MATH-524 / 5 crédits

Enseignant: Chandak Rajita Ramesh

Langue: Anglais

## 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

## 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

Board and slides

## Expected student activities

Attending lectures and problem classes; interacting in class.

Final Exam

## Supervision

 Office hours No Assistants Yes Forum Yes

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.

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Nonparametric estimation and inference
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Nonparametric estimation and inference
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Nonparametric estimation and inference
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Nonparametric estimation and inference
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Nonparametric estimation and inference
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel

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