A NOTE ON THE PROPERTIES OF STEIN-RULE AND INEQUALITY RESTRICTED ESTIMATORS WHEN THE REGRESSION MODEL IS OVER-FITTED
A NOTE ON THE PROPERTIES OF STEIN-RULE AND INEQUALITY RESTRICTED ESTIMATORS WHEN THE REGRESSION MODEL IS OVER-FITTED
摘要
This paper considers the effect of an erroneous inclusion of regressors on the risk propertiesof the Stein-rule,positive-part Stein-rule and inequality restricted and pre-test estimators in a linearregression model.The two Stein-rule estimators are considered when extraneous information is availablein the form of a set of multiple equality constraints on the coefficients,while the inequality estimatorsare considered under the case of a single inequality constraint.It is shown that the inclusion ofwrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-ruleestimators,and no effect at all on the inequality restricted and pre-test estimators when there is asingle inequality constraint.
基金
support provided by a General Research Fund under Grant No.9041467 from the Hong Kong Research Grant Council
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