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Test equating is a critical step in the development and maintenance of standardized tests. It is required in many different contexts: random parallel forms equating, vertical equating of forms for use in successive age groups, equating congeneric tests (i.e., tests measuring the same underlying factor), and linking of tests that are not strictly congeneric (i.e., predicting scores on one test from scores on one or more other tests). In classical test theory, equating is limited to the equipercentile method applied to test scores from randomly equivalent groups of examinees; prediction requires calibrating data from groups of examinees who have taken both tests in counter-balanced order. In modern item response theory, equating can be extended to non-equivalent groups when the test forms have some items in common; prediction can be calibrated at the item level rather than the score level. Discussion of these topics will be illustrated by results from the equating of the paper-and-pencil version of the Armed Services Vocational aptitude battery (ASVAB) and the prediction of scores from the National Assessment of Educational Progress (NAEP) linked to state educational achievement test scores.

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Title: Pseudo-Lorenz Curve and Meausre of Association
Speaker: Professor Somesh Das Gupta
Indian Statistical Institute
Date: October 5, 2001
Location: Funger Hall 308
Time: 11:00 a.m.

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The pseudo -Lorenz curve of a positive random variable Y with respect to another positive random variable X will be introduced, and a measure of association between Y and X using this pseudo-Lorenz curve and the Lorenz curve of Y will be defined. Some properties of this measure of association will be proved and this measure will be illustrated by some concrete examples. By using the Neyman-Pearson Lemma it will be shown that this pseudo Lorenz curve lies above the Lorenz curve of Y.To assess monotone dependence between Y and X some other concepts will be introduced. Lastly, multivariate generalizations of Lorenz curve will be discussed.

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Title: Probabilistic analysis of Random Trees via Urn Models
Speaker: Professor Hosam M. Mahmoud
Department of Statistics, George Washington University
Date: October 12, 2001
Location: Funger Hall 222
Time: 11:00 a.m.

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We analyze the asymptotic composition of a class of nonclassic Polya urn models (not necessarily of fixed row sum) by embedding the discrete urn process into a renewal process with rewards. A subclass of the models considered has banded matrix urn schemes and serves as a natural modeling tool for the size of a class of random bucket trees. The class of urns considered extends known results for multicolor urns with constant row sums. The same asymptotic average results are shown to hold in the larger class. This provides an average-case analysis for the size of certain random bucketed multidimensional quad trees and -d trees, which are all new results. Some bucket trees have urn schemes with constant row sum, a special case that helps detect phase changes in the limiting distribution of the (normed) size of the tree. For these special cases one can appeal to a more developed urn theory to find a joint limiting distribution of the normed size up to a threshold value of the capacity of a bucket. Once that cut-off point is surpassed, normality ceases to hold. This case appears in paged binary trees (threshold 116), m-ary search trees (threshold 26), and bucket recursive trees (threshold 26). The asymptotic normality results and the phase change after the threshold in these trees are already known and we only provide alternative proofs via a unified urn models approach.

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Title: Two Statistical Problems in Genetics: mutation detection based on functional
data and class prediction using DNA Microarray Data
Speaker: Professor Efstathia Bura
Department of Statistics, George Washington University
Date: October 19, 2001
Location: Funger Hall 308
Time: 11:00 a.m.

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A new technique, denaturing high performance liquid chromatography (dHPLC), allows for detection of any heterozygous sequence variation in a gene without prior knowledge of the precise location of the sequence change. The results of a dHPLC analysis are recorded in real-time in the form of a chromatogram that is sequence specific. We present two methods to classify an individual based on the observed chromatogram as a homozygous wild-type, or as a carrier of a specific variant for the given DNA segment by comparison to representative chromatograms that are obtained from the training set of individuals with known variant status. The first approach consists of finding a parsimonious parametric model and then classifying each newly observed curve based on comparing the most discriminating characteristic, the main mode, to the main mode of the training curves. The second approach consists of finding empirical estimates of the modes of each chromatogram, and using a bootstrap test for equality with the corresponding estimates of the training curves. We apply both methods to data on the breast cancer susceptibility gene BRCA1.
I will also briefly present a current research project, where the dimension of the regression of a binary or multicategory response variable on gene expression levels is estimated using sliced inverse regression. The resulting reduced data are then used to predict type of breast cancer; i.e., whether the cancer is due to a mutation in BRCA1 or BRCA2 or it is a sporadic case.
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Title: A new alternative to Bayes factors: the resolution of Lindley's paradox through the posterior distribution of the likelihood ratio.
Speaker: Professor Murray Aitkin
Department of Statistics, University of Newcastle and Education Statistics Services Institute
Date: November 2, 2001
Location: Funger Hall 222
Time: 11:00 a.m.

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The Lindley paradox (correctly formulated by Bartlett) is the basis for the claim that Bayes factors (or the Schwarz BIC criterion), unlike P-values, can provide strong support for a point null hypothesis against a general alternative hypothesis. A difficulty of Bayes factors is well known: that as the sample size increases they can give strong support to any point null hypothesis, regardless of the data or the hypothesis. This talk points to a basic inconsistency between Bayes factors and posterior distributions of the parameter; the latter do not show the paradoxical feature of the former. By transforming the posterior distribution from the parameter to the likelihood ratio, the Bayes conclusions become consistent with P-value conclusions, though the latter need reformulation as measures of strength of evidence. The posterior distribution of the likelihood ratio can be extended to general models with nuisance parameters, providing a general theory of Bayesian point null hypothesis testing which does not suffer from the Lindley paradox and gives conclusions consistent with P-value conclusions, when the latter are correctly reformulated.

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Title: Modified Maximum Likelihood Estimators Based on Ranked Set Samples
Speaker: Dr. Gang Zheng, Office of Biostatistics Research, National Heart, Lung and Blood Institute

Date: November 9, 2001
Location: Funger Hall 222
Time: 11:00 a.m.

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Ranked set sampling (RSS) is a cost efficient sampling technique when measuring sampling units is difficult or expensive, but ranking them without quantification is relatively easy. Maximum likelihood estimator (MLE) using ranked set samples has no closed form expression and may no longer be efficient when the ranking is imperfect. In this talk, we introduce a modified maximum likelihood estimator (MMLE), which is based on a partial likelihood function, using RSS. The results show that the MMLE based on RSS has the same form as the MLE using simple random samples (SRS) except that the SRS in the MLE is replaced by the corresponding RSS. The results also show that, for the location and scale parameters, the MMLE using RSS is more efficient than the MLE using SRS with the same sample size. Under the perfect judgment ranking, numerical examples show that the MMLE based on RSS has good efficiency relative to the MLE based on RSS, i.e., there is minor loss of efficiency due to using a partial likelihood function for inference. However, when the judgment ranking is imperfect, simulation results show that the MMLE based on RSS is more robust than the MLE using RSS.

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Title: Urban Heat Island Effect in the Greater Washington Metropolitan Area

Speaker: Dr. Dr. Ivan Cheung, Department of Geography, The George Washington University

Date: November 30, 2001
Location: Funger Hall 321
Time: 3:00 p.m



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The contact person is Reza Modarres at Reza@gwu.edu

or 202-994-6359.