id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-275	Wang, Yonghong	Multidimensional Structural Regression Model for Causal Inference under Strongly Ignorable Treatment Assignment	2010	7	.pdf	application/pdf	2982	109	60	n nATE Y Y X X n n β β+ ≈ − − − + = ] )( [] )( [ 00 10 010 011 10 011 1 eX nn n eX nn n + + − +−+ + − + ββ α ββ α Moreover x t t n XVar Σ= 1)( ， t t t V n eVar 1)( = Therefore 1 1 ' 01012 10 1 11 10 011 1 1)()( )( ) )( ( V nnn n eX nn n Var x +−Σ− + =+ + − + ββββ ββ α 0 0 ' 01012 10 0 00 10 010 0 1)()( )( ) )( ( V nnn n eX nn n Var x +−Σ− + =+ + − + ββββ ββ ATE E Y Y E E X X n n β β+ = − − + = ATEx =−+− μββαα )()( 0101 (3) Asymptotically normality: Based on above demonstration, we know ( )E ATE ATE= Also because of 0 1 1 0 1 0 1 0 0 1 ( ) ( )	cache/ijassa-275.pdf	txt/ijassa-275.txt