On Being Bayes and Unbiasedness: Bayes and Unbiasedness

Siamak Noorbaloochi; Glen Meeden

doi:10.1007/s13171-017-0097-3

On Being Bayes and Unbiasedness: Bayes and Unbiasedness

Siamak Noorbaloochi, Glen Meeden

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

1 Scopus citations

Abstract

Assuming squared error loss, we show that finding unbiased estimators and Bayes estimators can be treated as using a pair of linear operators that operate between two Hilbert spaces. We note that these integral operators are adjoint and then investigate some consequences of this fact. An extension to loss functions that can be defined via an inner product is also presented.

Original language	English (US)
Pages (from-to)	152-167
Number of pages	16
Journal	Sankhya A
Volume	80A
DOIs	https://doi.org/10.1007/s13171-017-0097-3
State	Published - Jan 1 2018

Bibliographical note

Funding Information:
Acknowledgments. Research was supported in part by IIR 12-340 –HSR&D grant, Department of Veterans Affairs, Veterans Health Administration, Office of Research and Development.

Publisher Copyright:
© 2017, Indian Statistical Institute.

Keywords

Bayes estimators
Consistency
Squared error loss
Unbiasedness

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10.1007/s13171-017-0097-3

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abstract = "Assuming squared error loss, we show that finding unbiased estimators and Bayes estimators can be treated as using a pair of linear operators that operate between two Hilbert spaces. We note that these integral operators are adjoint and then investigate some consequences of this fact. An extension to loss functions that can be defined via an inner product is also presented.",

keywords = "Bayes estimators, Consistency, Squared error loss, Unbiasedness",

author = "Siamak Noorbaloochi and Glen Meeden",

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AU - Meeden, Glen

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N2 - Assuming squared error loss, we show that finding unbiased estimators and Bayes estimators can be treated as using a pair of linear operators that operate between two Hilbert spaces. We note that these integral operators are adjoint and then investigate some consequences of this fact. An extension to loss functions that can be defined via an inner product is also presented.

AB - Assuming squared error loss, we show that finding unbiased estimators and Bayes estimators can be treated as using a pair of linear operators that operate between two Hilbert spaces. We note that these integral operators are adjoint and then investigate some consequences of this fact. An extension to loss functions that can be defined via an inner product is also presented.

KW - Bayes estimators

KW - Consistency

KW - Squared error loss

KW - Unbiasedness

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JF - Sankhya A

ER -

On Being Bayes and Unbiasedness: Bayes and Unbiasedness

Abstract

Bibliographical note

Keywords

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