Introduction to HOIF: Higher-Order Influence Function Estimators for the ATE
Introduction | Background | Key Features | Mathematical Background | The HOIF Framework | U-Statistics Formulation | Sample Splitting | Installation | Setting up the Python backend | No Python at all? | Quick Start Example | Generate Simulated Data | Split the Sample | Estimate (Misspecified) Nuisance Functions on the Nuisance Sample | The First-Order AIPW Estimator and its Bias | Compute the eHOIF Estimator (with sample splitting) | Compute the sHOIF Estimator (without sample splitting) | Debias the AIPW Estimator | Visualize Convergence | Main Function: hoif_ate() | Arguments | Return Value | Advanced Usage | Using Basis Expansion | Sample Splitting (Cross-Fitting) | Regularized Gram Matrix Inversion | Pure R Backend | Computational Details | Python Backend (ustats) | Pure R Implementation | Performance Considerations | Practical Recommendations | Choosing the Transformation Method | Choosing the Order | Use a GPU if Available | Troubleshooting | Python Backend Issues | Numerical Instability | Extreme Propensity Scores | References