Nonparametric estimation and inference
Summary
Nonparametric models are used to identify nonlinear relationships within data. This course gives a graduate-level overview of nonparametric statistical estimation and inference theory.
Content
- Kernel Smoothing methods (Stone's theorem, kernel density estimation and regression and local polynomial kernel estimation)
- Estimation consistency and minimaxity (nonparametric minimax rates, relevant empirical process theory results)
- Model selection (bias-variance tradeoff, curse of dimensionality, VC dimension)
- Inference methods (functional approximations, variance estimation, jackknife, bootstrapping)
- Regression and classification trees
- K-nearest neighbours and SVM algorithms
- Semi-parametric regression (partially linear models)
Keywords
Nonparametrics, inference, empirical process theory, machine learning, adaptive methods
Learning Prerequisites
Required courses
Courses on basic probability and statistics (e.g., MATH-240, MATH-230) and a first course on linear regression (e.g., MATH-341). A basic understanding of any programming language (e.g. R, Python, Julia, Matlab)
Recommended courses
Statistical Inference (MA-562).
Important concepts to start the course
Basic statistics, probability and linear algebra
Learning Outcomes
By the end of the course, the student must be able to:
- Assess / Evaluate properties of nonparametric estimation methods
- Interpret construction of complex statistical models
- Prove consistency and convergence results
- Choose appropriate estimation and inference methods
Transversal skills
- Demonstrate a capacity for creativity.
- Demonstrate the capacity for critical thinking
- Assess one's own level of skill acquisition, and plan their on-going learning goals.
- Use both general and domain specific IT resources and tools
Teaching methods
Board and slides
Expected student activities
Attending lectures and problem classes; interacting in class.
Assessment methods
Final Exam
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Hastie, Trevor, et al. The elements of statistical learning: data mining, inference, and prediction. Vol. 2. (2009)
Györfi, László, et al. A distribution-free theory of nonparametric regression. Vol. 1. (2002)
Wasserman, Larry. All of nonparametric statistics (2006)
Notes/Handbook
Will be shared on course Moodle.
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Nonparametric estimation and inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Nonparametric estimation and inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Nonparametric estimation and inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Nonparametric estimation and inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Nonparametric estimation and inference
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional