Bariance and Variance Estimators: Reproduction Repository & Robustness Supplements // Speeding UP Your Sample Variance in Big-Data Environments!

Deterministic Reproduction of Results from https://doi.org/10.48550/arXiv.2503.22333

This repository contains a Python 3.11 script (executed in a virtualized cloud environment) for deterministic simulation of a-denominator based sample variance estimators. It computes Bias², Variance, and Mean Squared Error (MSE), alongside bootstrapped standard errors (SEs), as a robustness check in support of Ch. 7 (Simulation Study on MSE across Denominator Values) in v5.
Additionally, empirical runtime plots assess the performance of the Bariance estimator under varied data conditions, such as large-scale gamma-distributed samples, in a local Java SE 21 environment—supporting Ch. 9 (Empirical Runtime Analysis) and Appendix C (Java Runtime Robustness Checks) of v5.

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Code

• MSEVarEstimsSimulationsWithBootstrapedSEs.py
  Main simulation script. Evaluates multiple sample variance estimators using a fixed-seed normal distribution N(0,1). Calculates Bias², Variance, MSE, and bootstrapped confidence intervals. Python 3.11.

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Runtime Figures

Local Execution Environment:

• Java Runtime: SE 21
• OS: macOS 13.0
• Architecture: aarch64
• Cores: 10 (single-threaded benchmark)
• Max JVM Memory: 4096 MB

These runtime plots replicate and extend the analysis in Ch. 9 and Appendix C (Robustness Checks) of v5:

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Requirements

🐍 Python 3.11+

Install dependencies via:

pip install numpy matplotlib seaborn scipy

♨️ Java 21+

SE 21