Inference in Linear Models with Nonstochastic Biased Factors | ||
| The Egyptian Statistical Journal | ||
| Article 4, Volume 40, Issue 2, December 1996, Pages 172-181 PDF (6.96 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1996.314788 | ||
| 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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