對於聯立方程式模型其係數參數的估計問題, 在利用雙重 k 級估計法時, 必須先確立(k1; k2) 值。關於 (k1; k2) 的最適值, 我們根據Gao & Lahiri (2002) 的概念, 先給定k1 為k 級估計法中最適的k 值, 並在此條件下找出最佳的k2 值; 另外則是同時尋找(k1; k2) 的最適值。我們利用Matlab 計算出其值。另一方面, 針對貝氏估計法, 其係數參數之貝氏解為事後分配poly-t 的期望值, 利用馬可夫鏈蒙地卡羅法可得其數值解。最後我們利用Matlab 以模擬方式來比較這些估計量, 雖然同時尋找(k1; k2) 之最適值其均方差最小但是其偏差項卻不是最小的。

The problem of using the double-k estimator to estimate the parameters in the simultaneous equation model is the choice of (k1; k2). Using the concept from Gao & Lahiri(2002), we find the optimal value of k2 under the given optimal value of k1. Then we use Matlab to find the optimal value of (k1; k2) simultaneously. On the other hand, the Bayesian estimator which is the expectation of the ploy-t distribution may be obtained by using Markov Chain Monte Carlo method. Finally, we compare these estimators by using simulation. We find that the estimator using optimal value of (k1; k2) simultaneously has the minimal value of mean square error, even though it has larger bias than others.

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