Table 1 MSE of memory-type ratio and conventional ratio estimators.
\(\:{\varvec{\uprho\:}}_{\mathbf{Y}\mathbf{X}}\) | n | \(\:\varvec{\lambda\:}=\:0.1\) | \(\:\varvec{\lambda\:}=\:0.2\) | \(\:\varvec{\lambda\:}=\:0.3\) | \(\:\varvec{\lambda\:}=\:0.5\) | \(\:\varvec{\lambda\:}=\:0.75\) | |||||
\(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | ||
0.75 | 50 | 1684.564 | 57.705 | 1684.564 | 169.128 | 1684.564 | 268.443 | 1684.564 | 497.696 | 1684.564 | 912.845 |
100 | 772.964 | 37.647 | 772.964 | 83.219 | 772.964 | 126.667 | 772.964 | 255.592 | 772.964 | 443.241 | |
200 | 357.593 | 17.621 | 357.593 | 38.195 | 357.593 | 66.390 | 357.593 | 110.321 | 357.593 | 211.715 | |
300 | 232.755 | 12.042 | 232.755 | 24.902 | 232.755 | 38.812 | 232.755 | 73.966 | 232.755 | 135.976 | |
500 | 130.052 | 6.842 | 130.052 | 15.572 | 130.052 | 23.312 | 130.052 | 44.901 | 130.052 | 87.315 | |
0.80 | 50 | 1386.321 | 61.730 | 1386.321 | 135.572 | 1386.321 | 214.098 | 1386.321 | 408.530 | 1386.321 | 779.512 |
100 | 601.559 | 29.283 | 601.559 | 63.306 | 601.559 | 103.500 | 601.559 | 192.825 | 601.559 | 361.707 | |
200 | 295.843 | 15.241 | 295.843 | 32.418 | 295.843 | 47.407 | 295.843 | 93.385 | 295.843 | 172.788 | |
300 | 193.462 | 10.231 | 193.462 | 20.749 | 193.462 | 33.598 | 193.462 | 60.482 | 193.462 | 109.599 | |
500 | 114.152 | 5.757 | 114.152 | 11.518 | 114.152 | 19.506 | 114.152 | 35.951 | 114.152 | 066.601 | |
0.85 | 50 | 1072.357 | 49.307 | 1072.357 | 107.423 | 1072.357 | 160.986 | 1072.357 | 330.921 | 1072.357 | 588.912 |
100 | 475.455 | 23.436 | 475.455 | 53.800 | 475.455 | 82.333 | 475.455 | 148.521 | 475.455 | 289.185 | |
200 | 234.995 | 12.093 | 234.995 | 23.911 | 234.995 | 40.235 | 234.995 | 71.945 | 234.995 | 131.431 | |
300 | 143.728 | 7.592 | 143.728 | 16.547 | 143.728 | 25.453 | 143.728 | 48.379 | 143.728 | 086.577 | |
500 | 87.631 | 4.457 | 87.631 | 9.685 | 87.631 | 15.531 | 87.631 | 25.600 | 87.631 | 048.349 | |
0.90 | 50 | 751.155 | 35.897 | 751.155 | 70.741 | 751.155 | 110.616 | 751.155 | 223.772 | 751.155 | 394.228 |
100 | 319.649 | 15.176 | 319.649 | 35.479 | 319.649 | 57.721 | 319.649 | 107.874 | 319.649 | 194.950 | |
200 | 160.736 | 8.034 | 160.736 | 16.716 | 160.736 | 26.954 | 160.736 | 50.332 | 160.736 | 092.379 | |
300 | 105.941 | 5.516 | 105.941 | 10.544 | 105.941 | 17.813 | 105.941 | 34.241 | 105.941 | 061.083 | |
500 | 59.303 | 3.141 | 59.303 | 6.738 | 59.303 | 10.475 | 59.303 | 19.608 | 59.303 | 036.399 | |
0.95 | 50 | 363.060 | 17.036 | 363.060 | 36.569 | 363.060 | 59.418 | 363.060 | 114.124 | 363.060 | 208.338 |
100 | 172.228 | 8.628 | 172.228 | 17.518 | 172.228 | 27.332 | 172.228 | 53.374 | 172.228 | 92.085 | |
200 | 81.364 | 4.201 | 81.364 | 8.389 | 81.364 | 13.015 | 81.364 | 26.045 | 81.364 | 47.510 | |
300 | 51.623 | 2.637 | 51.623 | 5.702 | 51.623 | 8.576 | 51.623 | 16.294 | 51.623 | 29.323 | |
500 | 29.589 | 1.539 | 29.589 | 3.452 | 29.589 | 5.438 | 29.589 | 9.543 | 29.589 | 17.590 | |
