Biased regression estimators and comparisons according to the mean square error criterion

XV SUMMARY To combine estimators is an important problem that arises in statistics. Combining estimators as scalar valued has been inve~igated by many research workers. But on the corresponding problem of combining estimator as matrix valued, this is not the case, for except for a few cases, we can find nothing in the literature. Therefore in the first chapter of the thesis combining estimators as matrix valued has been investigated and we have shown that the combined estimator is better than combined ones respectively. Comparing estimators and to decide which one is better is an important problem. In the literature many known estimators has been compared according to MSE matrix and MSE scalars. Liu(1993) has iefined a new biased estimator and he has shown that his estir.ator has advantages to Ridge and Stein estimators. But there is almost nothing in the literature about compering Liu estimator with other known estimators. For this reason in chapter two we have compared Liu estimator with some other known estimators according to MSE matrix or MSE scalar. It is known that whenever the problem involves mult ::ol linearity ridge regression method is used for any estir.ation to overcome this problem. Using RRE as terminal point vari.us better estimators than ridge estimator has been defined. We know that Liu estimator which has advantages to ridge estimator is used to overcome estimation problem in cases involving mul ticol 1 inearity.XIV ediciden daha iyi olabilecek yeni yanlx tahmin edicileri üçüncü bölümde tanımlamaya çalıştık. Yapılanları desteklemesi açısından dördüncü bölümde, kaynaklarda sıkça kullanılan iki veri grubu ele alınarak, sayısal örnekler verildi.