Statistical Modelling

eth zurich fall 2025

Contents

[click titles to navigate]
  1. The Linear Model
    1. Linear Model Assumption
    2. On Stochastic Components
    3. Examples
    4. Additional Assumptions
  2. Ordinary Least Squares
    1. OLS estimator
    2. OLS under the SLM
    3. Geometric Interpretation
    4. Link to MLE under the SCLM
    5. An intuition for the OLS parameters
  3. Distributional Properties of OLS
    1. Moments under WCLM
    2. Estimator for Deviation Variance
    3. Distributions under SCLM
    4. Asymptotic Normality
  4. Tests and Confidence Intervals
    1. Basic Test Statistics
    2. Basic Confidence Interval
    3. Test and CI Distributions
    4. F-test and its Geometric Interpretation
    5. Coefficient of Determination
  5. Correlation and Regression
    1. Correlation
    2. Empirical Correlation
    3. Partial Correlation
    4. Rank Correlations
  6. Optimality, GLS and WLS
    1. Optimality of OLS
    2. Generalized Assumptions
    3. Generalized Least Squares
    4. Weighted Least Squares
    5. Unknown Heteroscedastic Errors
    6. Misspecification of the Linear Model
  7. Verifying Model Assumptions
    1. Tukey-Anscombe Plot
  8. Model Selection
    1. Problem Definition
    2. Bias-Variance Tradeoff
    3. Forward and Backward Selection
    4. Information Criteria
  9. Generalized Linear Models
  10. Nonparametric Regression
  11. High-Dimensional Linear Models