Schedule

Term Fall 2027: 2027-08-23 through 2027-12-10.

Unit	Topic focus
Week 0 — Readiness review from Mathematical Statistics I	likelihood score and Fisher information, sufficiency and exponential families, convergence Slutsky and the delta method, loss risk and elementary Bayes estimators, projections and quadratic forms, reproducible simulation workflow
Week 1 — Statistical decisions, actions, loss, and risk	estimands and action spaces, loss functions, risk and its interpretation, procedures as decision rules, comparing procedures under alternative losses
Week 2 — Tests as decision rules and the Neyman-Pearson lemma	null and alternative sets, size level and power, type I and type II error, power functions, most powerful tests and the Neyman-Pearson lemma, randomized tests
Week 3 — Uniformly most powerful tests and monotone likelihood ratios	uniformly most powerful tests, monotone likelihood ratio structure, one-parameter exponential families, two-sided problems and unbiased tests, where uniform optimality fails
Week 4 — Confidence-test duality, pivots, and exact procedures	inverting a test family, pivotal quantities, exact intervals for discrete models, coverage versus decision, compatibility sets
Week 5 — Likelihood-ratio, score, and Wald procedures	the three classical statistics, regularity conditions, asymptotic equivalence and finite-sample disagreement, parameterization sensitivity, boundary problems
Week 6 — Nuisance parameters, profiling, and local alternatives	profile likelihood, conditioning and invariance, orthogonality and information loss, local alternatives and contiguity, asymptotic power comparisons
Week 7 — First-half synthesis and a calibration study	choosing among exact and asymptotic procedures, reading a testing argument for its assumptions, repairing a flawed derivation, a simulated size and power study
Week 8 — Normal linear models, projections, and quadratic forms	projection geometry, distribution of quadratic forms, Cochran-style decompositions, t and F distributions from the geometry, analysis of variance identities
Week 9 — Multiplicity, multiple comparisons, and selective inference	regression and analysis-of-variance tests, family-wise error rate, false discovery rate, planned contrasts versus data-dependent selection, introductory selective inference
Week 10 — Randomization, permutation, and exact conditional inference	tests built from the assignment mechanism, permutation distributions, exact conditional tests, randomization validity and causal identification, design-based reasoning
Week 11 — Bootstrap, jackknife, and resampling calibration	the plug-in principle, percentile basic and studentized intervals, jackknife bias and variance, Monte Carlo tests and simulation error, where the bootstrap fails
Week 12 — Distribution-free inference and rank procedures	sign and signed-rank procedures, the rank-sum test, what a rank procedure estimates, asymptotic relative efficiency, behaviour under skewness and unequal shapes
Week 13 — Robust inference, influence, and M-estimation	contamination models and breakdown, influence functions, M-estimators and their estimating equations, sandwich variance, robust versus efficient tradeoffs
Week 14 — Bayes rules, admissibility, minimaxity, and shrinkage	Bayes rules under loss, admissibility and complete class ideas, minimax rules, shrinkage and the Stein phenomenon, predictive decisions and model comparison
Week 15 — Comparative inference synthesis and the bridge onward	one estimand through five procedures, what each approach licenses and forbids, reporting assumptions and sensitivity, where the graduate sequence goes next

The LMS remains authoritative for section logistics and graded details.