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Balancing Efficiency and Feasibility: A Sensitivity Analysis of the Augmentation Parameter in the Finite Selection Model

Safaa K. Kadhem

Abstract

This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance, and mean squared error to different values of the augmentation parameter. The results demonstrate that moderate augmentation improves covariate balance while maintaining estimation efficiency. However, excessive augmentation may increase variance and reduce estimator stability. The findings provide practical guidelines for selecting the augmentation parameter in applied experimental design settings.

Balancing Efficiency and Feasibility: A Sensitivity Analysis of the Augmentation Parameter in the Finite Selection Model

Abstract

This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance, and mean squared error to different values of the augmentation parameter. The results demonstrate that moderate augmentation improves covariate balance while maintaining estimation efficiency. However, excessive augmentation may increase variance and reduce estimator stability. The findings provide practical guidelines for selecting the augmentation parameter in applied experimental design settings.
Paper Structure (18 sections, 1 theorem, 9 equations, 4 figures, 3 tables)

This paper contains 18 sections, 1 theorem, 9 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Methodology
  4. Data-Generating Process
  5. Treatment Assignment Mechanisms
  6. Evaluation Metrics
  7. Monte Carlo Setup and Sample Splitting
  8. Robustness Checks
  9. Theoretical Justification for MSE Minimization
  10. Design-Based Evaluation: Neyman's Variance
  11. Results and Discussion
  12. Optimal $\epsilon$ Selection
  13. Graphical Sensitivity Analysis
  14. Robustness to Covariate Structure and Error Distribution
  15. Numerical Results at $\epsilon^*$
  16. ...and 3 more sections

Key Result

Lemma 1

Assume that the joint distribution of the covariates and outcomes is such that the conditional variance $\text{Var}(\hat{\tau} \mid ASMD \le \epsilon)$ is a decreasing function of $\epsilon$ and that the acceptance probability $p(\epsilon) = P(ASMD \le \epsilon)$ is strictly increasing and concave i

Figures (4)

  • Figure 1: Covariate balance (ASMD) as a function of $\epsilon$. Tighter constraints (smaller $\epsilon$) yield better balance across all sample sizes.
  • Figure 2: Mean squared error (MSE) as a function of $\epsilon$. The curves exhibit a U-shaped pattern, with minima at the optimal $\epsilon^*$ indicated by vertical lines. Bootstrap standard errors are shown as shaded bands.
  • Figure 3: Acceptance probability as a function of $\epsilon$. For all sample sizes, the acceptance probability at the optimal $\epsilon^*$ is effectively zero, reflecting the extreme strictness of the MSE-minimizing constraint.
  • Figure 4: Variance Reduction Ratio (VRR) relative to Complete Randomization. The vertical dashed line indicates the optimal $\epsilon^*=0.006$. Shaded bands represent 95% confidence intervals.

Theorems & Definitions (2)

  • Lemma 1: Convexity of MSE
  • proof : Proof Sketch