On the Asymptotic Efficiency of the Empirical Characteristic Function Estimator in the Exponential Proportional Hazards Model

Description

This dataset contains all replication materials for the article: "Characteristic Function Method via the Dirac Delta Function: Parameter Estimation for Normal and Exponential Distributions under Random Censoring" (submitted). The repository includes: 1. Data: Leukemia remission data from Freireich et al. (1963) as reproduced in Kalbfleisch & Prentice (2002), Table 1.1. Two CSV files are provided: leukemia_6mp.csv (6-MP treatment group, n=21, 9 events) and leukemia_placebo.csv (placebo group, n=21, all events). 2. Code: Python scripts (numpy, scipy, pandas) that reproduce all Monte Carlo tables and verify every theoretical result in the paper: - Exact bias and variance formulas for the exponential PHM estimator (Theorem 6.6). - Asymptotic normality and efficiency (Theorem 7.2). - Weibull PHM extension (Theorem 7.5). - Cauchy MCF vs ML comparison (Table 4). - Real data analysis (Section 7.3). - Fisher information matrix verification. 3. README.md: Detailed instructions, file descriptions, dependency list, and reproducibility notes. 4. requirements.txt: Python package dependencies (numpy, scipy, pandas). All simulations use fixed random seeds (seed=42) for full reproducibility. Results match the tables and theorems in the paper to Monte Carlo accuracy.

Steps to reproduce

1. Extract the downloaded archive (if zipped) to a local folder. 2. Open a terminal/command prompt and navigate to the code/ directory: cd code 3. Run the Python scripts in the following order (each script generates output CSV files in the results/ folder): - 01_exponential_phm_mc.py (produces Tables 2 & 3: bias, variance, efficiency) - 02_cauchy_mc.py (produces Table 4: MCF vs ML for Cauchy, ~5 min) - 03_weibull_phm_mc.py (produces Table 5: Weibull PHM efficiency) - 04_real_data_analysis.py (produces real data estimates and CIs, Section 7.3) - 05_fisher_information.py (verifies Fisher information matrix, Lemma 7.1 & Theorem 7.2) - 06_exact_formulas_check.py (verifies all closed-form formulas, e.g., bias, variance) 4. All results are saved as CSV files in the results/ folder. Compare them with the tables in the paper. NOTES: - All scripts use a fixed random seed (seed=42) for full reproducibility. - The data files (leukemia_6mp.csv, leukemia_placebo.csv) are in the data/ folder and are automatically loaded by the scripts. - Script 02_cauchy_mc.py may take about 5 minutes; for a quick test, reduce N_LIST in the script.

Institutions

• National University of Uzbekistan

  Tashkent, Tashkent

Categories

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