Complete Lecture Notes (PDF 1.3MB)

- Regression Analysis and Prediction Risk
- Models and Methods

Chapter 1: Sub-Gaussian Random Variables (PDF)

- Gaussian tails and MGF
- Sub-Gaussian Random Variables and Chernoff Bounds
- Sub-Exponential Random Variables
- Maximal Inequalities

Chapter 2: Linear Regression Model (PDF)

- Fixed Design Linear Regression
- Least-Squares Estimation
- The Gaussian Sequence Model
- High-Dimensional Linear Regression

Chapter 3: Misspecified Linear Models (PDF)

- Oracle Inequalities
- Nonparametric Regression

Chapter 4: Matrix Estimation (PDF)

- Basic Facts About Matrices
- Multivariate Regression
- Covariance Matrix Estimation
- Principal Component Analysis

Chapter 5: Minimax Lower Bounds (PDF)

- Optimality in a Minmax Sense
- Reductions to Finite Hypothesis Testing
- Lower Bounds Based on Two Hypotheses
- Lower Bounds Based on Many Hypotheses
- Application to the Gaussian Sequence Model