Table 2: Approximate bias, variance, and mean squared error of the method of moments and the maximum likelihood estimators (based on observations) for the two-dimensional MA parameters and from 1000 replications.


Bias Var MSE Bias Var MSE
MME 0.02842 0.00010879 0.00091649 −0.07858 0.00001209 0.0061869
MLE 0.0006 0.0002023 0.00020266 −0.00604 0.00006244 0.00009892

Bias Var MSE Bias Var MSE
MME 0.0149 0.00037173 0.00059374 −0.00746 0.0002023 0.00025795
MLE −0.00184 0.0003022 0.00030558 0.00066 0.00016793 0.00016837

Bias Var MSE Bias Var MSE
MME 0.00576 0.00025984 0.00029302 0.0065 0.00023986 0.00028211
MLE −0.00044 0.00022068 0.00022087 −0.00024 0.0002023 0.00020236


Bias Var MSE Bias Var MSE
MME 0.02638 0.00004406 0.00073996 0.03274 0.00001688 0.00108879
MLE 0.00012 0.00002248 0.00002249 0.00004 0.00010879 0.00010879

Bias Var MSE Bias Var MSE
MME −0.0422653 0.00021173 0.00199808 0.0123275 0.00097912 0.00113109
MLE −0.00058 0.00002248 0.00002281 0.00026 0.00000402 0.00008408