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1 /6 / Kernel : Mukerjee-stern Kernel Shrunken Shrunken 7799 ｦﾁ LSIR Carlo Monte Mukerjee-stern

2 /6 / ABSTRACT:- Ths research was concernng to study monotone nonparametrc methods for estmatng the nonparametrc regresson functon.e treatment outler to acheve a monotone functon ncreasng or decreasng. So we wll use the monotone methods to treatment outler but after estmate the regresson functon wth use kernel estmator Nadarya - Watson these methods are:- - Mukerjee method takes averages of mamums and mnmum of subsets of the data was used to adjust the ntal kernel regresson estmates and use the researcher specal case when ｦﾁ Algorthm least square sotonc regresson. In the epermental aspect comparson was done of whch s the best methods through the smulaton procedure usng Mote Carlo method usng fve models. Whle n the applcaton aspect practcal applcaton was done on data represent the measurements for blood pressure patents. In both aspects we use two of the mportant statstcal measures whch are Mean square error and cency. We fnd through the applcaton that the best method s Mukerjee method for general case as t has mnmum Mean square error and mamum cency : { } n X n , X + ｦﾅ,..., 08 X :-6 n X 9499 ｦﾅ Kernel {Nadaraya-watson} Kernel

3 /6 / Mukerjee & stern Kernel {pool-adjacent- volators} Nadaraya-watson [4] kernel :-6 n 69 6ﾓ X 6 ﾆ K y 6 h T 64 n 69 6ﾓ X ﾆ K h k kernel Kernel aussan T h kernel : :Mukerjee-stern [5][7] [4] Mukerjee & stern X Kernel {ncreasng} {IR} N.W Kernel :-6 / X U,,,..., n 306

4 /6 / mn { T : ﾝ } 958 9:-6 ma { T : ﾜ } Mukerjee-stern :-6 ｦﾁ 6ﾓｦﾁ + ｦﾁ :-6 n ﾆ[ T 6ﾓｦﾁ n ﾆ[ 6ﾓ 6ﾓ ] ] ｦﾁ & ｦﾁ {ncreasng} ｦﾁ:- +.5 ｦﾁ {ncreasng} :LSIR [6][3] [] [] {IR} Regresson,LSIR} {Least Square Isotonc {one-dmenson} {LSIR} {PAV}

5 /6 / PAV X T :-6 T ﾜ T ﾜﾜT n :-6 * T, n T,..., > T T T {, + } , + T T : [ w Av {, + } T [ w ﾜ Av, + + w + w + + T ] + 6ﾓ T , Av ﾓ T {IR} 47:-6 p p T * Av s, p ﾆT r w r / ﾆw r r s r s T X {LSIR} T * ]

6 /6 / : basc Vsual , U : t ,50,0,50,, :-6 Where f X e 3 X : 6ﾓ + ｦﾐ 6ﾓ 6 X 9 f X X Sn e ｦﾅ X 6ﾓ + 6 X X X + + / ｦﾅ + 6ﾓ 4 ｦﾅｦﾅ f + f f ｦﾅ X ﾊ X ﾊ X ﾊ [ 0, / 3 ] [ / 3, / 3 ] [ / 3,] ,4,3,, ｦﾁ T *,

7 /6 / dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t

8 /6 / dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t

9 /6 / dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t

10 /6 / dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t

11 /6 / dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t

12 /6 / Model ｦﾁ T * ｦﾁ T * t B-Spln K-NN Kernel

13 /6 / :-6 - Barlow, R.E.; and Brunk, H.D. 97 "The Isotonc Regresson Problem and ts Dual". Journal of the Amercan Statstcal Assocaton, 67, 337, Barlow, R.; Batholomew, D.; Bremmer, J.; and Brunk, H. 97 "Statstcal Inference under order Restrctons", John Wley and Sons, New ork. 3- Dykstra, R.L and Robertson, T. 98 "An algorthm for sotonc regresson for two or more ndependent varables ". Annals of Statstcs,, 3, Mukarjee, H. and Stern, S. 994 "Feasble nonparametrc estmaton of multargument monotone functons". Journal of Amercan Statstcal Assocaton, 89, 45, Mukerjee,H. 988 "Monotone nonparametrc regresson". The Annals of Statstcs,6, Robertson, T.; Wrght, F.; Dykstra, R. 988 "Order-Restrcted Statstcal Inference" John Wley and Sons; New ork. 7- Strand, M. 3 "Comparson of methods for monotone nonparametrc multple regresson".bometrcs 3,3,, : : " "

JGSS統計分析セミナー2009－傾向スコアを用いた因果分析－

JGSS統計分析セミナー2009－傾向スコアを用いた因果分析－日本版総合的社会調査共同研究拠点研究論文集 [10] JGSS Research Seres No.7 JGSS 2009 JGSS JGSS Statstcal Analyss Semnar: Causalty Analyss based on the Propensty Score Kana MIWA JGSS Research Center Osaka Unversty of Commerce