Cheng and Amin (1983) proposed the maximum product of spacing estimation method as an alternative to maximum likelihood estimation. They stated that MPS behaves better in small sample cases than MLE and gives consistent estimators where MLE fails (Eg. J shaped distribution). In addition, MPS follows the same asymptotic property as MLE.
My question is, can there be any situations where MLE performs better than MPS in terms of MSE and Bias? Simulation studies in some literature showed that MLE can be better than MPS (For example), but when such cases happen, I want to know the reason behind it.