On Generalized Likelihood Estimation Based on the Logarithmic Norm Relative Entropy Article Swipe
Himanshi Singh
,
Abhik Ghosh
,
Nil Kamal Hazra
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2510.13179
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2510.13179
Traditional likelihood based methods for parameter estimation get highly affected when the given data is contaminated by outliers even in a small proportion. In this paper, we consider a robust parameter estimation method, namely the minimum logarithmic norm relative entropy (LNRE) estimation procedure, and study different (generalized) sufficiency principles associated with it. We introduce a new two-parameter power-law family of distributions (namely, $\mathcal{M}^{(α,β)}$-family), which is shown to have a fixed number of sufficient statistics, independent of the sample size, with respect to the generalized likelihood function associated with the LNRE. Then, we obtain the generalized minimal sufficient statistic for this family and derive the generalized Rao-Blackwell theorem and the generalized Cramér-Rao lower bound for the minimum LNRE estimation. We also study the minimum LNRE estimators (MLNREEs) for the family of Student's distributions particularly in detail. Our general results reduces to the classical likelihood based results under the exponential family of distributions at specific choices of the tuning parameter $α$ and $β$. Finally, we present simulation studies followed by a real data analysis, which highlight the practical utility of the MLNREEs for data contaminated by possible outliers. Along the way we also correct a mistake found in a recent paper on related theory of generalized likelihoods.
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- Type
- preprint
- Landing Page
- http://arxiv.org/abs/2510.13179
- https://arxiv.org/pdf/2510.13179
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W4415274624
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https://openalex.org/W4415274624Canonical identifier for this work in OpenAlex
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https://doi.org/10.48550/arxiv.2510.13179Digital Object Identifier
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On Generalized Likelihood Estimation Based on the Logarithmic Norm Relative EntropyWork title
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preprintOpenAlex work type
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2025Year of publication
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2025-10-15Full publication date if available
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Himanshi Singh, Abhik Ghosh, Nil Kamal HazraList of authors in order
- Landing page
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https://arxiv.org/abs/2510.13179Publisher landing page
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https://arxiv.org/pdf/2510.13179Direct link to full text PDF
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YesWhether a free full text is available
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0Total citation count in OpenAlex
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