Does the generalized mean have the potential to control outliers?

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...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods Vol. 50; no. 8; pp. 1709 - 1727
Main Authors: Mukhopadhyay, Soumalya, Das, Amlan Jyoti, Basu, Ayanendranath, Chatterjee, Aditya, Bhattacharya, Sabyasachi
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 18.04.2021
Taylor & Francis Ltd
Subjects:
Dominating population
Experimentation
Inference
Maximum likelihood estimators
MLE
Outliers (statistics)
Parameter estimation
power means
robustness
ISSN:0361-0926, 1532-415X
Online Access:Get full text
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Summary: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.
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2019.1652320