Table 2 PRE of the estimators with respect to \(\bar{y}^*_\text {reg}\) for different values of k for Pop II
From: Some classes of estimators in the presence of non-response using auxiliary attribute
Estimator | \(\gamma\) | \(\delta\) | \(\eta\) | \(\psi\) | k | |||
|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | |||||
\(\bar{y}^*_{\text {M}2}\) | – | – | \(C_p\) | \(\beta _2(\varphi )\) | 101.20 | 101.56 | 101.93 | 102.29 |
– | – | \(\beta _2(\varphi )\) | \(C_p\) | 101.21 | 101.58 | 101.95 | 102.32 | |
– | – | 1 | \(C_p\) | 101.20 | 101.56 | 101.93 | 102.29 | |
– | – | 1 | \(\beta _2(\varphi )\) | 101.20 | 101.56 | 101.93 | 102.29 | |
\(\bar{y}^*_{\text {S}2(R)}\) | – | – | 1 | 0 | 101.20 | 101.56 | 101.93 | 102.29 |
\(\bar{y}^*_{\text {S}2(1)}\) | – | – | 1 | 0 | 101.56 | 102.03 | 102.51 | 102.98 |
\(\bar{y}^{*}_{\text {S}2(2)}\) | – | – | 1 | 0 | 115.99 | 114.28 | 113.40 | 112.94 |
\(\bar{y}^*_{\text {M3}}\) | 1 | 1 | n | \(1-n/N\) | 111.48 | 110.64 | 110.29 | 110.18 |
1 | 1 | N | P | 118.59 | 116.52 | 115.45 | 114.88 | |
1 | 1 | N | \(k_p\) | 118.48 | 116.43 | 115.37 | 114.81 | |
\(\bar{y}^*_{\text {M1}}\) | – | – | 1 | 0 | 119.10 | 116.93 | 115.81 | 115.20 |
\(\bar{y}^*_{\text {S}1(1)}\) | – | – | 1 | 0 | 119.10 | 116.93 | 115.81 | 115.20 |
\(\bar{y}^{*}_{\text {S}1(2)}\) | – | – | 1 | 0 | 128.32 | 123.85 | 121.40 | 119.92 |