Two Kinds of Weighted Biased Estimators in Stochastic Restricted Regression Model

Table 2

Estimated MSE values of the  𝛽_WME(𝑤),  𝛽_AURE(𝑘),  𝛽_SRRE(𝑘),  𝛽_𝑅(𝑘,𝑤),  𝛽_AULE(𝑑),  𝛽_SRLE(𝑑),  and 𝛽_𝐿(𝑑,𝑤).

𝑘/𝑑	0.05	0.2	0.35	0.5	0.65	0.8	0.95
𝑤=0.1
𝛽WME(𝑤)	0.60151	0.60151	0.60151	0.60151	0.60151	0.60151	0.60151
𝛽AURE(𝑘)	0.76165	0.75567	0.74866	0.74762	0.75796	0.78318	0.82518
𝛽SRRE(𝑘)	0.41703	0.51719	0.73716	1.03859	1.39457	1.78595	2.19912
𝛽𝑅(𝑘,𝑤)	0.60114	0.59690	0.59313	0.59629	0.61141	0.64173	0.68896
𝛽AULE(𝑑)	0.81855	0.77043	0.75027	0.74698	0.75178	0.75815	0.76189
𝛽SRLE(𝑑)	2.14397	1.61925	1.18918	0.85375	0.61297	0.46682	0.41533
𝛽𝐿(𝑑,𝑤)	0.68163	0.62681	0.60098	0.59311	0.59447	0.59859	0.60131
𝑤=0.5
𝛽WME(𝑤)	0.43737	0.43737	0.43737	0.43737	0.43737	0.43737	0.43737
𝛽AURE(𝑘)	0.76165	0.75566	0.74865	0.74762	0.75796	0.78318	0.82518
𝛽SRRE(𝑘)	0.41703	0.51719	0.73715	1.03859	1.39456	1.78595	2.19912
𝛽𝑅(𝑘,𝑤)	0.43712	0.43468	0.43422	0.44166	0.46166	0.49719	0.54976
𝛽AULE(𝑑)	0.81855	0.77043	0.75027	0.74698	0.75178	0.75815	0.76189
𝛽SRLE(𝑑)	2.14397	1.6192	1.18918	0.85375	0.61297	0.46682	0.41533
𝛽𝐿(𝑑,𝑤)	0.54173	0.48007	0.44844	0.43588	0.43373	0.43556	0.43724
𝑤=0.9
𝛽WME(𝑤)	0.41955	0.41955	0.41955	0.41955	0.41955	0.41955	0.41955
𝛽AURE(𝑘)	0.76165	0.75566	0.74865	0.74762	0.75796	0.78318	0.82518
𝛽SRRE(𝑘)	0.41703	0.51719	0.73715	1.03859	1.39456	1.78595	2.19912
𝛽𝑅(𝑘,𝑤)	0.41931	0.417072	0.41696	0.42487	0.44540	0.48150	0.53465
𝛽AULE(𝑑)	0.81855	0.77043	0.75027	0.74698	0.75178	0.75815	0.76189
𝛽SRLE(𝑑)	2.14397	1.6192	1.18918	0.85375	0.61297	0.46682	0.41533
𝛽𝐿(𝑑,𝑤)	0.52654	0.46414	0.43187	0.41881	0.41628	0.41786	0.41942