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Course Criteria
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3.00 Credits
Theory of uniformly most powerful tests, unbiased tests, and invariant tests, maximin tests, confidence sets, asymptotic theory for standard large sample likelihood based tests, theory of linear rank tests.
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3.00 Credits
Local asymptotic normality and its applications; M-estimation; minimum distance methods; robust inference; quasilikelihood and applications to generalized linear models; kernel density estimation; adaptive estimators and tests with applications to proportional hazard models.
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3.00 Credits
Nonparametric estimation and hypothesis testing, relative efficiency, exchangeable random variables, ranking and distribution free statistics, generalized U-Statistics, generalized linear rank statistics, limiting distributions of certain nonparametric statistics, density estimation and related topics.
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3.00 Credits
Essential elements of decision theory, game theoretic approach, minimax theorem, Bayesian Inference and decision rules, admissibility and minimaxity results, minimax estimation of normal and Poisson means, multiple decision problems, gamma-minimaxity.
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3.00 Credits
Review of standard discrete distributions and generating functions, two-way and higher-dimensional contingency tables, chi-squared and other goodness-of-fit tests, binary response models, log-linear models, multinomial response models, introduction to generalized linear models.
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3.00 Credits
Theoretical foundations for the generalized linear model are introduced. Applications to Gaussian, binary, polytomous, and counts data are considered. Topics include hierarchical model building, estimation algorithms, analysis of deviance, and diagnostics. Extensions include overdispersed data, mixed generalized linear models, longitudinal data, and spatial data.
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3.00 Credits
The jacknife and bootstrap, bootstrap confidence intervals, prepivoting, asymptotic validity and invalidity, bootstrap accuracy and Edgeworth expansions, bootstrap for regression and autoregression, bootstrapping Markov chain models, moving block bootstrap for general weakly dependent data.
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3.00 Credits
Discrete time Markov chains, continuous time Markov chains, queueing processes, renewal processes, Markov random fields, point processes, Brownian motion and diffusion.
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3.00 Credits
Stopping times, optional stopping theorem, Anscombe's theorem, renewal theorem and associated results, SPRT for simple and composite hypotheses, nonlinear renewal theory, sequential point and interval estimation. In addition to these topics, current results from the literature will be presented.
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3.00 Credits
Selected topics concerning recent developments in statistics.
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