Nonparametric estimation and inference

MATH-524 / 5 credits

Teacher: Chandak Rajita Ramesh

Language: English

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

Reference week

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