A Weighted Estimation for Risk Model

Table 2

Exact efficiencies of 𝜇_𝑤 relative to other estimators by using 𝐿₂-optimal weights, 𝛾=1, 𝜈=10.

Sample size	𝛼	𝑤𝐿2-opt	𝑤=1/𝑛	𝑤𝐿1-opt	MSE (𝜇𝑤)	MSE (𝑋)	EFF (𝜇𝑤(𝑋))
𝑛=10	0.8	0.10396	0.1	0.10541	0.4007	0.4034	1.0068
	1.8	0.11446			0.1406	0.1647	1.1717
	3	0.11847			0.0365	0.0493	1.3501
𝑛=20	0.8	0.05015	0.05	0.05130	0.2017	0.2017	1.0001
	1.8	0.05255			0.0766	0.0824	1.0759
	3	0.05463			0.0217	0.0247	1.1367
𝑛=30	0.8	0.03323	0.03333	0.03390	0.1344	0.1345	1.0003
	1.8	0.03425			0.0528	0.0549	1.0399
	3	0.03529			0.0155	0.0164	1.0628
𝑛=50	0.8	0.02021	0.02	0.02020	0.0968	0.1063	1.0978
	1.8	0.02159			0.0514	0.0592	1.1536
	3	0.02298			0.0274	0.0352	1.2849
𝑛=100	0.8	0.01001	0.01	0.01005	0.0765	0.0830	1.0845
	1.8	0.01002			0.0542	0.0576	1.0637
	3	0.01002			0.0380	0.0400	1.0526