برآوردگر جديدي از نوع ليو اصلاح شده

New Estimators of Modified Liu

ﯾﮑﯽ از روش ﻫﺎي رﻓﻊ ﻣﺸﮑﻞ ﻫﻤﺨﻄﯽ در ﻣﺪل ﻫﺎي ﺧﻄﯽ، اﺳﺘﻔﺎده از ﺑﺮآوردﮔﺮ ﻟﯿﻮ اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺑﺮآوردﮔﺮ ﺟﺪﯾﺪي را ﺑﺎ ﺗﻌﻤﯿﻢ ﺑﺮآوردﮔﺮ ﻟﯿﻮ اﺻﻼح ﺷﺪه ﻟﯽ و ﯾﺎﻧﮓ )2012( اراﺋﻪ ﺷﺪه اﺳﺖ. اﯾﻦ ﺑﺮآوردﮔﺮ ﺑﺮ اﺳﺎس ﯾﮏ اﻃﻼع ﭘﯿﺸﯿﻦ از ﺑﺮدار ﭘﺎراﻣﺘﺮﻫﺎ در ﻣﺪل رﮔﺮﺳﯿﻮن ﺧﻄﯽ و ﺑﺮآوردﮔﺮ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ آ ﮐﺪﻧﯿﺰ و ﮐﺎﭼﯿﺮاﻧﻼر )1995( ﺑﻪ دﺳﺖ ﻣﯽ آﯾﺪ. ﺑﺎ اﺳﺘﻔﺎده از ﻣﻌﯿﺎر ﻣﺎﺗﺮﯾﺲ ﻣﯿﺎﻧﮕﯿﻦ ﺗﻮان دوم ﺧﻄﺎ، ﺷﺮاﯾﻂ ﺑﺮﺗﺮي اﯾﻦ ﺑﺮآوردﮔﺮ ﺑﺮ ﺑﺮآوردﮔﺮ ﻟﯿﻮ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ ﺑﻪ دﺳﺖ آورده ﻣﯽ ﺷﻮد. ﺑﻪ ﻣﻨﻈﻮر ﻣﻘﺎﯾﺴﻪ رﻓﺘﺎر اﯾﻦ ﺑﺮآوردﮔﺮ ﺑﺎ ﺑﺮآوردﮔﺮﻫﺎي ﻣﻮﺟﻮد، ﯾﮏ ﻣﺜﺎل ﻋﺪدي و ﯾﮏ ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪ ﺳﺎزي اﻧﺠﺎم ﺷﺪه اﺳﺖ.

One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.