B. M. Golam Kibria () (Department of Statistics, Florida International University) A.K.Md. E. Saleh (Department of Mathematics and Statistics, Carleton University)
Abstract
This paper combines the idea of preliminary test and ridge regression methodology, when it is suspected that the regression coefficients may be restricted to a subspace. The preliminary test ridge regression estimators (PTRRE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. The bias and the mean square errors (MSE) of the proposed estimators are derived under both null and alternative hypotheses. By studying the MSE criterion, the regions of optimality of the estimators are determined. Under the null hypothesis, the PTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the PTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both ridge parameter k and departure parameter (triangle symbol) are provided. Some graphical representations have been presented which support the findings of the paper. Some tables for maximum and minimum guaranteed relative efficiency of the proposed estimators have been provided. These tables allow us to determine the optimum level of significance corresponding to the optimum estimators among proposed estimators. Finally, we concluded that the optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative ridge parameter, k.
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Publisher Info
Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS364.
Length: 26 pages Date of creation: 11 Mar 2002 Date of revision: Handle: RePEc:pqs:wpaper:0082005
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General