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Statistical Inference

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Statistical inference notes on asymptotic tools, information and sufficiency, estimation theory, lower bounds, and nonparametric tests.

Start Here

For a structured pass through statistical inference, read the modules in this order:

  1. Asymptotic Tools
  2. Information and Sufficiency
  3. Estimation Theory and Lower Bounds
  4. Nonparametric Tests

Module Map

ModuleScope
Asymptotic ToolsLLN, asymptotic approximation, and delta method
Information and SufficiencyFisher information, sufficient statistics, and factorization
Estimation Theory and Lower BoundsUMVU, CRLB, Rao-Blackwell, and Lehmann-Scheffe
Nonparametric TestsSign, Wilcoxon, Mann-Whitney, and Kruskal-Wallis tests

Notes

Asymptotic Tools

AreaNoteStatus
AsymptoticsLaw of Large Numbersdraft
AsymptoticsDelta Methoddraft

Information and Sufficiency

AreaNoteStatus
InformationFisher Informationdraft
SufficiencySufficiencydraft
SufficiencyNeyman Factorization Theoremdraft

Estimation Theory and Lower Bounds

AreaNoteStatus
UMVUUMVUEdraft
Lower boundCramér-Rao Lower Bounddraft
UMVURao-Blackwell Theoremdraft
UMVULehmann-Scheffé Theoremdraft

Nonparametric Tests

AreaNoteStatus
OverviewNonparametric Tests Overviewdraft
TestSign Testdraft
TestWilcoxon Signed Rank Testdraft
TestWilcoxon Rank Sum Testdraft
TestMann-Whitney U Testdraft
TestKruskal-Wallis Testdraft

Concept Map

  • Asymptotic convergence: law of large numbers and delta method.
  • Information and sufficiency: Fisher information, sufficient statistics, and factorization.
  • Estimation theory: UMVU theory, Rao-Blackwell improvement, Lehmann-Scheffe uniqueness, and Cramer-Rao lower bounds.
  • Nonparametric testing: sign test, Wilcoxon tests, Mann-Whitney U, and Kruskal-Wallis.

Planned Notes

  • Complete Statistics
  • Fisher’s Exact Test
  • Bayesian inference
  • Bootstrap methods
  • Friedman Test
  • Runs Test

4 items under this folder.