Department of Mathematics and Statistics Calendar February 14 - 20, 2005 Monday, February 14, 2005 Tuesday, February 15, 2005 10:45 AM MATH 115 Instructors Meeting 400 MSc Wednesday, February 16, 2005 10:30 AM Algebra Seminar 400 MSc Dr. Corneliu HOFFMAN, BGSU "Flips for Algebraic Groups, II" 11:30 AM Statistics Seminar **140 MSc** *note location change* Dr. N. BALAKRISHNAN, Visiting Lukacs Professor "Progressive Censoring V: Goodness-of-Fit Tests" 12:30 PM Calculus Seminar 459 MSc TBA 3:30 PM Analysis Seminar 400 MSc Dr. Juan BES, BGSU "TBA" **3:30 PM Statistics Candidate Colloquium** 459 MSc "Robust Estimation via Measurement Error Model Likelihoods with Applications to Location-Scale Models" Thursday, February 17, 2005 **3:30 PM Statistics Candidate Colloquium** 459 MSc "Diagnostic Measures and Selection Criteria for Mixed Models Based on Kullback-Leibler Information" ABSTRACT: This talk consists of two parts. In the first part, a diagnostic defined in terms of the Kullback-Leibler directed divergence is developed for identifying cases which impact the prediction of the random effects in a mixed model. The diagnostic compares two conditional densities governing the prediction of the random effects: one based on parameter estimates computed using the full data set; the other based on parameter estimates computed using a case-deleted data set. We present the definition of the diagnostic and a computational formula for its evaluation. We illustrate the effectiveness of the measure using a simulated data set. The performance of the measure is also investigated in an application where exam scores are modeled using a mixed model containing a fixed exam effect and a random subject effect. In the second part, we extend the results of Shibata (1997) to propose five bootstrap-corrected variants of AIC, denoted by AICb1-AICb5, for the purpose of small-sample mixed model selection. These variants are asymptotically equivalent, and provide asymptotically unbiased estimators of the expected Kullback-Leibler discrepancy between the true model and a fitted candidate model. The performance of the criteria is investigated in a simulation study where the random effects and the errors for the true model are generated from a Gaussian distribution. Parametric, semiparametric, and nonparametric bootstrapping are employed. Our results indicate that under parametric bootstrapping, the variants exhibit the best overall bias properties. For correctly specified or overfit models, the criterion originally introduced by Efron (1983, 1986), AICb1, provides a less biased estimator of the expected discrepancy than AIC and the other proposed variants. The criterion originally introduced by Cavanaugh and Shumway (1997), AICb2, exhibits a higher success rate in identifying the correct model than AIC and the other variants. Overall, the bootstrap AIC variants appear to serve as effective tools for selecting a mixed model of appropriate dimension. Friday, February 18, 2005 **12:00 PM Calendar Information due to Cyndi for inclusion in next week's calendar listing** **1:30 PM Director of Service Mathematics Candidate Colloquium** 459 MSc "Wavelets, Multiscale Analysis and Their Applications" ABSTRACT: We begin with a brief overview of wavelet analysis. We then compare wavelet transforms with Fourier transforms and state their properties. Multiresolution analysis provides a natural framework of the construction of wavelets. We describe its insight by an illustration from a coarse approximation to a higher resolution approximation. The computational efficiency and accuracy of the multiscale methods have allowed us to make improvements in many applications. Several wavelet based multiscale computational methods will be introduced. Applications on image processing and numerical solutions of partial differential equations will be mentioned. Saturday, February 19, 2005 Sunday, February 20, 2005
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