This lecture will be on non-parametric and high dimensional statistics. We will study just a few concepts and estimators, and will study in details their mathematical properties. We will consider two main fields:
- Non-parametric statistic: in this setting, we aim at estimating a non-parametric object, typically a density or a regression function. Classical parametric approaches do not apply here. We will consider several classical estimators (Kernel-based, through an orthonormal basis, etc), and study their theoretical properties.
- High-dimensional linear models: in this setting, we consider the classical linear model in high dimension. Classical approaches such as least squares cannot be applied. We will consider the two most classical estimators, Lasso and Ridge, and study their theoretical properties.
- Kursleiter*in: Prof. Dr. Alexandra Carpentier