ESTIMATOR

Population I

Population II

BIAS(.)

MSE

BIAS(.)

MSE

$t_1=s_y^2$

0

5395.289

0

1,313,625.261

$t_2=s_y^2\left(\frac{S_x^2}{s_x^2}\right)$

8.151

3276.421

236.154

924,946.481

$t_3=s_y^2\left(\frac{S_x^2+{\kappa }_x}{s_x^2+{\kappa }_x}\right)$

6.956

2740.349

235.656

924,324.375

$t_4=s_y^2\left(\frac{S_x^2-C_x}{s_x^2-C_x}\right)$

8.512

3006.373

236.187

925,017.011

$t_5=s_y^2\left(\frac{S_x^2-{\kappa }_x}{s_x^2-{\kappa }_x}\right)$

9.518

3186.399

236.445

925,569.577

$t_6=s_y^2\left(\frac{S_x^2{\kappa }_x-C_x}{s_x^2{\kappa }_x-C_x}\right)$

8.279

2965.067

236.159

924,956.421

$t_7=s_y^2\left(\frac{S_x^2{C}_x-{\kappa }_x}{s_x^2{C}_x-{\kappa }_x}\right)$

10.002

3275.722

236.517

925,721.916

$t_8=s_y^2\left(\frac{S_x^2+M_x}{s_x^2+M_x}\right)$

4.530

2377.418

233.201

918,641.426

$t_9=s_y^2\left(\frac{S_x^2+Q_1}{s_x^2+Q_1}\right)$

6.126

2609.91

232.889

917,976.121

$t_{10}=s_y^2\left(\frac{S_x^2+Q_3}{s_x^2+Q_3}\right)$

2.934

2181.488

227.099

905,689.896

$t_{11}=s_y^2\left(\frac{S_x^2{C}_x+M_x}{s_x^2{C}_x+M_x}\right)$

3.656

2314.033

232.485

917,116.922

${\widehat{S}}_{PM}^2=s_y^2\left\{\frac{S_x^2{\kappa }_x+M_x^2}{s_x^2{\kappa }_x+M_x^2}\right\}$

0.708

1993.270

207.653

865,134.030