Table 1 Summary of ML estimation of the regression model for the simulated data
From: Estimation of a linear model with two-parameter symmetric platykurtic distributed errors
Sample size ( n) | Parameter | Estimate | Standard error | Wald 95% confidence limits | Chi-square | Pr > chi-square | |
|---|---|---|---|---|---|---|---|
Lower | Upper | ||||||
100 | β 0 | 4.0747 | 0.2515 | 3.5817 | 4.5677 | 262.46 | <.0001 |
β 1 | 1.9914 | 0.0216 | 1.9491 | 2.0337 | 8,510.03 | <.0001 | |
β 2 | 2.9998 | 0.0010 | 2.9978 | 3.0019 | 8,263,598 | <.0001 | |
σ | 1.0668 | 0.0754 | 0.9288 | 1.2254 |  |  | |
1,000 | β 0 | 3.8958 | 0.0696 | 3.7593 | 4.0323 | 3,129.59 | <.0001 |
β 1 | 2.0062 | 0.0065 | 1.9935 | 2.0189 | 96,198.0 | <.0001 | |
β 2 | 2.9999 | 0.0001 | 2.9997 | 3.0000 | 1.408E9 | <.0001 | |
σ | 1.0242 | 0.0229 | 0.9803 | 1.0701 |  |  | |
3,000 | β 0 | 4.0504 | 0.0407 | 3.9707 | 4.1301 | 9,916.51 | <.0001 |
β 1 | 1.9938 | 0.0036 | 1.9867 | 2.0009 | 303,055 | <.0001 | |
β 2 | 2.9999 | 0.0000 | 2.9999 | 3.0000 | 3.731E9 | <.0001 | |
σ | 1.0037 | 0.0130 | 0.9786 | 1.0294 |  |  | |
5,000 | β 0 | 4.0012 | 0.0315 | 3.9394 | 4.0630 | 16,095.1 | <.0001 |
β 1 | 2.0013 | 0.0028 | 1.9957 | 2.0068 | 506,637 | <.0001 | |
β 2 | 3.0000 | 0.0000 | 3.0000 | 3.0000 | 6.34E10 | <.0001 | |
σ | 0.9988 | 0.0100 | 0.9794 | 1.0186 |  |  | |
10,000 | β 0 | 4.0052 | 0.0220 | 3.9620 | 4.0483 | 33,060.4 | <.0001 |
β 1 | 1.9981 | 0.0020 | 1.9942 | 2.0019 | 1,031,236 | <.0001 | |
β 2 | 3.0000 | 0.0000 | 3.0000 | 3.0000 | 9.55E11 | <.0001 | |
σ | 0.9850 | 0.0070 | 0.9714 | 0.9987 |  |  | |