北京雁栖湖应用数学研究院

2024年09月10日 至 12月12日

This course will assume you attended my previous two courses, which covered the book All of Statistics by Wasserman. In particular, I'll assume you have a broad theoretical basis in statistics and probability, understanding concepts such as random variables, CDFs, pdfs, convergence in probability/distribution, parametric and nonparametric models, the bootstrap, and maximum likelihood estimation. In addition, make sure you are familiar with the practical and theoretical details of linear and logistic regression (e.g. Chapter 13 of Wasserman). More specifically, this course will build upon the nonparametric methods introduced in Chapter 20-21 of Wasserman, so please read or revise those.

1. Review of random variables, convergence, confidence sets
2. Statistical functionals, the empirical CDF, the nonparametric delta method
3. Concentration inequalities (Chernoff bound, sub-Gaussian random variables, Bernstein and McDiarmid inequalities)
4. Empirical probability and processes, uniform Glivenko-Cantelli bounds, Vapnik-Chervonenkis theory
5. Bootstrap confidence intervals of first and second order accuracy
6. Density estimation and bandwidth selection methods
7. Nonparametric regression, variance estimation and confidence bands
8. The normal means problem, adaptive estimation and random radius confidence balls

Wasserman, All of Nonparametric Statistics
Wasserman, 36-705 Intermediate Statistics
Efron and Tibshirani, An Introduction to the Bootstrap
James et al, Introduction to Statistical Learning
Hastie et al, Elements of Statistical Learning

Graduate , 博士后 , Researcher

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