STAT 5372 -- Nonparametric Statistics -- Fall 2025
Basic Information
Course instructor:
Dr. Alex
Trindade, 233 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu.
Course Meets: 12:30-13:50 TR, face-to-face in Math 010.
Office Hours: TR 2:00-3:00, W 4:00-5:00, or by appointment.
Required Books
Nonparametric Statistics, by Larry Wasserman, 2006, Springer.
Useful Books/Notes
Nonparametric Statistical Methods, 3rd ed., by Hollander, Wolfe, & Chicken, 2015, Wiley.
Computational Statistics , 2nd ed., by Givens & Hoeting, 2012, Wiley.
Empirical Likelihood, by Art Owen, 2001, CRC Press.
Bootstrap Methods and their Application, by Davison & Hinkley, 1997, Cambridge.
Introduction to the Theory of Nonparametric Statistics, by Randles & Wolfe, 1979, Wiley.
Notes for Nonparametric Statistics, by Garcia-Portugues (online).
Course Objectives and Syllabus
This course provides an overview of modern nonparametric
statistics. "Nonparametric" can be defined quite broadly, but it tends to mean something rather
different now than it has in the past. Focusing primarily on a modern view of nonparametric
statistics, the course aims to acquaint students with as many of those areas as possible, including
some coverage of classical rank-based nonparametrics. The goal is to introduce a wide range of interesting nonparametric concepts and tools, since this is where most of statistical
methodological research is currently taking place. Some of those ideas are theoretical, others
are computational and methodological. Theory will be introduced when it is useful and
relevant, although some proofs may be skipped in the interest of time. Prerequisite: STAT 5329 (Math-Stat). List of topics:
- The empirical distribution function. (Empirical distribution functions; Statistical functionals; Influence functions; The jackknife; The bootstrap; Bootstrap confidence intervals; Empirical likelihood.)
- Hypothesis testing. (Permutation tests; Rank tests; Bootstrap tests.)
- Density estimation. (The bias-variance trade-off; Cross-validation; Kernels; Kernel density estimation; The curse of dimensionality; Kernel density classification.)
- Nonparametric regression. (Local regression; Basis expansions,
splines, and penalized regression; Quantile regression;
Nonparametric regression and generalized linear
models.)
Expected Student Learning Outcomes
By the end of the course students will be familiar with the theory and practical aspects of modern Nonparametric Statistics.
Methods of Assessing the Expected Learning Outcomes
The course grade will be based on 5 Assignments (broken up into 12
weekly homework sets), which will constitute 50% of your grade. In
addition, there will be two semester tests, each worth 25%. The traditional grading scale will be used:
- A: 90-100%.
- B: 80-89%.
- C: 70-79%.
- D: 60-69%.
- F: 0-59%.
The test schedule is as follows:
- Test 1: Thu Oct 2 (after completion of Assignments 1-2 and Hwk 5).
- Test 2: Thu Nov 13 (after completion of Assignments 3-4 and Hwk 10).
Assignments
Each Assignment will consist of three
sections: (1) Mathematical concepts and derivations; (2) Simulation
studies; (3) Analysis of real data. They will be posted here:
Weekly homework sets will will have you complete portions of each
Assignment. The sets will be posted on Canvas and due on weekends. No late submissions will be accepted.
Notes and code snipets
Lecture notes will follow approximately the slides of Patrick Breheny, I will deviate and make changes on the board as we go through the course. The accompanying R code is to help you reproduce the examples and will be very useful for the Assignments.
- Lecture 1: Introduction; the empirical distribution function. (slides, code).
- Lecture 2: Statistical functionals and influence functions. (slides, code).
- Lecture 3: The functional delta method. (slides, code).
- Lecture 4: Connections between parametric and nonparametric theory. (slides).
- Lecture 5: The jackknife. (slides).
- Lecture 6: The bootstrap. (slides, code).
- Lecture 7: The geometry of the bootstrap. (slides, code).
- Lecture 8: Bootstrap confidence intervals. (slides, code).
- Lecture 9: Empirical likelihood. (slides, code).
- Lecture 10: Permutation tests. (slides, code).
- Lecture 11: Rank tests. (slides, code).
- Lecture 12: Relative efficiency. (slides).
- Lecture 13: Bootstrap tests. (slides, code).
- Lecture 14: Smoothing concepts. (slides, code).
- Lecture 15: Kernel density estimation. (slides, code).
- Lecture 16: Kernel density classification. (slides, code).
- Lecture 17: Introduction to nonparametric regression. (slides, code, functions to source).
- Lecture 18: Local regression I. (slides, code).
- Lecture 19: Local regression II. (slides, code).
- Lecture 20: Local likelihood. (slides, code).
- Lecture 21: Splines. (slides, code).
Datasets
The Lectures and Assignments will rely on access to these Datasets.
Policies
- Required/Recommended Texas Tech Policies can be found on the
Canvas course page.
- Use of Generative AI Tools. The use of generative AI (GAI) for working assignments is not forbidden, but it should be used with discretion. I view GAI as another way to collaborate with peers on solving problems. This can used incorrectly, e.g. when you simply copy your smart friends work (or ask GAI to solve the problem directly), or can be used correctly, e.g., when you discuss with friends the results/steps needed to find a solution after you have put some thought into it (or use GAI more like a search engine to query side questions and digest literature). Remember: you do NOT want to surrender your thought process to the "tool" (friend or GAI); the "tool" will not be available during tests!
- Electronic Devices in Tests. In the spirit of keeping costs down, I will permit the usage of apps on smart devices (phones, tablets, laptops, etc.), but any kind of communication or accessing of the web via these devices is forbidden.
- Collaboration. My policies on this are as follows.
- Homeworks: Discussion with peers regarding material/concepts covered in the
course is permitted, and is encouraged since it usually leads to greater comprehension. However, each person must write up his/her own
solution to a particular problem, and not simply have someone else do it for them.
- Tests: Any form of collaboration on tests, including e-device communication or trying to see what the person next to you is writing, is strictly forbidden and will not be tolerated.
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