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

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

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

• https://go.epfl.ch/MATH-524