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Course Criteria
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3.00 Credits
Recent development in model-based estimation in survey sampling. A super population approach to inference on finite population quantities will be taken. Both Bayesian and classical approaches to sampling and related applications including small area estimation will be emphasized.
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3.00 Credits
The relevant matrix theory, multivariate random vectors and their distributions, multivariate normal distribution (MVN), sampling from MVN and inference for population mean vector, covariance matrix, correlation matrix, multivariate ANOVA, principal component analysis, factor analysis, discriminant analysis and classification.
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3.00 Credits
Theory of the linear model is introduced. Topics include a review of relevant linear algebra, distribution theory, the full and non-full rank linear models, ordinary and generalized least squares and maximum likelihood estimation, prediction, interval estimation and hypothesis tests, estimability, analysis of variance, restricted models, reparameterization, and mixed models.
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3.00 Credits
Theoretical foundations of spatial statistics, models for spatial data, and methods for model fitting, statistical inference, and spatial prediction are considered. Analysis of lattice data, images, continuous spatial variation and spatial point patterns.
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3.00 Credits
Linear processes, autoregressive-moving average models, predication, parameter estimation, model fitting and testing.
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3.00 Credits
Historical and recent advances in experimental design are considered. Designs including factorial, fractional factorial, central composite, incomplete block, cyclic, row-column, and simplex are discussed. Response surface and mixture models are considered. Optimal designs for linear and nonlinear models are developed.
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3.00 Credits
Selected topics in the theory of multivariate analysis at an advanced level.
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3.00 Credits
Basics of S programming language, objects in S+, graphics in S+, smoothing techniques and data summaries, linear models, generalized linear models, modern nonlinear regression techniques, multivariate statistics, survival analysis.
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3.00 Credits
Introduction to the theory and methods of the Bayesian approach to data analysis and statistical inference.
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3.00 Credits
Exponential families; more on sufficiency, completeness, ancillarity, and UMVUE; C-R lower bound and Fisher information for single and multiparameter cases; equivariance; large sample theory; likelihood estimation and asymptotic efficiency.
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