On the mean squared error, the mean absolute error and the like

Shaul K. Bar-Lev; Benzion Boikai; Peter Enis

doi:10.1080/03610929908832390

On the mean squared error, the mean absolute error and the like

Shaul K. Bar-Lev
, Benzion Boikai
, Peter Enis

Department of Statistics

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

Abstract

The problem of finding the minimizer of the r^th-mean error, E(|X-c|^r), r = 1,2, . . . , is revisited, via a unified approach. The approach is discussed for arbitrary r and is illustrated for r = 1 (mean absolute error), r = 2 (mean squared error), and r = 4. This approach is also discussed in the context of maximum likelihood estimation in a class of symmetric distributions which includes, among others, the Laplace and the normal distributions.

Original language	English
Pages (from-to)	1813-1822
Number of pages	10
Journal	Communications in Statistics - Theory and Methods
Volume	28
Issue number	8
DOIs	https://doi.org/10.1080/03610929908832390
State	Published - 1999

Keywords

MSE
Maximum Likelihood Estimation
Prediction

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610929908832390

Cite this

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abstract = "The problem of finding the minimizer of the rth-mean error, E(|X-c|r), r = 1,2, . . . , is revisited, via a unified approach. The approach is discussed for arbitrary r and is illustrated for r = 1 (mean absolute error), r = 2 (mean squared error), and r = 4. This approach is also discussed in the context of maximum likelihood estimation in a class of symmetric distributions which includes, among others, the Laplace and the normal distributions.",

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AU - Enis, Peter

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N2 - The problem of finding the minimizer of the rth-mean error, E(|X-c|r), r = 1,2, . . . , is revisited, via a unified approach. The approach is discussed for arbitrary r and is illustrated for r = 1 (mean absolute error), r = 2 (mean squared error), and r = 4. This approach is also discussed in the context of maximum likelihood estimation in a class of symmetric distributions which includes, among others, the Laplace and the normal distributions.

AB - The problem of finding the minimizer of the rth-mean error, E(|X-c|r), r = 1,2, . . . , is revisited, via a unified approach. The approach is discussed for arbitrary r and is illustrated for r = 1 (mean absolute error), r = 2 (mean squared error), and r = 4. This approach is also discussed in the context of maximum likelihood estimation in a class of symmetric distributions which includes, among others, the Laplace and the normal distributions.

KW - MSE

KW - Maximum Likelihood Estimation

KW - Prediction

UR - https://www.scopus.com/pages/publications/28344455366

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DO - 10.1080/03610929908832390

M3 - Article

AN - SCOPUS:28344455366

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JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 8

ER -

On the mean squared error, the mean absolute error and the like

Abstract

Keywords

ASJC Scopus subject areas

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