3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 6749 798 98945799 988997894 96799 74 98599446 988997894 9894 9.6 9.6 4994 77 98959 9597 748 99949 7.6 9.6 94.6 989683 9 54 89 9853 799 98599446 988997894 9894 86749 798 98945799 9889978946 97984 98649 9898 98947 54 798 98945799 988997894 8478 98798 94 6 9947 94 9963.6 889 69 94 589 6749 798 98945799 988997894 956799 997 Kernel 9 39 546 98599446 9894 8478 98798 9947 958 98 3893 599446 886749:-6-5946 Mukerjee-stern 958 49 9894597 9 98577 98749 98577 987849 88949947 984444 88499 87748 9679 Kernel 956799 798 683.Shrunken - 957997 59 783 985946 989483 49 946799 98598 98693 8798 98683 Shrunken 7799 ｦﾁ 359 5946 94693 968 7 985946 989483.6 3-69994 98945799 9894 8 989979 983893 LSIR 897984 98649 9898.6 49 54 89 9853 9699 4 8 98599446 9 6898 954497 95 9979 986594 987593 984 878 9679 878 94984 54 9849 984944 9 6898 948 95979 94 7998 Carlo Monte 9 9449 9699 98599446 9 6898 98546 783 499 869 794 9944 59 9394 485 9879 6 987984 9895446 9 9838 983 94 5946 Mukerjee-stern 4 9894548 9 4 98599446 9894693.6 304
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 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 0. 5. - 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. - 989679:-6 477 9895799 9 9739 989984 989539444 979989 54 9685 94989 98789 958 4577 47 987896 4 9898499 783 78 97978 478 783 994 6 949 987896 87 9 6898 6749 979989 97978 9895799.6 577 546 98 9895799 9845 783 499 467 54 5989 974 9 7 798 98949 94 9947 9 94 9963 958 9 9895799 988997894 4798 88499 984 49 9499 849 945 6 9947 9 99636 649 98 889 69 799 987896 4 9898499 783 56 94984 94944 974.6 { } n X 59589 4979 9874 9879444 9897 9 n 9 989979, 594 94984 08 X + ｦﾅ,..., 08 X 9895799:-6 n 958 94 938 798 98945799 989997 67499 958 49 9459949 783 949 798 9947 54 X 9499 ｦﾅ 594 4938 986594 9879444 5 594 359 94 957.6 9 6749 798 98945799 947998 997 Kernel 88598 989484 {Nadaraya-watson} 86749 798 98945799 9 39 8494 9583 98599446 989778 87748 997 Kernel 88598 989484 478 94 59.6 305
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 9864 989483 4 9695 9 68 989534 Mukerjee & stern 88945799 988997894 9894.6 958 49 9894597 9 9864 989474974 9845 88577 98749 98577 987849 88949947 984444 88499 87748 997 Kernel 478 94 59.6 9499 9864 9894 98394 54 938 69994 {pool-adjacent- volators} 958 94 8 9869994 798 7593 54 598 47 9849 968 957 9499 54 598 47 94739 9 9849 968 594 546 9869994 4474 983 97593 9444 849 7646.6 9849 98694-98599446 988997894 9894 86749 798 9895799 49 97998 997 Nadaraya-watson [4] 957 9979 kernel 86749 798 9895799 988997894:-6 n 69 6ﾓ X 6 ﾆ K 60 63 60 63 y 6 h T 64 n 69 6ﾓ X 6 60 63 ﾆ K 60 63 6 h 64 958 94.k 9 798 kernel 958 96799 798 Kernel aussan 86749 T 8 794 59 h 994 8 0.. 77 6749 798 9895799 997 kernel 49 97984 98649 9898 8478 798 9895799 94 6 99476 96799 98599446 988997894 9894 9894:-6 -- 5946 -:Mukerjee-stern [5][7] [4] 47 989534 Mukerjee & stern 9 497 546 98945799 988997894 94 589 783 98499 97 59 9877489 984 478 98798 989679 946 59589 7949 799 994 98499 989484 783 X 9 39 9679 798 98945799 9894 9894 946799 997 Kernel 98989449 44 7 96799 9947 {ncreasng} 97 639443 9699 99938 8896799 98947 54 98945799 9894.{IR} 77 6749 798 98945799 947998 997 N.W Kernel 4494 7748 89 98997 97 989468 989799 98598 9894:-6 / X U,,,..., n 306
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 mn { T : ﾝ } 958 9:-6 ma { T : ﾜ } 784 59 9878 98799 85946 Mukerjee-stern 9894 6 9899476 4:-6 ｦﾁ 6ﾓｦﾁ + ｦﾁ 9 9789 98683 4:-6 n ﾆ[ T 6ﾓ ｦﾁ n ﾆ[ 6ﾓ 6ﾓ ] ] ｦﾁ 95 59 45 47 59 53 88649 98749 784 594 986934 989947 & ｦﾁ 49 94399 997 9897894 {ncreasng} 88798 78999 99479.6 7887 9 97998 598 693 8798 98683 4 77996 06 0 ｦﾁ:- +.5 ｦﾁ 0 7 9444 59 9947 {ncreasng} 87 98 47 9 9897894 99474.6 -- 98945799 9894 8 989979 983893 -:LSIR [6][3] [] [] 95 989649 9856464 88945799 9894 {IR} 98945799 9894 8 989979 983893 Regresson,LSIR} {Least Square Isotonc 9884 4798 8 847 798 98945799 9894 54 598 47 9849 968 957.{one-dmenson} 867 538 699949 59 798 98945799 9894 89 989979 983893 {LSIR} 783 94999 749 54 9894749. 78 98699949 798 783 5 5978 47 59 54 985989 984 447 549 9849 968 957 958 9 9869994 9897 9897998 4 69994 {PAV} 98698 88546 54 598 9894 98654 9845 6 9849 968 9576 9499 54 598 47 94739 9 9849 968 594 8 9869994 7 849 753 958 5489 47 37 59 98777 98749 9 98949947 98749 98947 94 899 49 649 9853 984 58 794 974 9 98553 9797 987748.6 307
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 835 9869994 PAV 49 98999 983 9497 987939 989984 8 X 949 98949947 9869994 794 9476 649 997 9583 9499476 95 98949947 4 65 65 9583 94 49 9838 9583 98649 989444.6 9873 T 597 9583 98494 59589 79:-6 T ﾜ T ﾜ...... ﾜT n 595 89 98649 989484 47 9444 59 98649 989444 94:-6 * T, n T,..., > T + 97 + T 6985 98945994 9894 5949 497 T {, + } 54 989497, + T 9589 89 65 77 98979 98948 9884 7 54 649 T 944 95 59899 94 789 97789 989474974:-6 98654 [ w Av {, + } T [ w ﾜ Av, + + w + w + + T ] + 6ﾓ T 54 598 779 779 597 9583 98499 889477 9 94, Av 97849 97789 989474974.6 99 566 887 5949 497 6ﾓ T 97 + 789 53 38 9583 9899 98958.6 779 586 9583 98494 99 5 987984 9583 94 38 9583 9894 98493.6 77 9838 9583 9894 989947 98958 594 98945799 9894 {IR} 47:-6 p p T * Av s, p ﾆT r w r / ﾆw r r s r s 99 94 T 4 798 9947 54 X 8798 98945799 9894 08 594.{LSIR} 96799 989979 983893 8798 98945799 9894 T * ] 98945799 9894 308
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 9849 984944-3 35 49 9895979:-6 9 97797 9994 88 basc Vsual 8894 986499 95979 98499 98958 79996 7799 9 7984 847 98949699 9879444 984 7 9847 98969 986494 0, U 9 94 9899699 9879444 78 397746 9499 989958 98394 9 98798 549 847 649 989849 9879444 9897997 783 98479 98984:-6 6 9847 98969 9864946 9847 98946 9847 985474 9864946 47 t 794 594 3 95499 749,50,0,50,,50 9499 989984 988997894 984 49 98947997 7849 54 49 9895979 4 79894:-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 64 6 7 X 64 63 X + + / ｦﾅ + 6ﾓ 4 ｦﾅ ｦﾅ f + f f ｦﾅ............... 3 4 5 X ﾊ X ﾊ X ﾊ [ 0, / 3 ] [ / 3, / 3 ] [ / 3,] 9 7999 49 9895979 96799 600 49 878 94984 9 9984 98945799 9894599446 9 794 989444 54 984798 5,4,3,, 9 6898 87 984798 47 9 649 95 9979 986594 9 774 59 97 95499 98749 878 989984 98479 9589 54 98984 98699 9847 98969 47 9 649 95 9979 986594 9 5974 59 97 95499 987496 944 59 8956 9 649 987593 984 9 5974 59 97 95499 98749 54 78 989984 98479 9589 54 98984 98699 9847 98969 47 9 649 987593 9 774 59 97 95499 987496 98956 649 95 9979 986594 8896799 47 9 96796 6 6 ｦﾁ 4987 95 9979 6594 968 9 5 T 783 98984.6 *, 98967946 0. 309
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 478 44 649 95 9979 986594 987593 984 8894984 98948 dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t 3 0 0 0 0 0.06439 0.04563 0.0063 0.69355 0.4353343 0.483775 0.346455 0.0583 0.99689 0.909338 930866 66365 0.06763 0.04535 0.006 0.69085 0.4405033 0.433555 0.3430044 0.057437 0.998793.07395 0.69807 743357 0.9948678 0.999637 0.999959 0.896505 0.988656 0.993096 0.9464773 0.9974463 0.99904 0.8473 0.97074 0.98675 0.06473 0.04568 0.006 0.6333905 0.43497 0.48888 0.383077 0.057 0.99684 0.938 953090 67478 0.999470 0.9999796.0000045 0.977835.0008347 0.9988094 0.988845 0.9999566 0.9999889 0.96980 0.996668 0.998045 3
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 478 44 649 95 9979 986594 987593 984 8894984 98394 dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t 3 0 0 0 0 0.9555 0.0740838 0.0738 0.7705983 0.60803 9759 0.436689 0.355 0.39950.07677 0.78546 0.75888 0.339 0.0740870 0.0745 0.856336 0.60893 0.60099 0.46079 0.3587 0.33.54097 0.8045948 0.767749 0.9968459 0.9999568 0.999990 0.899894 0.99363 0.99560 0.946730 0.998993 0.9996375 0.859365 0.975879 0.9890 0.30874 0.0740839 0.0738 0.7943359 0.605554 9808 0.4430349 0.35560 0.39960.9049 0.788343 0.760074 0.9988336 0.9999986.0000000 0.97064.0004097 0.999805 0.984503 0.9999988 0.9999968 0.96889 0.99608 0.9983404 3
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 478 3 44 649 95 9979 986594 987893 984 8894984 983983 dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t 3 0 0 0 0 0.4789 960 0.609 0.8568340 0.74657 0.7084897 0.4939838 0.4066888 0.4034065.64533 0.90467 0.885455 536 0.6084 0.865 0.9459886 0.7340047 0.7564 4760 0.436785 0.4067649.3768343 0.950575 0.96447 0.969 0.993340 0.9973759 0.905755 0.9679307 0.9763639 0.97969 0.98335 0.997436 0.845603 0.95749 0.9680805 0.4878 759 96 0.8744069 0.7875 0.7099855 055855 0.407040 0.4035709.035469 0.97757 0.885677 0.9973356.000743.0000595 0.9799030 0.9989850 0.997893 0.977059 0.999366 0.999596 0.967356 0.99343 0.996470 3
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 478 4 44 649 95 9979 986594 987593 984 8894984 98997 dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t 3 0 0 0 0 0.47549 0.945 0.87398 0.8366866 0.7005003 0.6993363 0.486740 0.399496 0.3963677.539 0.8958 0.87704 0437 0.780 0.309 0.96946 0.734889 0.773569 3987 0.43378 0.4056.37043 0.95537 0.9883 0.949086 0.970485 0.976838 0.8694703 0.95445 0.96476 0.907068 0.9663836 0.977085 0.8389863 0.9379747 0.954893 0.43466 0.958 0.86550 0.866547 0.708 0.70078 0.49749 0.399306 0.396346.89906 0.899733 0.8749047 0.9950670 0.999388.0007804 0.9655657 0.99988 0.9988980 0.977458 0.9998585.0003359 0.9679080 0.9998 0.996347 33
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 478 5 44 649 95 9979 986594 987593 984 8894984 98699 dstrbuton Sample sze ｦﾁ T * Unform Eponental Normal t 3 0 0 0 0 0.0667667 0.7050 0.9857 5770 0.044388 0.0349333 0.09756 0.0804 0.0059689 0.448870 0.3657 0.07948 0.0663085 0.6840 0.9854 0.849084 0.045793 0.0354 0.0943778 0.0800767 0.0059639 496765 0.99340 0.08953.000383.000866.000039 0.8956457 0.979008 0.9869 0.98870.00059.0008353 0.855468 0.949043 0.97708 0.0667736 0.7053 0.98573 0.60969 0.044394 0.0349577 0.093408 0.080869 0.005970 0.4568863 0.43804 0.079530 0.9998956 0.9999973 0.9999985 0.9779636.00096 0.999304 0.994805 0.999478 0.9997778 0.98785 0.99307 0.9966685 34
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 9 546 98599446 9894 783 49 54 49 499 63 485 9879 98 49 799 94349 98799 783 98939 485 98796 98499 984 9 967999 938 499 869 794 9944 59 8789 9844 9394 485 9879 987984 989544.6 98 9 799 989944 4938 989849 9844546 9 485 9879 987984 989544 49389 98499 989496 889 49 96799 99844 8895799 98456 989984 9898 4938 94349 98799 783 98939 485 9879 987984 989984 98394 4938 94349 98799 783 98939 485 9879 989544.6 478 6 44 95 9979 986594 987593 984 89943 9394 485 9879 987984 989544 Model 485 987984 485 989544 ｦﾁ.5903440 9.9345440.6457970.05446 0.966306 0.9783637 T *.594937 0.9977.000 0.993444 989949-9548 9679 796 6 6 ｦﾁ 7 96796.5. 0 39 9679 T * - 7598 799 47 9 9548 47 79 9847 98969 7 9847 985474 39 9847 98944 9 39.t 3 47 98349-546 98599446 9894 783 98945799 98654 989777.6-546 649 98945799 988997894 938 B-Spln K-NN6...9866 783 98499 9 589 7 589 9 997 Kernel 9 39 546 98599446 9894.6 3-9699 98599446 9894 8798 98945799 988997894 54 598 9839494 9839 9879444 35
3948 98789 98963974 9897994 9498876 046 06 /6 / 50 86 086 0 9893979 989444:-6 - Barlow, R.E.; and Brunk, H.D. 97 "The Isotonc Regresson Problem and ts Dual". Journal of the Amercan Statstcal Assocaton, 67, 337, 40-47. - 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, 708-76. 4- Mukarjee, H. and Stern, S. 994 "Feasble nonparametrc estmaton of multargument monotone functons". Journal of Amercan Statstcal Assocaton, 89, 45, 77-80. 5- Mukerjee,H. 988 "Monotone nonparametrc regresson". The Annals of Statstcs,6,74-750. 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,, 65-78. 9893979 98794:-6 8-98497:6 4994 77 98959 95976 7 6 "6749 798 9895799 988997894 96799 74 98599446 988997894 9894 97 546 7984 889699 49"6 998 99449 54 789 98945393 784 9894799 98946397-4997 8797.6 36