Conflict among the Shrinkage Estimators Induced by W, LR AND LM Tests under a Student's t Regression Model

다국어 초록 (Multilingual Abstract)

The shrinkage preliminary test ridge regression estimators (SPTRRE)
based on Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM)
tests for estimating the regression parameters of the multiple linear regression
model with multivariate Student's t error distribution are considered
in this paper. The quadratic biases and risks of the proposed estimators
are compared under both null and alternative hypotheses. It is observed
that there is con
ict among the three estimators with respect to their risks
because of certain inequalities that exist among the test statistics. In the
neighborhood of the restriction, the SPTRRE based on LM test has the
smallest risk followed by the estimators based on LR and W tests. However,
the SPTRRE based on W test performs the best followed by the LR and
LM based estimators when the parameters move away from the subspace of
the restrictions. Some tables for the maximum and minimum guaranteed
eciency of the proposed estimators have been given, which allow us to
determine the optimum level of signicance corresponding to the optimum
estimator among proposed estimators. It is evident that in the choice of the
smallest signicance level to yield the best estimator the SPTRRE based on
Wald test dominates the other two estimators.

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