A Simplified Approach for Two-Dimensional Optimal Controlled Sampling Designs

Table 16

Comparison of various values of 𝑉(𝑌) for the 4 × 4 population.

𝑉(𝑌)
Sample	𝑝(𝑠)	(𝑌)𝑠	S-S	TN-1	TN-2	Proposed estimator
1	0.1	10.250	0.578125	0.242813	0.329531	0.14453
2	0.1	9.875	0.052031	0.199453	0.342539	0.19799
3	0.0	9.375	0.005781	0.199453	0.221133	0.33097
4	0.0	9.750	0.208125	0.196563	0.167656	0.22546
5	0.0	9.750	0.023125	0.208125	0.052031	0.15609
6	0.3	9.250	0.023125	0.196563	0.248594	0.23346
7	0.0	9.250	0.023125	0.231250	0.040469	0.469727
8	0.0	10.375	0.005781	0.095391	0.383008	0.260156
9	0.1	10.250	0.023125	0.254375	0.398906	0.317960
10	0.0	9.870	0.052031	0.182109	0.319414	0.186445
11	0.0	10.250	0.208125	0.439375	0.375781	0.109844
12	0.0	10.750	0.578125	0.416250	0.387344	0.237031
13	0.0	10.250	0.023125	0.450938	0.271719	0.109844
14	0.0	10.750	0.578125	0.404688	0.352656	0.294844
15	0.1	10.375	0.283281	0.268828	0.359883	0.266881
16	0.0	9.750	0.023113	0.231250	0.387344	0.317969
17	0.2	10.875	0.144531	0.268828	0.296289	0.276831
18	0.0	10.875	0.052031	0.291953	0.307852	0.213906
19	0.1	10.750	0.578125	0.370000	0.375781	0.278953
20	0.0	10.750	0.023125	0.346875	0.260156	0.341094
𝐸[Var(𝑌)]			0.187202	0.246281	0.255927	0.24603500
Bias			−0.056548	0.002531	0.012177	0.00228500
𝑉[Var(𝑌)]			0.0444260	0.002652	0.016581	0.00216700
(Bias)^2			0.0031977	0.0000064	0.000148	0.00000522
MSE[Var(𝑌)]			0.0476237	0.0026584	0.016729	0.00217222
(Bias)^2/MSE[Var(𝑌)]			0.0671451	0.0024112	0.0088585	0.00240309