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.

**KM**: Kloke and McKean (2015). Nonparametric Statistical Methods Using R

**ET**: Efron and Tibshirani (1994). An Introduction to the Bootstrap**FM**: Friendly and Meyer (2015). Discrete Data Analysis with R**G**: Good (2005). Permutations, Parametric, and Boostrap Test of Hypothesis**Ha**: Hall (1992). The Bootstrap and Edgeworth Expansion**HP**: Henderson and Parmeter (2015). Applied Nonparametric Econometrics**HMT**: Hoaglin, Mosteller, and Tukey (1983). Understanding Robust and Exploratory Data Analysis**HWC**: Hollander, Wolfe, and Chicken (2013). Nonparametric Statistical Methods**Lo**: Lovasz (2012). Large Networks and Graph Limits**L**: Lehmann (2006). Nonparametrics Statistical Methods Based on Ranks**MQJH**: Müller, Quintana, Jara, and Hanson (2015). Bayesian Nonparametric Data Analysis**PE**: Patrangenaru and Ellingson (2015). Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis**RW**: Rasmussen and Williams (2006). Gaussian Processes for Machine Learning**S**: Silverman (1986). Density Estimation for Statistics and Data Analysis**T**: Tsybakov (2009). Introduction to Nonparametric Estimation**W**: Wasserman (2006). All of Nonparametric Statistics

**B**: Basu (1980). Randomization Analysis of Experimential Data: The Fisher Randomization Test**Bh**: Bhattacharya (2015). Power of Graph-Based Two-Sample Tests**BHLLSW**: Buja, Cook, Hofmann, Lawrence, Lee, Swayne, and Wickham (2009). Statistical Inference for Exploratory Data Analysis and Model Diagnostics**CB**: Carpenter and Bithell (2000). Bootstrap Conidence Intervals: When, Which, What? A Practical Guide for Medical Statisticians**Ch**: Chatterjee (2012). Matrix Estimation by Universal Singular Value Thresholding**C**: Critchlow (1986), A Unified Approach to Constructing Nonparametric Rank Tests**D83**: Diaconis (1983). Theories of Data Analysis: From Magical Thinking Through Classical Statistics**DE**: Diaconis and Efron (1983). Computer Intensive Methods in Statistics**DHa**: Diaconis and Holmes (1994). Gray Codes for Randomization Procedures**DHb**: Diaconis and Holmes (1994). Three Examples of the Markov Chain Monte Carlo Method**Ef**: Efron (1987). Better Bootstrap Confidence Intervals**Ef14**: Efron (2014). Estimation and Accuracy after Model Selection**ENK**: Eklund, Nichols, and Knutsson (2015). Can Parametric Statistical Methods Be Trusted for fMRI Based Group Studies?**FR**: Friedman and Rafsky (1979). Multivariate Generalizations of the Wolfowitz and Smirnov Two-Sample Tests**F**: Friendly (1994). Mosaic Displays for Multi-Way Contingency Tables**GH**: Greenacre and Hastie (1987). The Geometric Interpretation of Correspondence Analysis**H**: Holmes (2008). Multivariate Data Analysis: The French Way**JWH**: Josse, Wager, and Husson (2014). Confidence Areas forFixed-Effects PCA**NWC**: Nahhas, Wolfe, and Chen (2002). Ranked Set Sampling: Cost and Optimal Set Size**MRR**: Marin, Pudlo, Robert, and Ryder (2012). Approximate Bayesian Computational Methods**MW**: Milan and Whittaker (1995). Application of the Parametric Bootstrap to Models that Incorporate a Singular Value Decomposition**NH**: Nichols and Holmes (2001). Nonparametric Permutation Tests For Functional Neuroimaging: A Primer with Examples**PT**: Pagano and Tritchler (1983). On Obtaining Permutation Distributions in Polynomial Time**RH**: Rousseeuw and Hubert (2015). Statistical Depth Meets Computational Geometry: A Short Survey**SMN**: Silver, Montana, and Nichols (2011). False Positives in Neuroimaging Genetics Using Voxel-Based Morphometry Data**Tu**: Tukey (1974). Mathematics and the Picturing of Data**WHE**: Wager, Hastie, and Efron (2014). Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife**WRR**: Witztum, Rips, and Rosenberg (1994). Equidistant Letter Sequences in the Book of Genesis

- TryR provides an adequate initiation to R http://tryr.codeschool.com/
**W16**: Wasserman (2016). Lecture Notes on Nonparametric Bayesian Methods**G16**: Gimond (2016). Lecture Notes on Median Polish**I05**: Ibrahim (2005). Lecture Notes on Surivival Analysis**Ho**: Holmes (1997). Lecture Notes on Computer Intensive Methods in Statistics**Lo**: Love (2010). Bootstrap-t Confidence Intervals (Link to blog entry)

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

- Nan Bi (nbi [at] stanford [dot] edu)

Office hours:- Wednesdays from 2:30 to 3:30 pm in 420-147
- Thursdays from 10:30 to 11:30 am in Fishbowl at Sequoia

- Lexi Guan (lguan [at] stanford [dot] edu)

Office hours:- Monday from 10:00 to 11:00 am in Bowker at Sequoia
- Friday from 4:00 to 5:00 pm in Fishbowl at Sequoia

- Midterm Project Proposal (3 pages with references, 10%, due by April 29th)
- Final Project (12 pages plus references, 40% due by June 3rd)
- Projects can be done alone or in pairs
- Weekly homework (40%)
- Class participation (10%)

Some optional guidelines:

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

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

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 |

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 |

- We will deduct 20% from maximum scores for each late day
- Each student can hand in
**one**homework late (within two days after the deadline) - Please contact me in case of emergencies