Table 1 PRE of the estimators with respect to \(\bar{y}^*_\text {reg}\) for different values of k for Pop I
From: Some classes of estimators in the presence of non-response using auxiliary attribute
Estimator | \(\gamma\) | \(\delta\) | \(\eta\) | \(\psi\) | k | |||
|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | |||||
\(\bar{y}^*_{\text {M}2}\) | – | – | \(C_p\) | \(\beta _2(\varphi )\) | 100.94 | 101.39 | 101.85 | 102.30 |
– | – | \(\beta _2(\varphi )\) | \(C_p\) | 100.95 | 101.41 | 101.87 | 102.33 | |
– | – | 1 | \(C_p\) | 100.94 | 101.39 | 101.85 | 102.30 | |
– | – | 1 | \(\beta _2(\varphi )\) | 100.94 | 101.39 | 101.85 | 102.30 | |
\(\bar{y}^*_{\text {S}2(R)}\) | – | – | 1 | 0 | 100.94 | 101.39 | 101.85 | 102.30 |
\(\bar{y}^*_{\text {S}2(1)}\) | – | – | 1 | 0 | 101.22 | 101.81 | 102.40 | 102.99 |
\(\bar{y}^{*}_{\text {S}2(2)}\) | – | – | 1 | 0 | 118.34 | 114.94 | 113.55 | 112.93 |
\(\bar{y}^*_{\text {M3}}\) | 1 | 1 | n | \(1-n/N\) | 114.65 | 112.36 | 111.49 | 111.18 |
1 | 1 | N | P | 125.51 | 120.09 | 117.82 | 116.73 | |
1 | 1 | N | \(k_p\) | 125.21 | 119.88 | 117.65 | 116.58 | |
\(\bar{y}^*_{\text {M1}}\) | – | – | 1 | 0 | 126.32 | 120.65 | 118.27 | 117.11 |
\(\bar{y}^*_{\text {S}1(1)}\) | – | – | 1 | 0 | 126.32 | 120.65 | 118.27 | 117.11 |
\(\bar{y}^{*}_{\text {S}1(2)}\) | – | – | 1 | 0 | 135.75 | 126.43 | 122.47 | 120.40 |