Table 3 MSE of memory-type exponential ratio and conventional exponential ratio estimators.
\(\:{\varvec{\uprho\:}}_{\mathbf{Y}\mathbf{X}}\) | n | \(\:\varvec{\lambda\:}=\:0.1\) | \(\:\varvec{\lambda\:}=\:0.2\) | \(\:\varvec{\lambda\:}=\:0.3\) | \(\:\varvec{\lambda\:}=\:0.5\) | \(\:\varvec{\lambda\:}=\:0.75\) | |||||
\(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}\) | \(\:{\varvec{t}}_{\varvec{e}\varvec{r}\varvec{s}\varvec{t}}^{\varvec{M}}\) | ||
0.75 | 50 | 287.204 | 15.025 | 287.204 | 30.622 | 287.204 | 49.801 | 287.204 | 94.347 | 287.204 | 169.915 |
100 | 137.540 | 7.522 | 137.540 | 15.083 | 137.540 | 24.845 | 137.540 | 48.176 | 137.540 | 80.284 | |
200 | 66.382 | 3.823 | 66.382 | 7.542 | 66.382 | 12.318 | 66.382 | 24.384 | 66.382 | 41.518 | |
300 | 45.932 | 2.820 | 45.932 | 4.953 | 45.932 | 7.625 | 45.932 | 15.232 | 45.932 | 26.176 | |
500 | 27.052 | 1.837 | 27.052 | 2.972 | 27.052 | 4.946 | 27.052 | 8.109 | 27.052 | 14.679 | |
0.80 | 50 | 255.414 | 13.429 | 255.414 | 29.969 | 255.414 | 45.223 | 255.414 | 83.560 | 255.414 | 147.409 |
100 | 124.594 | 6.858 | 124.594 | 13.343 | 124.594 | 22.232 | 124.594 | 40.725 | 124.594 | 78.522 | |
200 | 65.596 | 3.968 | 65.596 | 7.017 | 65.596 | 10.631 | 65.596 | 19.167 | 65.596 | 35.686 | |
300 | 38.434 | 2.506 | 38.434 | 4.892 | 38.434 | 6.530 | 38.434 | 13.099 | 38.434 | 23.081 | |
500 | 22.654 | 1.631 | 22.654 | 2.687 | 22.654 | 4.334 | 22.654 | 7.331 | 22.654 | 13.830 | |
0.85 | 50 | 218.007 | 11.628 | 218.007 | 24.288 | 218.007 | 40.116 | 218.007 | 79.100 | 218.007 | 121.875 |
100 | 108.828 | 6.216 | 108.828 | 12.334 | 108.828 | 18.258 | 108.828 | 37.720 | 108.828 | 64.205 | |
200 | 50.623 | 3.114 | 50.623 | 6.133 | 50.623 | 9.417 | 50.623 | 17.803 | 50.623 | 31.901 | |
300 | 33.970 | 2.276 | 33.970 | 3.956 | 33.970 | 6.261 | 33.970 | 11.363 | 33.970 | 20.344 | |
500 | 19.378 | 1.447 | 19.378 | 2.435 | 19.378 | 3.583 | 19.378 | 6.654 | 19.378 | 12.734 | |
0.90 | 50 | 188.256 | 10.158 | 188.256 | 18.942 | 188.256 | 32.542 | 188.256 | 60.608 | 188.256 | 111.353 |
100 | 85.711 | 4.887 | 85.711 | 9.628 | 85.711 | 15.201 | 85.711 | 30.890 | 85.711 | 55.922 | |
200 | 42.142 | 2.654 | 42.142 | 4.534 | 42.142 | 7.802 | 42.142 | 14.811 | 42.142 | 26.205 | |
300 | 28.955 | 1.963 | 28.955 | 3.321 | 28.955 | 5.070 | 28.955 | 9.717 | 28.955 | 17.081 | |
500 | 17.722 | 1.351 | 17.722 | 2.056 | 17.722 | 3.202 | 17.722 | 6.011 | 17.722 | 10.408 | |
0.95 | 50 | 145.571 | 8.072 | 145.571 | 16.923 | 145.571 | 25.886 | 145.571 | 49.223 | 145.571 | 84.633 |
100 | 69.035 | 4.035 | 69.035 | 8.260 | 69.035 | 12.683 | 69.035 | 23.019 | 69.035 | 42.619 | |
200 | 34.492 | 2.226 | 34.492 | 3.933 | 34.492 | 6.163 | 34.492 | 11.225 | 34.492 | 19.472 | |
300 | 23.946 | 1.719 | 23.946 | 2.534 | 23.946 | 4.165 | 23.946 | 7.849 | 23.946 | 13.446 | |
500 | 13.747 | 1.164 | 13.747 | 1.714 | 13.747 | 2.336 | 13.747 | 4.344 | 13.747 | 7.702 | |
