. Friday, February 10, 2006, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Charles Champ, Georgia Southern Univeristy.

Title:  MEWMA Charts Useful in Monitoring for a Shift in the Covariance Matrix, II

Abstract: (See abstract above)
 
 

3. Friday, April 28, 2006, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Bryan Griffin, Georgia Southern Univeristy.

Title:  Logistic regression with correlated data: Comparison of marginal and random-effect models

Abstract: Data obtained from longitudinal designs or from naturally occurring groups and
clusters are often correlated. For binary correlated data, both marginal and random-effect
logistic regression models may be used, but coefficients from these two models estimate
different parameters and have different interpretations. Marginal logistic regression models
provide population-averaged estimates while random-effect models estimate subject-specific
(or cluster-specific) coefficients. This difference does  not arise in linear marginal and
random-effect models. Differences between  marginal and random-effect linear and logistic
regression models will be discussed and illustrated.

Fall 2005 Talks

Date
Speaker
Title
Friday, September 30, 3:00 p.m - 4:00 p.m., MP3311
(Joint with Department Colloquium)		 Mavis Pararai, Georgia Southern Univ. Measurement errors in generalized poisson regression model
Friday, October 7,  2:00 p.m - 3:00 p.m., 
MP3311		 Charles Champ, Georgia Southern Univ Properties of Multivariate Control Charts with Estimated Parameters
Friday, October 14,  2:00 p.m - 3:00 p.m., MP3311 Charles Champ, Georgia Southern Univ Double Sampling Hotelling's T2 Charts
Friday, October 21,  2:30 p.m - 4:00 p.m., MP3311 Laura Frost and Michele McGbony, Dept of Chemistry, Georgia Southern DNA Basics:  What is All the Excitement?
Friday, October 28,  2:30 p.m - 4:00 p.m., MP3311 Broderick Oluyede, Georgia Southern Univ. On the approximation of transformed life 
distributions with applications, I
Tuesday, November 4,  8:00 p.m - 9:00 p.m., MP3311 Broderick Oluyede, Georgia Southern Univ. On the approximation of transformed life 
distributions with applications, II

1. Friday,  September 30, 2005, 3:00 p.m. - 4:00 p.m., Room: MP 3314

Speaker:  Mavis Pararai, Georgia Southern Univeristy.

Title: Measurement errors in generalized poisson regression model.

Abstract: Count data regression models have been widely used in statistics to model response variables that are assumed to be observed without error. This assumption might be violated as some counts could potentially be under- or over-reported. A mixture of the generalized Poisson distribution and the quasi-binomial distribution II is used to develop the generalized Poisson regression model for underreported counts. The generalized Poisson regression model for underreported counts is found to perform better than the negative binomial regression model for underreported counts. The generalized Poisson-Poisson mixture regression model is also developed to model counts that are accurately-, under- and over-reported. This model is compared to the Negative Binomial-Poisson mixture regression model and the two models seem to be equivalent in their performance.

2. Friday,  September 30, 2005, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Charles Champ, Georgia Southern Univeristy.

Title:  Properties of Multivariate Control Charts with Estimated Parameters.

Abstract: The Hotelling's T2 multivariate exponentially weighted moving average (MEWMA), and several multivariate cumulative sum (MCUSUM) charts are examined in this paper.  Two descriptions are given of each chart with estimated parameters for monitoring the mean of a vector of quality measurements. For each chart, one description explains how the chart can be applied with estimated parameters in practice and the other description is useful for analyzing the run length performance of the chart. It is shown that, if the covariance matrix is in-control, the run length distribution of most of these charts depends only on the distributional parameters through the size of the process shift in terms of statistical distance. Simulation is used to provide performance analyses and comparisons of these charts. An example is given to illustrate the MCUSUM and MEWMA charts when parameters are estimated.

3. Friday,  October 14,  2005, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Charles Champ, Georgia Southern Univeristy.

Title:  Double Sampling Hotelling's T2 Charts.

Abstract: Two double sampling T2 charts are introduced. They only differ in how the second sample is used to suggest to the practitioner the state of
the process. An optimal method using a genetic algorithm is given for designing these charts based on the average run length of the (ARL).
Comparisons are made with various other control charting procedures. Some recommendations are given.

4. Friday,  October 21,  2005, 2:30 p.m. - 4:00 p.m., Room: MP 3311

Speaker:  Laura D. Frost and Michele D. McGibony, Department of Chemistry, Georgia Southern Univeristy.

Title: DNA Basics:  What is All the Excitement?

Abstract: In the past 60 years the molecule deoxyribonucleic acid (DNA) has gone from a chemical unknown to a biotechnological tool of major importance. This interactive session will provide information to the non-biochemist on topics from the structure and function of DNA and the kind of information that it houses in the cell to how we can use it for cloning, paternity testing, DNA fingerprinting, and why people are interested in sequencing the human genome.

5. Friday,  October 28,  2005, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Broderick Oluyede, Georgia Southern Univeristy.

Title: On the approximation of transformed life distributions with applications, I

Abstract:
Stochastic relations and closure results for weighted distributions are presented. Exponential approximations to the class of increasing failure rate (IFR) and decreasing failure rate (DFR)  weighted distributions with monotone weight functions are obtained. These include approximations via transformed and length-biased exponential distributions. Some bounds and moment-type inequalities for weighted life distributions are also presented.

6. Friday,  November 4,  2005, 2:00 p.m. - 3:00 p.m., Room: MP 3311

Speaker:  Broderick Oluyede, Georgia Southern Univeristy.

Title: On the approximation of transformed life distributions with applications, II

Abstract:
Stochastic relations and closure results for weighted distributions are presented. Exponential approximations to the class of increasing failure rate (IFR) and decreasing failure rate (DFR)  weighted distributions with monotone weight functions are obtained. These include approximations via transformed and length-biased exponential distributions. Some bounds and moment-type inequalities for weighted life distributions are also presented.
 
 
   

Please contact Dr. Broderick Oluyede for questions or comments regarding this seminar.