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Course Criteria
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3.00 Credits
Masters-level research as in 299, but must be conducted for an offcampus employer. Final report required. Prerequisite: enrollment in Statistics M.S. or Ph.D. program, prior to candidacy. 1-9 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)
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1.00 - 10.00 Credits
For Statistics M.S. students only. Reading or research program under the supervision of a Statistics faculty member. May be repeated for credit. 1-10 units, Aut (Staff), Win (Staff), Spr (Staff), Sum (Staff)
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3.00 Credits
May be repeated for credit. 3 units, Sum (Staff)
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2.00 - 4.00 Credits
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman- Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series. 2-4 units, Aut (Walther, G)
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2.00 - 4.00 Credits
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman- Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series. 2-4 units, Win (Siegmund, D)
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2.00 - 4.00 Credits
Elementary decision theory; loss and risk functions, Bayes estimation; UMVU estimator, minimax estimators, shrinkage estimators. Hypothesis testing and confidence intervals: Neyman- Pearson theory; UMP tests and uniformly most accurate confidence intervals; use of unbiasedness and invariance to eliminate nuisance parameters. Large sample theory: basic convergence concepts; robustness; efficiency; contiguity, locally asymptotically normal experiments; convolution theorem; asymptotically UMP and maximin tests. Asymptotic theory of likelihood ratio and score tests. Rank permutation and randomization tests; jackknife, bootstrap, subsampling and other resampling methods. Further topics: sequential analysis, optimal experimental design, empirical processes with applications to statistics, Edgeworth expansions, density estimation, time series. 2-4 units, Spr (Siegmund, D)
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3.00 Credits
The linear model: simple linear regression, polynomial regression, multiple regression, anova models; and with some extensions, orthogonal series regression, wavelets, radial basis functions, and MARS. Topics: normal theory inference (tests, confidence intervals, power), related distributions (t, chi-square, F), numerical methods (QR, SVD), model selection/regularization (Cp, AIC, BIC), diagnostics of model inadequacy, and remedies including bootstrap inference, and cross-validation. Emphasis is on problem sets involving substantial computations with data sets, including developing extensions of existing methods. Prerequisites: consent of instructor, 116, 200, applied statistics course, CS 106A, MATH 114. 2-4 units, Aut (Owen, A)
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3.00 Credits
Extension of modeling techniques of 305: binary and discrete response data and nonlinear least squares. Topics include regression, Poisson loglinear models, classification methods, clustering. May be repeated for credit. Prerequisite: 305 or equivalent. 2-4 units, Win (Efron, B)
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2.00 - 4.00 Credits
Unsupervised learning techniques in statistics, machine learning, and data mining. 2-4 units, Spr (Hastie, T)
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3.00 Credits
(Same as MATH 230A.) Mathematical tools: asymptotics, metric spaces; measure and integration; Lp spaces; some Hilbert spaces theory. Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Weak convergence and characteristic functions; central limit theorems; local limit theorems; Poisson convergence. Prerequisites: 116, MATH 171. 2-4 units, Aut (Diaconis, P)
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