MVUE Under Synthetic Contamination: Mean Estimation

Characterizing the minimum-variance unbiased estimator for mean estimation under recursive synthetic contamination.

14.5%

Max Variance Reduction

0.3%

GLS vs Joint Gap

0.5

Phase Transition at alpha

~1.00

MC Validation Ratio

4

Estimator Families

Variance Comparison Across Methods

Improvement Over Uniform Weighting (%)

Variance Scaling with T (alpha=0.7)

Monte Carlo Validation Ratios

Estimator Variance for Selected (T, alpha) Configurations

T	alpha	Uniform	Non-Unif.	GLS-FP	Joint Opt	Improv.
3	0.3	0.3547	0.3569	0.3506	0.3505	1.2%
3	0.7	0.4184	0.3992	0.3850	0.3849	8.0%
3	0.9	0.4929	0.4309	0.4321	0.4278	13.2%
5	0.3	0.2114	0.2166	0.2094	0.2093	1.0%
5	0.7	0.2680	0.2507	0.2382	0.2378	11.3%
5	0.9	0.3488	0.2908	0.3028	0.2989	14.3%
8	0.3	0.1323	0.1370	0.1313	0.1312	0.8%
8	0.7	0.1768	0.1633	0.1534	0.1530	13.5%
8	0.9	0.2483	0.1996	0.2125	0.2122	14.5%
10	0.5	0.1224	0.1184	0.1146	0.1145	6.5%

Monte Carlo Validation (n=100,000)

T	alpha	Opt Theory	Opt Empir.	Opt Ratio	Unif Theory	Unif Empir.	Unif Ratio
3	0.3	0.3505	0.3502	0.999	0.3547	0.3548	1.000
3	0.7	0.3849	0.3852	1.001	0.4184	0.4179	0.999
5	0.3	0.2093	0.2098	1.002	0.2114	0.2110	0.998
5	0.7	0.2378	0.2380	1.001	0.2680	0.2685	1.002
8	0.3	0.1312	0.1315	1.002	0.1323	0.1320	0.998
8	0.7	0.1530	0.1528	0.999	0.1768	0.1770	1.001