Nonparametric Statistics

Links to course content

• Syllabus

• Schedule and assignments

• Reading list and bibliography

Lecture notes

• Mathematical Foundations

• Inequalities and Identities

• Probability Foundations

• Sets, Combinatorics, and Probability

• Hypothesis tests, stratified tests, combining tests

• Confidence sets

• Inference when there are nuisance parameters

• Causal inference

• Pseudo-random numbers, integers, samples, and permutations

• Introduction to permutation tests; application to gender bias in teaching evaluations

• Classical permutation tests based on ranks

• Tests of randomness and independence

• Simulating/randomizing \(P\)-values in permutation tests

• Simulated \(P\)-values are exact \(P\)-values for randomized tests

• Abstract permutation tests based on projections

• Combining tests

• E-values

• Nonparametric confidence bounds for constrained means

  • Bounds based on the empirical distribution

    • Markov’s inequality and the Kolmogorov-Smirnov distance

    • The Gaffke bound

  • Dollar-Unit Sampling and taint

  • Penny sampling

  • Tests based on martingales and supermartingales

    • Wald’s Sequential Probability Ratio Test (SPRT)

    • The SPRT for sampling without replacement

    • The SPRT with nuisance parameters

    • The Kaplan-Wald confidence bound

    • Kaplan’s martingale test

    • Introduction to election auditing and the Kaplan-Markov Inequality

    • Supermartingale tests related to the SPRT

• Resampling methods: Bootstrap, Jackknife, and permutation

• Fisher’s exact test

• Inference from stratified samples

  • Inference about the mean of binary populations

  • Inference about bounded populations

• Statistical inference

• Goodness of Fit Tests

• Density estimation and inference; inverse problems

• Election Audits