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314788

Inference in Linear Models with Nonstochastic Biased Factors

Article

Last updated: 28 Dec 2024

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Abstract

Obenchain (1977) claimed that ridge techniques with nonstochastic of biased factors don't generally yield "new" normal theory statistical inference than that used in least squares technique, and that the t and F statistics are identical under both techniques. Theorems (1)-(3), in this paper, prove that this is true when using the unbasid ordinary least squares estimator S2 of σ2 Moreover, a counter example is introduced to show that the normal theory doesn't apply when using the ridge regression estimator Sr2 of σ2 instead of using the least squares estimator S2.

DOI

10.21608/esju.1996.314788

Keywords

Ordinary Least Squares (OLS), Sum of Squares of Errors under Least Squares (SSEols), Sum of Squares of Errors under Ridge (SSEr), Best Linear Unbiased Estimator (BLUE), Uniformly Minimum Variance Unbiased Estimator (UMVUE), Mean Square Error (MSE), Canonical Parametrization

Authors

First Name

Abdul-Mordy

Last Name

Azzam

MiddleName

H.

Affiliation

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Orcid

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Volume

40

Article Issue

2

Related Issue

43152

Issue Date

1996-12-01

Publish Date

1996-12-01

Page Start

172

Page End

181

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_314788.html

Detail API

https://esju.journals.ekb.eg/service?article_code=314788

Order

4

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Inference in Linear Models with Nonstochastic Biased Factors

Details

Type

Article

Created At

28 Dec 2024