Deriving generalized means as least squares and maximum likelihood estimates

Roger L. Berger

doi:10.1080/00031305.1992.10475904

Deriving generalized means as least squares and maximum likelihood estimates

Roger L. Berger

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

3 Scopus citations

Abstract

Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates. The well-known arithmetic, geometric, and harmonic means are all examples of generalized means. We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set. We also investigate models that have generalized means as their maximum likelihood estimates.

Original language	English (US)
Pages (from-to)	276-278
Number of pages	3
Journal	American Statistician
Volume	46
Issue number	4
DOIs	https://doi.org/10.1080/00031305.1992.10475904
State	Published - Nov 1992
Externally published	Yes

Keywords

Arithmetic mean
Exponential family
Geometric mean
Harmonic mean

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

Access to Document

10.1080/00031305.1992.10475904

Cite this

@article{5c729f80ed504679a4ca8821e1731c1f,

title = "Deriving generalized means as least squares and maximum likelihood estimates",

abstract = "Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates. The well-known arithmetic, geometric, and harmonic means are all examples of generalized means. We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set. We also investigate models that have generalized means as their maximum likelihood estimates.",

keywords = "Arithmetic mean, Exponential family, Geometric mean, Harmonic mean",

author = "Berger, {Roger L.}",

note = "Funding Information: *Roger L. Berger is Professor, Statistics Department, North Carolina State University, Raleigh, NC 27695-8203. George Casella is Professor, Biometrics Unit, Cornell University, Ithaca, NY 14853- 7801. This research was supported by National Science Foundation Grant DMS91-00839 and National Security Agency Grant 90F-073. Part of this work was performed at the Cornell Workshop on Conditional Inference, sponsored by the Army Mathematical Sciences Institute and the Cornell Statistics Center, Ithaca, NY, June 2-14, 1991.",

year = "1992",

month = nov,

doi = "10.1080/00031305.1992.10475904",

language = "English (US)",

volume = "46",

pages = "276--278",

journal = "American Statistician",

issn = "0003-1305",

publisher = "American Statistical Association",

number = "4",

}

TY - JOUR

T1 - Deriving generalized means as least squares and maximum likelihood estimates

AU - Berger, Roger L.

N1 - Funding Information: *Roger L. Berger is Professor, Statistics Department, North Carolina State University, Raleigh, NC 27695-8203. George Casella is Professor, Biometrics Unit, Cornell University, Ithaca, NY 14853- 7801. This research was supported by National Science Foundation Grant DMS91-00839 and National Security Agency Grant 90F-073. Part of this work was performed at the Cornell Workshop on Conditional Inference, sponsored by the Army Mathematical Sciences Institute and the Cornell Statistics Center, Ithaca, NY, June 2-14, 1991.

PY - 1992/11

Y1 - 1992/11

N2 - Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates. The well-known arithmetic, geometric, and harmonic means are all examples of generalized means. We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set. We also investigate models that have generalized means as their maximum likelihood estimates.

AB - Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates. The well-known arithmetic, geometric, and harmonic means are all examples of generalized means. We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set. We also investigate models that have generalized means as their maximum likelihood estimates.

KW - Arithmetic mean

KW - Exponential family

KW - Geometric mean

KW - Harmonic mean

UR - http://www.scopus.com/inward/record.url?scp=84952489361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952489361&partnerID=8YFLogxK

U2 - 10.1080/00031305.1992.10475904

DO - 10.1080/00031305.1992.10475904

M3 - Article

AN - SCOPUS:84952489361

SN - 0003-1305

VL - 46

SP - 276

EP - 278

JO - American Statistician

JF - American Statistician

IS - 4

ER -

Deriving generalized means as least squares and maximum likelihood estimates

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this