تقدير اصغر معيار تربيعي غير متحيز لنموذج تحليل التباين ثنائي التقسيم المختلط بوجود التفاعل مع التطبيق

Abstract

This research deals with the estimation of variance components of a suggested tow- way analysis of variance mixed model with interaction.The estimation is worked out by the approachcalled Minimum Norm Quadratic Unbiased Estimator(MINQUE). The (MINQUE) is suggested by C.R.Rao. and is used even now by several authors to certain types of data analysis. Here in this work we consider the projection matrix and then the iterated (MINQUE).We apply the approach to a real data which represent fourfixed types of sands as the first factor, and three randomlychosen types of tomatoas the second factor and interaction exists between the two factor. The initial values of estimators are obtained by the usual two-way analysis of variance with interactionand then these initial values arein(MINQUE) . Also the standard errors of estimator are computed. The final results obtained are very encouraging. All algorithm are programmed by mat lab system.