Research Article
Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models
Table 4
Absolute Bias and MSE of parameter estimates from the Bayesian estimation of the Gumbel copula with different sample sizes.
| Parameter | Absolute Bias | MSE | = 0.25 | = 100 | = 500 | = 1000 | = 100 | = 500 | = 1000 |
| | 0.0200 | 0.0115 | 0.0028 | 0.0747 | 0.0147 | 0.049 | | 0.0224 | 0.0073 | 0.0048 | 0.0699 | 0.0133 | 0.0053 | | 0.0356 | 0.0043 | 0.0058 | 0.0625 | 0.0120 | 0.0051 | | 0.0019 | 0.0016 | 0.0010 | 0.1138 | 0.0136 | 0.0051 | | 0.0465 | 0.0087 | 0.0012 | 0.0637 | 0.0108 | 0.0062 | | 0.0103 | 0.0101 | 0.0032 | 0.0766 | 0.0105 | 0.0067 | | 0.0431 | 0.0281 | 0.0083 | 0.0149 | 0.0094 | 0.0079 |
| = 0.50 | = 100 | = 500 | = 1000 | = 100 | = 500 | = 1000 |
| | 0.0149 | 0.0073 | 0.0009 | 0.0409 | 0.0083 | 0.0039 | | 0.0066 | 0.0074 | 0.0037 | 0.0437 | 0.0100 | 0.0042 | | 0.0076 | 0.0082 | 0.0005 | 0.0492 | 0.0075 | 0.0036 | | 0.0007 | 0.0005 | 0.0004 | 0.0689 | 0.0085 | 0.0034 | | 0.0500 | 0.0117 | 0.018 | 0.0477 | 0.0084 | 0.0049 | | 0.0018 | 0.0011 | 0.0030 | 0.0467 | 0.0089 | 0.0046 | | 0.9005 | 0.8391 | 0.4918 | 0.8443 | 0.7433 | 0.1588 |
| = 0.75 | = 100 | = 500 | = 1000 | = 100 | = 500 | = 1000 |
| | 0.0079 | 0.0013 | 0.0001 | 0.0499 | 0.0111 | 0.0015 | | 0.0085 | 0.0062 | 0.0030 | 0.0665 | 0.0125 | 0.0125 | | 0.0060 | 0.0037 | 0.0012 | 0.0464 | 0.0110 | 0.0014 | | 0.0032 | 0.0018 | 0.0008 | 0.0795 | 0.0121 | 0.0030 | | 0.0142 | 0.0123 | 0.0120 | 0.0544 | 0.0085 | 0.0025 | | 0.0099 | 0.0080 | 0.0040 | 0.0855 | 0.0147 | 0.0058 | | 0.2271 | 0.1321 | 0.1045 | 0.5613 | 0.4351 | 0.0105 |
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