gsba604

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Module 1. Linear Regression Methods in Fixed, Moderate and High dimensions
- Ordinary Least Squares (OLS)
  - Estimation
    - BLUE, Gauss-Markov Theorem
  - Confidence Sets
    - Confidence Interval for a single Linear Parametric Function (LPF)
    - Confidence Regions for multiple LPFs
    - Simultaneous Confidence Intervals for multiple LPFs
    - Prediction Interval
  - Hypothesis Testing
    - Testing for the signifance of a single LPF
      - Testing for the signifance of individual predictors: t-test
    - ANOVA Table and testing hypothesis involving several LPFs
      - Testing for the signifance of the entire model: F-test
- Variable/Model Selection
  - Forward Selection
  - Backward Selection
  - AIC, BIC, Cp
  - Best Subset
  - Cross Validation (CV) [Download CV Slides from ISL]
- Penalized/Shrinkage Methods For Moderate and High dimensional problems
  - Multicollinearity and VIF
  - Curse of Dimensionality
  - Ridge
  - Lasso
  - Computational complexity, path algorithms, LARS and glmnet
  - Selecting the penalty parameter by CV
  - Elastic Net
  - Group Lasso
  - Fused Lasso
- Categorical Predictors
- Least Squares in Heteroskedastic Models
  - Generalized Least Squares
  - Weighted Least Squares
- Quantile Regression
- M-Estimation
  - Huber loss, Robustness and rlm R package
Module 2. Non-Linear Regression
- Transforming the Response: Box-Cox method
- Transforming the Predictors
  - Polynomial Regression
  - Regression Splines
  - Local Regression
  - Generalized Additive Models (GAM)
  - Dimension Reduction Methods
    - Principal Component Regression
    - Partial Least Squares
Module 3. Generalized Linear Models (GLM)
- Popular Models
  - Binary Data (Logit and Probit)
  - Multinomial Response Models
  - Count Data (Poisson GLM)
  - Models for Contingency tables
  - Connections between logistic and log-linear models
  - Quasi-likelihood Models
- General framework for studying theory and methods for GLMs
  - Moving Beyond Gaussianity
  - Exponential Dispersion Family
  - Divergence and general inference principles
- Random Effects, Correlated Responses and GLMM
  - Normal Linear Mixed Model
  - Generalized Linear Mixed Model (GLMM)
- High-dimensional (HD) Versions
  - Estimation in HD glm and glmnet R package
  - Hypothesis testing in HD glm
  - Estimation in HD lmm
  - Estimation in HD glmm with glmmlasso
  - Testing goodness of fit in glmm
Module 4. Causal Inference
- Causal Inference using regression on the treatment variables
  - Causal inference and predictive comparisons
  - Randomized experiments and Observational studies
  - Ignorable treatment assignments
- Causal inference using more advanced models
  - Imbalance and lack of complete overlap
  - Propensity score matching
  - Regression discontinuity
  - Estimating causal effects indirectly using instrumental variables

gsba604

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