انتخاب متغير و تشخيص ساختار در بعد بالا براي مدل هاي جمعي خطي-جزيي

Variable Selection and Structure Identification in High Dimension for Partial Linear Additive Models

در اﯾﻦ ﻣﻘﺎﻟﻪ ﯾﮏ روش دو ﻣﺮﺣﻠﻪ اي ﺑﺮاي اﻧﺘﺨﺎب ﻣﺘﻐﯿﺮ و ﺗﺸﺨﯿﺺ ﻣﺆﻟﻔﻪ ﻫﺎي ﺧﻄﯽ و ﻏﯿﺮﺧﻄﯽ در ﻣﺪل ﻫﺎي ﺟﻤﻌﯽ ﺑﺎ ﺑﻌﺪ ﺑﺎﻻ ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮد. در ﻣﺮﺣﻠﻪ اول، از ﯾﮏ روش ﻏﺮﺑﺎﻟﮕﺮي ﺑﺮاي ﮐﺎﻫﺶ ﺑﻌﺪ ﻓﻀﺎي ﻣﺘﻐﯿﺮﻫﺎ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد. اﯾﻦ روش ﻏﺮﺑﺎﻟﮕﺮي ﺑﺮ اﺳﺎس ﻫﻤﺒﺴﺘﮕﯽ ﻓﺎﺻﻠﻪ اي ﺑﯿﻦ ﻣﺘﻐﯿﺮﻫﺎي ﺗﻮﺿﯿﺤﯽ و ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺣﺎﺷﯿﻪ اي ﻣﺘﻐﯿﺮ ﭘﺎﺳﺦ ﺳﺎﺧﺘﻪ ﺷﺪه و زﻣﺎﻧﯽ ﮐﻪ ﻣﺘﻐﯿﺮ ﭘﺎﺳﺦ دم ﺳﻨﮕﯿﻦ ﻳﺎ داراي ﻣﻘﺎدﻳﺮ ﻓﺮﻳﻦ ﺑﺎﺷﺪ، ﻋﻤﻠﻜﺮد ﺧﻮﺑﯽ را از ﺧﻮد ﻧﺸﺎن ﻣﯽ دﻫﺪ. در ﻣﺮﺣﻠﻪ دوم، از روﺷﯽ ﻣﺒﺘﻨﯽ ﺑﺮ دو ﺗﺎﺑﻊ ﺗﺎوان ﺑﺮاي اﻧﺘﺨﺎب ﻫﻤﺰ ﻣﺎن ﻣﺆﻟﻔﻪ ﻫﺎي ﻏﯿﺮﺻﻔﺮ و ﺧﻄﯽ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد. ﮐﺎراﯾﯽ اﯾﻦ روش دو ﻣﺮﺣﻠﻪ اي ﺑﺎ ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪ ﺳﺎزي و ﺗﺤﻠﯿﻞ ﯾﮏ ﻣﺠﻤﻮﻋﻪ داده واﻗﻌﯽ ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ.

In this paper, we introduce a two-step procedure, in the context of high dimensional additive models, to identify nonzero linear and nonlinear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments and a real data analysis to evaluate the numerical performance of the proposed method.