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The MLE of Aigner, Amemiya, and Poirier is not the expectile MLE

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Abstract This article compares two asymmetric Gaussian likelihood models and their corresponding estimators. Recently, there has been confusion in the literature regarding these models and (1) whether they are the… Click to show full abstract

Abstract This article compares two asymmetric Gaussian likelihood models and their corresponding estimators. Recently, there has been confusion in the literature regarding these models and (1) whether they are the same, or (2) whether both of them can be used to estimate expectiles. After the comparison, it becomes clear that they are not the same and only one of these models is appropriate for that purpose. The similarity between these models is purely superficial. The historical origin of expectiles has also been disputed: some degree of credit can be shared between two papers.

Keywords: mle; mle aigner; poirier expectile; aigner amemiya; expectile mle; amemiya poirier

Journal Title: Econometric Reviews
Year Published: 2021

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