Performance of stochastic restricted and unrestricted two-parameter estimators in linear mixed models

• ==Performance of Stochastic Restricted and Unrestricted Two-Parameter Estimators in linear Mixed Models==
• ==Abstract==
• '''Keywords''': Linear mixed model, two parameter estimation, stochastic restricted two parameter estimation, matrix mean square error
• ==1. Introduction==
• We consider the linear mixed model (LMM) as follows:
• ==2. The proposed estimators==
• Under model (1), we have
• Where
• With
• Where
• By solving these equations similar to Eqs. (4) and (5), the following results are obtained
• ==3. Estimation of variance parameters==
• Solving Eqs. (21) and (23) yields the estimators
• ==4. Comparison of estimators==
• Where
• And
• '''Theorem 5.1'''
• '''Proof.'''
• ==6. A simulation study==
• ==7. Real data analysis==
• ==8. Conclusion==
• ==Disclosure statement==
• No potential conflict of interest was reported by the authors..
• ==Funding==
• The research was supported by the Slamic Azad University.
• ==References==
• Women's health services. Diss. North-West University, 2018.