Does the generalized mean have the potential to control outliers?

Soumalya Mukhopadhyay, Amlan Jyoti Das, Ayanendranath Basu, Aditya Chatterjee and Sabyasachi Bhattacharya

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 8, 1709-1727

Abstract: The efficacy of the generalized mean in controlling outliers is explored in this paper. We found that in the presence of outliers in the data, the generalized mean estimates the mean of the dominating population more accurately compared to the usual maximum likelihood estimator. Thus the generalized mean allows stable estimation of the target mean parameter without invoking the complications of sophisticated robust techniques. For example, while doing experimentation on the growth of species, the data on the size or growth rate of a particular species are often contaminated with those from other species, where the behavior of the latter component is similar to that of a bunch of outlying observations. To carry out realistic growth related inference on the mean growth of the primary component in this situation, the generalized mean is recommended as a useful tool to the experimental biologists. There are innumerable other real-life scenarios where a suitably chosen generalized mean can provide better input in doing inference with real data compared to the arithmetic and other standard means.

Date: 2021
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DOI: 10.1080/03610926.2019.1652320

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