Inference in Linear Models with Nonstochastic Biased Factors
Azzam, A. (1996). Inference in Linear Models with Nonstochastic Biased Factors. EKB Journal Management System, 40(2), 172-181. doi: 10.21608/esju.1996.314788
Abdul-Mordy H. Azzam. "Inference in Linear Models with Nonstochastic Biased Factors". EKB Journal Management System, 40, 2, 1996, 172-181. doi: 10.21608/esju.1996.314788
Azzam, A. (1996). 'Inference in Linear Models with Nonstochastic Biased Factors', EKB Journal Management System, 40(2), pp. 172-181. doi: 10.21608/esju.1996.314788
Azzam, A. Inference in Linear Models with Nonstochastic Biased Factors. EKB Journal Management System, 1996; 40(2): 172-181. doi: 10.21608/esju.1996.314788

Inference in Linear Models with Nonstochastic Biased Factors

The Egyptian Statistical Journal
Article 4, Volume 40, Issue 2, December 1996, Page 172-181  XML PDF (6.96 MB)
Document Type: Original Article
DOI: 10.21608/esju.1996.314788
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Author
Abdul-Mordy H. Azzam
Faculty of Commerce, Alexandria University, Egypt.
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.
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
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