Teaching - Stats 205

Introduction to Nonparametric Statistics

Description

Nonparametric analogs of the one- and two-sample t-tests and analysis of variance; the sign test, median test, Wilcoxon’s tests, and the Kruskal-Wallis and Friedman tests, tests of independence. Nonparametric regression and nonparametric density estimation, modern nonparametric techniques, nonparametric confidence interval estimates.

Textbooks

Required

Optional

Suggested Journal Articles

Instructor

Christof Seiler, Sequoia Hall 116 (christof.seiler [at] stanford [dot] edu)
Office hours: Wednesdays from 10:00 to 11:30 am in 105 at Sequoia

TA’s

Grading

Midterm Project Content

Some optional guidelines:

  1. State the problem
  2. Describe the data
  3. Review what statistical methods are available to analyze your data
  4. List their advantages and disadvantages, in particular compare nonparametric to parameteric methods
  5. Propose a solution using nonparametric methods
  6. List all the tasks that you plan to do: collecting data, programming, simulating data, estimating, testing, etc.

Final Project

Example of an excellent final project on using kernel density estimation to predict conflicts in the Congo:

Slides

No Topic(s) Background Material
Lecture 1 Logistics and Introduction KM Chapter 1
Lecture 2 Sign Test and Signed-Rank Wilcoxon KM Chapters 2.1, 2.2, and 2.3
Lecture 3 Robustness KM Chapter 2.5
Lecture 4 Bootstrap (Part 1) and Bootstrap (Example) KM Chapter 2.4
Lecture 5 Bootstrap (Part 2) KM Chapter 2.4
Lecture 6 Proportion Problems and \( \chi^2 \) Tests (Part 1) KM Chapters 2.6 and 2.7
Lecture 7 \( \chi^2 \) Tests (Part 2) KM Chapter 2.7
Lecture 8 Two-Sample Problems (Part 1) KM Chapters 3.1 and 3.2
Lecture 9 Two-Sample Problems (Part 2) KM Chapters 3.2 and 3.4
Lecture 10 Permutation Tests (Part 1) G Chapter 1
Lecture 11 Permutation Tests (Part 2) and Neuroimaging (Example) WRR and NH
Lecture 12 Rank-Based Linear Regression KM Chapters 4.1, 4.2, 4.3, 4.4, and 4.8
Lecture 13 Nonlinear Regression (Part 1) W Chapter 4
Lecture 14 Nonlinear Regression (Part 2) W Chapter 5
Lecture 15 Nonlinear Regression (Part 3) W Chapter 5
Lecture 16 Bayesian Nonparametrics (Part 1) W16
Lecture 17 Bayesian Nonparametrics (Part 2) and BNP in Practice W16
Lecture 18 ANOVA KM Chapters 5.1, 5.2, 8.1, 8.2, HMT, and G16
Lecture 19 Survival Analysis (Part 1) KM Chapters 6.1 and 6.2
Lecture 20 Survival Analysis (Part 2) and Midterm Proposal Discussion KM Chapters 6.1 and 6.2
Lecture 21 Ranked Set Sampling HWC Chapter 15 and NWC
Lecture 22 Wavelets HWC Chapter 13 and W Chapter 9
Lecture 23 Graph Limits or Graphons Lo Part 1 and Ch
Lecture 24 Inference for Data Visualization D83, BHLLSW, and JWH
Lecture 25 Multivariate Nonparametric Tests Tu, Ho, RH, and FR
Lecture 26 Bootstrap (Part 3) ET Chapters 12 and Ha, and Lo
Lecture 27 Bootstrap (Part 4) ET Chapters 14 and Ha
Lecture 28 Wrapup  

Homework

Assignment Deadline Solution
Homework 1 April 7th at 1:30 pm Solution 1
Homework 2 April 15th at 1:30 pm Solution 2
Homework 3 April 25th at 1:30 pm Solution 3
Homework 4 May 10th at 1:30 pm Solution 4
Homework 5 May 19th at 1:30 pm Solution 5
Homework 6 May 27th at 1:30 pm Solution 6

Late Homework Policy