2023
DOI: 10.1371/journal.pone.0282578
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Generalized statistics: Applications to data inverse problems with outlier-resistance

Abstract: The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function. In this way, we formulate inverse prob… Show more

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Cited by 4 publications
(1 citation statement)
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“…where φ κ is the κ-objective function, which converges to the classical objective function (9) in the limit κ → 0. The κ-objective function is not easily influenced by aberrant measurements (outliers), as it is based on κ-Gaussian criteria [49]. To demonstrate this, we compute the influence function Υ related to the objective function.…”
Section: Inverse Problems In the Context Of Kaniadakis κ-Statisticsmentioning
confidence: 99%
“…where φ κ is the κ-objective function, which converges to the classical objective function (9) in the limit κ → 0. The κ-objective function is not easily influenced by aberrant measurements (outliers), as it is based on κ-Gaussian criteria [49]. To demonstrate this, we compute the influence function Υ related to the objective function.…”
Section: Inverse Problems In the Context Of Kaniadakis κ-Statisticsmentioning
confidence: 99%