Performances of Preliminary Test Estimator for Error Variance Under Pitman Nearness

PENG Ping(彭萍),HU Guikai(胡桂开)

(School of Science,East China University of Technology,Nanchang 330013,China)

Abstract:In this paper,we investigate the properties of a general preliminary test estimators for error variance in a misspecified regression model under Pitman nearness criterion.The exact expressions of Pitman nearness probability are derived.The performance comparison and the effect of misspecified error are obtained.Numerical study and simulation example are also given to evaluate the performance of proposed estimators.

Key words:Preliminary test estimator;Error variance;Misspecified linear model;Pitman nearness criterion

1.Introduction

2.Comparison Under Pitman Nearness Criterion

3.Numerical Analysis

Tab.1 PC of PTE related to URE for λ2 =0

Tab.2 PC of PTE related to URE for λ2 ̸=0

4.Simulation Example

Tab.3 PC of PTE related to URE for n=20

From Table 3,we have the following results:1)The Pitman nearness probability of PTE related to URE is monotonous withFαincreasing;2)When the restricted conditions hold,RE dominates URE under PN.It is not affected by the misspecification of model.They are same to the analysis in theory and numerical analysis.

5.Concluding Remarks

In this paper,we consider the performance of a general pre-test estimators forσ2in the misspecified linear regression model under Pitman nearness criterion.We obtain the exact expressions of PC for PTE related URE.By theoretical analysis,we know that PC depends on the model specification error,the prior linear constraint error and the critical valueFα.Meanwhile,PC increases with the critical value increasing.Moreover,is a turning point of PC for PTE related to URE on the LS and MM components.The numerical results further show that RE is better than URE under PN when the linear constraint condition holds.Moreover,It is not affected by the misspecification of model.It is of interest to extend our results when the prior information is available in the form of inequality constraint on the coefficients.We will study it in the future.