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Course Criteria
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3.00 Credits
Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.
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3.00 Credits
Modern measure and integration theory in abstract spaces. Probability measures, random variables, expectations. Distributions and characteristic functions. Modes of convergence. Independence, zero-one laws, laws of large numbers, three-series theorem. Central limit problem. Conditional expectations, martingales and martingale convergence theorems.
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3.00 Credits
Sets and classes, sigma-fields and related structures, probability measures and extensions, random variables, expectation and integration, uniform integrability, inequalities, L_p-spaces, product spaces, independence, zero-one laws, convergence notions, characteristic functions, simplest limit theorems, absolute continuity, conditional expectation and conditional probabilities, martingales.
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3.00 Credits
Estimation inference for coefficients in autoregressive, moving average and mixed models and large sample. Distribution theory for autocovariances and their use in identification of time series models. Stationarity and seasonality. Extensions of theory and methods to multiple series including vector autoregressions, transfer function models, regression with time series errors, state space modelin
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3.00 Credits
Theory and methods of time series analysis from frequency point of view. Harmonic analysis, complex demodulation and spectrum estimation. Frequency domain structure of stationary time series and space-time processes. Sampling distributions of commonly used statistics.
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3.00 Credits
Survey of multivariate statistical theory. Multivariate distributions including the multinormal, Wishart, Hotelling's T, Fisher-Roy-Hsu, Wilks' and multivariate Beta distributions. Applications of maximum likelihood estimation, likelihood ratio testing and the union-intersection principle. Development of the theory of Hotelling's T tests and confidence sets, discriminant analysis, canonical correlation, multivariate analysis of variance and principal components.
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3.00 Credits
Zero sum two-person games and statistical inference. Bayesian methods and orthodox statistical estimation and testing; minimax decision rules; empirical Bayes procedures; Bayes sequential decision procedures.
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1.00 - 3.00 Credits
No course description available.
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3.00 Credits
Statistical inference with emphasis on the use of statistical models, construction and use of likelihoods, general estimating equations, and large sample methods. Includes introduction to Bayesian statistics and the jackknife and bootstrap.
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3.00 Credits
Principles of inference including introduction to Bayesian inference. Optimality results for regular estimation and hypothesis testing situations. Asymptotic results for estimators and tests based on likelihoods, general estimating equations and resampling plans.
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