Table 5.
Comparison of the various algorithms for estimating the location and scale of a 10-variate t distribution with 0.5 degrees of freedom. The column ln L lists the average converged log-likelihood, and the column Evals lists the average number of EM evaluations. Running times are averaged over 100 simulations with 200 sample points each. The number of parameters is 65, and the stopping criterion is 10−9
| D.F. | Method | EM |
PX-EM |
||||
|---|---|---|---|---|---|---|---|
| ln L | Evals | Time | ln L | Evals | Time | ||
| 1 | EM | −3981.5470 | 160 | 0.8272 | −3981.5470 | 15 | 0.0771 |
| q = 1 | −3981.5470 | 26 | 0.1363 | −3981.5470 | 10 | 0.0497 | |
| q = 2 | −3981.5470 | 22 | 0.1184 | −3981.5470 | 10 | 0.0510 | |
| q = 3 | −3981.5470 | 23 | 0.1216 | −3981.5470 | 10 | 0.0540 | |
| q = 4 | −3981.5470 | 24 | 0.1282 | −3981.5470 | 11 | 0.0555 | |
| q = 5 | −3981.5470 | 26 | 0.1381 | −3981.5470 | 11 | 0.0558 | |
| SqS1 | −3981.5470 | 29 | 0.1570 | −3981.5470 | 10 | 0.0509 | |
| SqS2 | −3981.5470 | 31 | 0.1646 | −3981.5470 | 10 | 0.0507 | |
| SqS3 | −3981.5470 | 30 | 0.1588 | −3981.5470 | 10 | 0.0507 | |
| 0.5 | EM | −3975.8332 | 259 | 1.3231 | −3975.8332 | 15 | 0.0763 |
| q = 1 | −3975.8332 | 31 | 0.1641 | −3975.8332 | 10 | 0.0506 | |
| q = 2 | −3975.8332 | 25 | 0.1343 | −3975.8332 | 10 | 0.0512 | |
| q = 3 | −3975.8332 | 27 | 0.1405 | −3975.8332 | 10 | 0.0544 | |
| q = 4 | −3975.8332 | 28 | 0.1479 | −3975.8332 | 10 | 0.0547 | |
| q = 5 | −3975.8332 | 30 | 0.1553 | −3975.8332 | 11 | 0.0552 | |
| SqS1 | −3975.8332 | 34 | 0.1829 | −3975.8332 | 10 | 0.0514 | |
| SqS2 | −3975.8332 | 38 | 0.2017 | −3975.8332 | 10 | 0.0513 | |
| SqS3 | −3975.8332 | 35 | 0.1895 | −3975.8332 | 10 | 0.0513 | |
| 0.1 | EM | −4114.2561 | 899 | 4.5996 | −4114.2561 | 16 | 0.0816 |
| q = 1 | −4114.2562 | 52 | 0.2709 | −4114.2561 | 10 | 0.0521 | |
| q = 2 | −4114.2561 | 36 | 0.1924 | −4114.2561 | 10 | 0.0533 | |
| q = 3 | −4114.2561 | 34 | 0.1820 | −4114.2561 | 10 | 0.0544 | |
| q = 4 | −4114.2561 | 36 | 0.1895 | −4114.2561 | 10 | 0.0544 | |
| q = 5 | −4114.2561 | 38 | 0.2041 | −4114.2561 | 11 | 0.0558 | |
| SqS1 | −4114.2561 | 51 | 0.2717 | −4114.2561 | 10 | 0.0522 | |
| SqS2 | −4114.2561 | 66 | 0.3492 | −4114.2561 | 10 | 0.0518 | |
| SqS3 | −4114.2561 | 54 | 0.2846 | −4114.2561 | 10 | 0.0519 | |
| 0.05 | EM | −4224.9190 | 1596 | 8.1335 | −4224.9190 | 17 | 0.0857 |
| q = 1 | −4224.9192 | 62 | 0.3248 | −4224.9190 | 10 | 0.0530 | |
| q = 2 | −4224.9192 | 47 | 0.2459 | −4224.9190 | 10 | 0.0539 | |
| q = 3 | −4224.9191 | 39 | 0.2006 | −4224.9190 | 10 | 0.0549 | |
| q = 4 | −4224.9191 | 40 | 0.2089 | −4224.9190 | 11 | 0.0564 | |
| q = 5 | −4224.9191 | 42 | 0.2239 | −4224.9190 | 11 | 0.0565 | |
| SqS1 | −4224.9191 | 60 | 0.3156 | −4224.9190 | 10 | 0.0543 | |
| SqS2 | −4224.9191 | 91 | 0.4809 | −4224.9190 | 10 | 0.0535 | |
| SqS3 | −4224.9191 | 64 | 0.3417 | −4224.9190 | 10 | 0.0535 | |