The purpose of this course is (i) to present the original Bootstrap theory (this shall include application in parameter estimation, regression and functional estimation) and ((i)
to study different bootstrap methods that are employed in some Machine learning algorithms. The content of the course will be mostly theoretical and students must have a strong background in mathematical statistics (basic probabilistic tools such as density, distribution, variance as well as convergence concepts including almost-sure and weak convergence).
Course 1. Nonparametric bootstrap (Efron’s method). Confidence interval for the empirical mean. Edgeworth development.
Course 2. Weighted bootstrap and Bayesien bootstrap. Prove the CLT in exercise.
Course 3. Bootstrap in regression. Parametric bootstrap.
Course 4. Empirical processes. Application to semiparametric model such as the Cox model. Local estimation (Nadaraya-Watson and k-NN).
Course 5. Cross validation.
Course 6. Bagging. Boosting.