Robust Linear Mixed Models with Kotz type Distributions

9th International Statistics Day Symposium (10 - 14 Mayıs 2014)


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We consider a semi-supervised clustering problem where the locations of the data objects are subject to uncertainty. Each uncertainty set is assumed to be either a closed convex bounded polyhedron or a closed disk. The final clustering is expected to be in accordance with a given number of instance level constraints. The objective function considered minimizes the total of the sum of the violation costs of the unsatisfied instance level constraints and a weighted sum of squared maximum Euclidean distances b...
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In industrial organizations, manufacturers aim to achieve target product performance with minimum variation. For that reason, finding optimal settings of product and process design parameters that make it possible to consistently achieve target product performance is an important design problem. In this study, we propose an alternative method to solve this problem for the case of an ordinal categorical product/process response. The method utilizes Random Forest (RF) for modelling mean and variance of the re...
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Currently, the presence of data uncertainty and noise raises critical issues to be handled on both theoretical and computational grounds. Therefore, robustification and robust optimization have gained attention from theoretical and practical points of view for the establishment of a modeling framework in mathematical optimization to immunize solutions against diverse uncertainties. Data of both the input and output variables, underlying the problems to be addressed, are affected by the noise of different ki...
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The traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies. To rectify the situation we propose a reparametrization of the model. We derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies.
Citation Formats
F. Gökalp Yavuz, “Robust Linear Mixed Models with Kotz type Distributions,” presented at the 9th International Statistics Day Symposium (10 - 14 Mayıs 2014), 2014, Accessed: 00, 2021. [Online]. Available: