STATS 300B - Theory of Statistics

Institution:

Stanford University

Subject:

Description:

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)

Credits:

2.00 - 4.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.stanford.edu/

Phone Number:

(650) 723-2300

Regional Accreditation:

Western Association of Schools and Colleges

Calendar System:

Quarter

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