STAT 5372 -- Nonparametric Statistics -- Fall 2023
Basic Information
Course instructor:
Dr. Alex
Trindade, 233 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu.
Course Meets: 15:30-16:50 TR, face-to-face in Math 112.
Office Hours: TWR 1:00-2:00, 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 approaches to multiple regression, additive models, thin-plate splines, regression trees.)
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 6 Assignments, each worth approx 1/6 of your grade. The traditional grading scale will be used:
- A: 90-100%.
- B: 80-89%.
- C: 70-79%.
- D: 60-69%.
- F: 0-59%.
Assignments
There will be 6 Assignment Sets. 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:
They will be due at the rate of approximately every other week, but some portion of it will be due every weekend. All work is to be uploaded to Blackboard. No late submissions will be accepted.
- Set 1 (due midnite Fri Sep 1): Assignment 1 # 1, 3, 5, 6, 8(a).
- The remaining Hwk Sets are on Blackboard.
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).
- Lecture 22: Multiple regression and additive models. (slides, code).
- Lecture 23: Tree-based methods. (slides, code).
Datasets
The Lectures and Assignments will rely on access to these Datasets.
Policies
- Required Texas Tech Policies can be found here.
- Recommended Texas Tech Policies can be found here.
- Use of Generative AI Tools. The use of generative AI tools (such as ChatGPT) is not permitted in this course; therefore, any use of AI tools for work in this class may be
considered a violation of Texas Tech's Academic Integrity policy and
the Student Code of Conduct since the work is not your own. The use of
unauthorized AI tools will result in referral to the Office of Student
Conduct.
- 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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