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Biased Estimation for Parameter Adjustment with Constraints

Gui Qingming Zhang Jianjun (Zhengzhou Institute of Surveying and Mapping, Zhengzhou, 450052)  
The biased estimation problem for parameter adjustment with constraints is considered when the ill conditioning is present in the normal matrix. We propose restricted ordinary ridge estimator and restricted principal component estimator by grafting the unrestricted biased estimation philosophy into the RLS estimator, and establish some important statistical properties. A numerical example is presented to illustrate that these restricted biased estimators are superior to the RLS estimator in sense of the reduced MSE.
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