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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.

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    $\begingroup$ MPS is not well-known and the article is not freely available to all, it may help to add a description of the MPS method. $\endgroup$
    – Wicher
    Commented Aug 8, 2022 at 21:42

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It is very rare to "know why this happens" as regards finite-sample performance of estimators. Most such "conclusions" are based on simulations -meaning that one wonders, "what if the design of the simulation matters for the result?"

While Maximum Product Spacings has a clear advantage over usual MLE, in that it works where MLE may not, whether it performs better "in small samples" is not a consensus in the literature, simply because there are too few such studies that examine the matter.

And I do not know of any published work that attempts to examine it theoretically. So maybe this is an opportunity for you to move beyond good intentions.

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