2011-2012 Colloquium
Speaker: Professor Yongcheng Qi, University of Minnesota Duluth
Date: Thursday, August 2, 2012, 2:30 pm - 3:30 pm
Room: RB 2044
Date: Thursday, August 2, 2012, 2:30 pm - 3:30 pm
Room: RB 2044
Title: Jackknife Empirical Likelihood Test for Equality of Two High Dimensional Means
Abstract: It has been a long history to test the equality of two multivariate means. One popular test is the so-called Hotelling T2 test. However, as the dimension diverges, the Hotelling T2 test performs poorly due to the possible inconsistency of the sample covariance estimation. To overcome this issue and allow the dimension to diverge as fast as possible, Bai and Saranadasa (1996) and Chen and Qin (2010) proposed tests without the sample covariance involved, and derived the asymptotic limits which depend on whether the dimension is xed or diverges under a specic multivariate model. We propose a jackknife empirical likelihood test which has a chi-square limit independent of the dimension, and the conditions are much weaker than those in the existing methods. A simulation study shows that the proposed new test has a very robust size with respect to the dimension, and is powerful too.
Abstract: It has been a long history to test the equality of two multivariate means. One popular test is the so-called Hotelling T2 test. However, as the dimension diverges, the Hotelling T2 test performs poorly due to the possible inconsistency of the sample covariance estimation. To overcome this issue and allow the dimension to diverge as fast as possible, Bai and Saranadasa (1996) and Chen and Qin (2010) proposed tests without the sample covariance involved, and derived the asymptotic limits which depend on whether the dimension is xed or diverges under a specic multivariate model. We propose a jackknife empirical likelihood test which has a chi-square limit independent of the dimension, and the conditions are much weaker than those in the existing methods. A simulation study shows that the proposed new test has a very robust size with respect to the dimension, and is powerful too.
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Speaker: Professor Zhengyan Lin, Department of Mathematics, College of Science, Zhejiang University, China
Time: Friday, July 13, 2012, 3:30 pm - 4:30 pm
Room: RB 2026
Title: m-Dependent Approximation and Its Applications
Abstract: We introduce the m-dependent approximation for a class of stationary processes. As its applications, under quite easy verifiable and more weaker conditions, we present limit theorems for weak and strong invariance principle, the maximum of the periodogram and spectral density estimation.
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Speaker: Shuhua Zhang (Tianjin University of Finance and Economics)
Title: DISCONTINUOUS GALERKIN METHODS FOR THE CALIBRATION OF THE EXTENDED CIR MODEL
Date and Location: September 7, 2011 at 11:00 am in RB 1021
Abstract. In this talk, the discontinuous Galerkin method is used to solve the calibration of the extended CIR model, and its optimal and superconvergence approximations are discussed. Also, some numerical examples are provided to validate the theoretical results and to compare the extended CIR model with the Vasicek models.
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Speaker: Professor George Stoica, (Chair of the Department of Mathematical Sciences, at University of New Brunswick (Saint John)
Title: CONTRIBUTIONS TO THE ASYMPTOTIC BEHAVIOUR OF EXCHANGEABLE SEQUENCES.
Time: Friday 10 February 2012, 12:30 pm â€" 1:30 p.m.
Room: RB 1047
Abstract: I present results obtained jointly with Deli Li on general weak laws of large numbers for exchangeable sequences, in the spirit of Kolmogorov-Feller and Gnedenko-Raikov, together with the rate of convergence therein.
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Speaker: Jing (Jane) He, PhD Candidate, School of Mathematics and Statistics, Carleton University
Title: THE LINEAR COMPLEXITY PROFILE AND CORRELATION MEASURE OF ORDER K OR A FAMILY OF INTERLEAVED SEQUENCES
Time: Friday, March 16, 2012, 3:30 pm - 4:30 pm
Room: RB 2047
Abstract: Families of pseudorandom sequences with low cross correlation have important applications in communications and cryptography. Among several known constructions, interleaved construction is a well-known method proposed by Gong that uses two sequences of the same period. The constructed sequences possess nice cryptographic properties. The interleaving framework can be used to generate many types of sequence families.
In this talk, we first review Legendre symbols, the notions of period of a sequence, linear complexity and correlation measures. The we interleave two Legendre sequences of odd prime periods p and q. We provide nontrivial upper bounds on the linear complexity profile for any periods p and q, and on the correlation measures of order k when k is in a specific range.
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Speaker: Dr. Xuemao Zhang, Department of Mathematical Sciences, Lakehead University
Title: Bias-corrected GEE Estimation for Longitudinal Data
Time: Friday, April 20, 2012, 3:30 pm - 4:30 pm
Room: RB 2024
Abstract: Generalized estimating equations (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are proposed when the sample size is small. One of these is based on bias correction and the other is based on a bias reduction. Simulations show that both methods do well in reducing bias.