Laplace's method and BIC model selection for least absolute value criterion

Jean Marc Bardet

doi:10.1016/j.spl.2022.109764

Laplace's method and BIC model selection for least absolute value criterion

Jean Marc Bardet

Université Panthéon-Sorbonne (Paris 1)

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in log(n) remains the same in the context of a selection of explanatory variables by least absolute value regression.

Original language	English
Article number	109764
Journal	Statistics and Probability Letters
Volume	195
DOIs	https://doi.org/10.1016/j.spl.2022.109764
Publication status	Published - 1 Apr 2023
Externally published	Yes

Keywords

BIC criterion
Laplace's method
Least absolute values regression
Model selection
Robust statistics

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10.1016/j.spl.2022.109764

Cite this

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abstract = "In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in log(n) remains the same in the context of a selection of explanatory variables by least absolute value regression.",

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AB - In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in log(n) remains the same in the context of a selection of explanatory variables by least absolute value regression.

KW - BIC criterion

KW - Laplace's method

KW - Least absolute values regression

KW - Model selection

KW - Robust statistics

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DO - 10.1016/j.spl.2022.109764

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Laplace's method and BIC model selection for least absolute value criterion

Abstract

Keywords

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