Simulation-Based Finite-Sample Normality Tests in Linear Regressions

Texte intégral

(1)9811. Simulation-Based Finite-Sample Normality Tests in Linear Regressions DUFOUR, Jean-Marie FARHAT, Abdeljelil GARDIOL, Lucien KHALAF, Lynda.

(2) Département de sciences économiques Université de Montréal Faculté des arts et des sciences C.P. 6128, succursale Centre-Ville Montréal (Québec) H3C 3J7 Canada http://www.sceco.umontreal.ca SCECO-information@UMontreal.CA Téléphone : (514) 343-6539 Télécopieur : (514) 343-7221. Ce cahier a également été publié par le Centre interuniversitaire de recherche en économie quantitative (CIREQ) sous le numéro 2897. This working paper was also published by the Center for Interuniversity Research in Quantitative Economics (CIREQ), under number 2897.. ISSN 0709-9231.

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(19) Wdeoh 5= Hpslulfdo vl}h dqg srzhu ri qrupdolw| whvwv> l1l1g1 revhuydwlrqv Vwdqgdug Whvwv PF Whvwv G ( #&. NV NVH YP Y PH DG DGH ME ME VZ VI ZE G IE G ( &! NV NVH YP Y PH DG DGH ME ME VZ VI ZE G IE G ( "!! NV NVH YP Y PH DG DGH ME Nx ME VI ZE G IE. 3 816 815 819 815 819 814 51< 41; 815 81; 81: 817 816 719 71; 817 814 816 813 61: 51: 716 814 814 816 819 813 71< 71; 71< 813 71< 61< 615 617 719 71: 814 71<. :15 :13 ;1: ;14 <14 ;16 31< 317 ;17 814 814 :14 717 4418 4513 4818 471< 4;14 4:15 31; 318 5915 4316 4314 461: <1< 5618 5615 6513 6516 731: 7313 71: :16 815 6616 6517 5<13 5<14. .. <315 <318 <619 <616 <61: <617 ;<18 ;:15 <515 <713 <713 <617 <713 <<17 <<17 <<1: <<1: <<1: <<1: <<18 <<17 <<17 <<1; <<1; <<1; <<1; 433 433 433 433 433 433 433 <814 433 433 433 433 433. . 6<19 6<16 8419 8317 8:18 881; 6:1; 6419 9715 9418 9418 6614 8<17 9;13 9<14 ;61: ;613 ;<14 ;;18 :913 :51: <71; <41< <41; 8917 <41< <817 <815 <<14 <<14 <<1; <<1; <<14 9919 <<13 <<1< <<1< ;518 <<1<. Oq. <;18 <;18 <<1: <<1: <<1< <<1< <81< <714 433 <<1< <<1< <:16 <<1< 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433. 44. w. 471; 471: 4;19 4:1< 5315 4<17 5415 4:17 5414 5918 5917 5517 5914 5318 5415 5:1; 5:15 6413 6315 6<17 6914 5917 7416 7418 6<13 7617 6618 6614 751; 7614 7;14 7:1< 951; 9519 9315 941: 9515 951< 9614. Q. 815 815 814 814 815 815 815 815 817 815 816 815 815 71< 71< 813 813 813 813 71; 71< 813 813 813 815 813 71; 71; 71< 71< 71; 71; 813 815 71< 71; 71; 815 71;. E. :16 :16 ;16 ;16 ;19 ;19 514 613 ;1: 719 71: :13 716 441: 441: 471: 471: 491< 491< 613 71< 5:1;9 4313 <1< 4614 ;1; 551: 551: 6417 6417 6<149 6<149 4519 5317 4<15 6519 6417 5916 5;13. F. <313 <313 <613 <613 <613 <613 <417 <413 <513 <61: <61: <519 <61;9 <<16 <<16 <<1: <<1: <<1: <<1: <<18 <<18 <<17 <<1;9 <<1;9 <<1: <<1: 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339. . 6;18 6;18 7<17 7<17 871; 871; 7:1; 8415 96169 8;16 8;17 631: 8:1: 9:1: 9:1: ;41; ;41; ;:19 ;:19 :<1; ;51< <71; 9 <31< <31; 8619 <313 <718 <718 <<13 <<13 <<1: <<1: <;19 9<15 <<14 <<1<9 <<1<9 :<1; <<1<9. Oq. <;17 <;17 <<19 <<19 <<1; <<1; <:18 <;15 <<1<9 <<1; <<1; <918 <<1; 4339 4339 4339 4339 433 9 4339 << 4339 4339 << 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339. w. 4719 4719 4:15 4:15 4<15 4<15 59169 5819 5416 5818 5814 5416 5817 531; 531; 591; 591; 5<1; 5<1; 741; 7413 5:15 7318 7318 691< 7414 641< 641< 7514 7514 7:14 7:14 961; 981:9 951< 9417 9419 9318 9514.

(20) Wdeoh 6= Hpslulfdo vl}h ri qrupdolw| whvwv edvhg rq uhjuhvvlrq uhvlgxdov q ( 58> n @ 9. nQ. NV NVH YP Y PH DG DGH VI VZ ZE G IE ME ME. Vwdqgdug whvwv 3 5 7 815 4419 5;19 813 4417 5;15 91; 451: 5;16 917 4513 5:14 917 4318 5513 81: <1: 531: 81: ;17 4719 814 915 4315 81: ;17 4718 813 919 4417 815 :1< 461< 51< 71; 91: 314 315 317. PF whvwv 3 5 7 815 816 815 815 816 815 815 815 813 815 815 813 815 815 816 815 815 816 816 815 813 818 816 815 817 815 813 813 816 814 817 814 814 815 815 71; 814 813 814. q @ 83> n @ ;. 3 816 818 :17 91< :15 91: 815 715 815 814 81: 61< 316. Vwdqgdug whvwv 5 7 9 :1< 481: 5<17 ;14 4916 6314 4318 4;1< 661< <1< 4:1< 6518 <18 481< 591< ;1< 471< 581: 918 <15 461: 714 813 91< 918 <15 461; 81: :19 4517 :16 4316 4816 814 917 ;17 318 31; 413. q @ 433> n @ 44. nQ NV NVH YP Y PH DG DGH VI ZE G IE ME ME. 3 819 818 :17 :19 :1; :19 71; 71< 814 71< 714 514. 5 ;13 :1< <19 <1: <1; <18 814 815 816 816 71: 419. Vwdqgdug whvwv 7 9 ; 4616 5314 6519 4614 4<1: 6515 4813 541; 6614 4814 5515 6617 4618 4;1< 5:1< 4615 4;18 5:19 919 ;19 4415 91; ;1; 4417 916 :1< 431; :13 <13 441< 81; :14 ;1< 418 417 416. nQ NV NVH YP Y PH DG DGH VI VZ ZE G IE ME ME. 3 91: 915 :13 :13 :17 :18 916 0 917 719 0 718 ;13. 5 ;14 :19 ;16 ;1< ;18 :14 :16 0 814 816 0 814 :14. 7 <1< <16 4316 4317 <1< 4313 :15 0 :18 815 0 818 913. 43 7:19 7:15 7;1; 7<16 6<1< 6<17 4817 481: 4817 4915 4315 418. q @ 633> n @ 4:. Vwdqgdug whvwv 9 ; 43 451: 4919 541; 4513 481< 531; 451< 4914 5318 4613 4915 5319 4513 4718 4:1< 4514 4719 4;14 ;16 ;17 4314 0 0 0 ;18 ;19 4317 81: 91: :19 0 0 0 81; 918 :14 816 71< 718. 3 71: 71: 71< 71< 71; 71; 813 813 816 813 71; 815 45 5:1< 5919 591< 5:14 5517 5518 441; 0 4514 <15 0 ;15 714 45. 5 813 813 71; 71; 71: 71: 718 718 71; 718 71; 71:. PF whvwv 7 9 813 71: 813 71: 71; 71< 71; 71< 813 71< 813 71< 71< 813 71< 813 814 814 71< 814 71; 71< 813 813. 47 6815 6713 6618 6619 5;13 5;15 4618 0 461; 431; 0 ;1; 61;. 49 761< 751: 7516 7517 6717 6719 4915 0 4919 4615 0 <1; 61:. 3 815 815 814 814 815 815 813 71< 813 813 814 813 71; ; 71: 71: 71; 71; 71: 71: 719 71: 71< 71: 71< 71;. +58> 9,. 431< 431: 471; 461; 451< 441< 4316 :16 4316 ;16 <1< 914 316. PF whvwv 5 7 813 814 813 814 813 71< 813 71< 813 71; 813 71; 816 815 813 813 816 815 814 71; 816 815 814 813 814 71<. 9 813 813 71< 71< 71; 71; 71; 71; 71; 815 71: 71: 813. 43 813 813 813 813 71< 71< 71; 71< 814 71; 814 71: Fdxfk| uhjuhvvruv Vwdqgdug whvwv= +q> n, @ +83> ;,. 4416 441; 4816 4718 4619 451< <14 813 <15 :18 4315 :16 31;. +433> 44,. 4414 431; 471: 4718 4717 4715 :1< 0 ;15 :18 ;18 :1; 418. +633> 4:,. 431: 4314 4518 4518 4518 4519 ;1; 0 <14 918 0 :19 814.

(21) Wdeoh 7= Hpslulfdo srzhu ri PF qrupdolw| whvwv edvhg rq uhjuhvvlrq uhvlgxdov. NV YP DG VI VZ ZE G IE ME ME NV YP DG VI VZ ZE G IE ME ME NV YP DG VI VZ ZE G IE ME ME NV YP DG VI VZ ZE G IE ME ME. E q @ 58 718 n @ 9 715 nQ @ 3 718. q @ 58 n@9 nQ @ 7. q @ 83 n@; nQ @ 3. q @ 83 n@; nQ @ 7. 61; 913 61; 816 619 518 <1; 713 514 515 517 619 517 :18 515 41< <13 915 81< 91: 81< 4815 81< ;1; 816 514 4;16 718 51; 618 619 451; 618 431; 614 417 4;19. F. :716 ;413 ;51: ;61: ;314 ;61: ;416 ;7139 ;618 9<17 ;919 <418 <41; <418 <413 <418 ;;17 <4199 ;:1< ;51: <91< <;19 <;1;9 <;1: <:13 <;1: <;19 <;1;9 <;19 <817 <;15 <<16 <<179 <<179 <;1< <<16 <<15 <<179 <;1< <:17. . 5519 5;19 641: 671< 681; 671< 4<1< 6717 6516 5317 5:1: 591: 6613 7318 7917 7318 5516 6<1< 691; 7618 7:15 8<19 981< :418 :615 :416 6<14 :31: 9714 8<1< 7;1< 8915 981; :81< ;6149 :81: 7316 :71< 981< ::16. Oq. :<1; ;:17 ;<16 <31: <31: <31: ;417 <319 ;;1; ;316 <31< <719 <919 <:1: <;1:9 <:1: ;;1; <:19 <613 <:1; <<13 <<1; <<1; <<1<9 <<1<9 <<1<9 <;1; <<1<9 <<1: <<18 <<19 <<1; <<1< <<1< 4339 <<1< <<16 <<1< <<1; <<1<. 46. w. 451: 4815 4919 4;19 4817 4;18 4816 4;1; 4<1<9 <1; 4718 5314 5419 5619 5515 5619 4:1< 5619 5617 4;14 5317 5914 5;1< 6614 5419 6615 5<14 661: 6813 4<1< 531; 6415 6713 6;13 5<1; 6;14 6416 6;17 6;15 5:1<. E q @ 58 619 n @ 9 51< nQ @ 5 616 613 71; 613 917 51< 514 <1;. q @ 83 718 n @ ; 61< nQ @ 5 719. 71; 4813 71: 4313 716 41: 4<15 q @ 83 815 n @ ; 514 nQ @ 9 519 51; 441< 51: 4614 519 414 4:16. F. . Oq. w. ;31; ;919 ;:17 ;:14 ;816 ;:14 ;713 ;:169 ;815 :914. 5719 5;17 6616 6:18 75149 6:19 5417 6:13 6713 6517. ;714 <413 <51< <713 <8149 <713 ;715 <61; <315 <413. 471< 4;14 4<18 5413 4<13 5413 4915 5415 5419 4619. <:1: <;1< <<14 <<13 <;14 <<13 <;1< <<149 <;1: <919 <;1< <<19 <<1:9 <<19 <<17 <<19 <<17 <<19 <<14 <;16. 7:19 8<17 9:14 :61; :;189 :61; 7319 :613 9818 9<14 851; 861; 971< ::18 ;:169 ::16 731< :917 9919 ;51;. <<15 <<1; <<1< <<1< <<1< <<1< <<1< <<1< <<1; <;1; <<1; 4339 4339 4339 4339 4339 <<18 4339 <<1; 4339. 5419 5;1: 6417 671; 5814 671; 6314 6814 681; 5616 5313 6517 6914 7319 6617 7319 651< 731; 7313 6517.

(22) NV YP DG VI ZE G IE ME ME NV YP DG VI ZE G IE ME ME. E q ( "!! <1: n ( "" <1; nQ ( ! 4518. 4913 4817 4:14 4619 91: 75149 q ( "!! 91; n ( "" 813 nQ ( % :15 441: 4416 5413 <1; 613 791;9. F. 4339 4339 4339 4339 4339 4339 4339 4339 <<1< 4339 4339 4339 4339 4339 4339 4339 4339 <<1<. . ;319 <414 <719 <:15 <:15 9919 <91< <714 <61; ;315 <314 <719 <:1; <:1; 9:1< <:19 <61; <:18. Wdeoh 7 +frqwlqxhg,. Oq. 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339. w. 6614 761; 7;16 851: 851< 831: 861< 8816 651< 6615 7;13 8519 8:19 8:1; 851; 8;16 8;17 6<1:. E q ( "!! :17 n ( "" :15 nQ ( # 4313. 4713 4618 4<18 4513 719 78149 q ( "!! 91: n ( "" 61: nQ ( ' 818 <1< <19 551: ;16 513 7;179. F. 4339 4339 4339 4339 4339 4339 4339 4339 <<1< 4339 4339 4339 4339 4339 4339 4339 4339 4339. . ;315 <31; <719 <:18 <:18 9:15 <:15 <61< <81; ;317 ;;18 <716 <;13 <;13 9:1: <:1: <618 <;15. Oq. 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339 4339. ryhuuhmhfw rwkhuzlvh1 Lq frqwudvw/ doo PF whvwv dfklhyh shuihfw vl}h frqwuro iru doo vdpsoh vl}hv1 Dq lqwhuhvwlqj h{shulphqw wkdw ehduv rq wklv sureohp lv uhsruwhg lq Zhlvehuj +4<;3,1 Zhlvehuj kdg srlqwhg rxw wkdw lq wkh frqwh{w ri qrupdolw| whvwv/ Prqwh Fduor uhvxowv edvhg rq gdwd vhwv zkhuh doo h{sodqdwru| yduldeohv duh gudzq iurp wkh xqlirup ru vwdqgdug qrupdo glvwulexwlrq duh qrw uhsuhvhqwdwlyh dqg wkdw vl}h sureohpv pd| rffxu1 Kh ghprqvwudwhg wklv zlwk d vshflf gdwd vhw iru wkh VZ whvw zlwk q ( #!1 Wkh dqdo|vlv khuh h{whqgv wklv revhuydwlrq lq wzr lpsruwdqw zd|v1 Iluvw/ zh vkrz wkdw sureohpv fdq rffxu iru doo frqyhqwlrqdo whvwv1 Vhfrqg/ wkh ghvljq pdwulfhv zh frqvlghu lqyroyh vdpsohv dv odujh dv "!! dqg $!! dqg duh txlwh olnho| wr eh hqfrxqwhuhg lq hfrqrphwulf sudfwlfh1 Dq lqwxlwlyh h{sodqdwlrq iru wkh hhfw ri gxpp| yduldeohv rq whvw vl}h lv wkh iroorzlqj1 Uhvlgxdov edvhg rq qrupdo uhjuhvvruv pd| plplf dq l1l1g1 vhulhv li n lv vpdoo hqrxjk/ uhodwlyh wr q1 Wkh dsshqghg lqglfdwru yduldeohv fdxvh nQ uhvlgxdov wr eh }hur/ dqg wkhvh vkrxog eh h{foxghg iurp wkh whvw surfhgxuh +exw duh qrw,1 Wklv surylghv d vlpsoh h{dpsoh zkhuh vwdqgdug glvwulexwlrqdo wkhru| idlov/ zkloh rxu dssurdfk zrunv zlwkrxw dq| gl!fxow|1 Uhjuhvvruv gudzq irup d Fdxfk| glvwulexwlrq +vhh Wdeoh 6, surylgh dqrwkhu dowkrxjk ohvv h{wuhph h{dpsoh ri vxfk vlwxdwlrqv1 Qrwh qdoo| wkdw lq Wdeoh 6 wkh ohyho grhv qrw dsshdu wr eh ehwwhu frqwuroohg dv wkh vdpsoh vl}h lqfuhdvhv1 Wklv lv vlpso| gxh wr wkh idfw wkdw/ lq wklv h{shulphqw/ wkh qxpehu ri uhjuhvvruv lqfuhdvhv zlwk vdpsoh vl}h1. 47. w. 6713 7914 831: 8817 8818 841< 8913 8:13 6915 6416 7;1< 861< 8<14 8<16 8715 8<16 8<1: 7614.

(23) 715 Whvw Srzhu 71514. Wkh orfdwlrq0vfdoh prgho. Lw lv hylghqw iurp Wdeoh 5 wkdw PF whvwv fruuhfw iru vl}h dqg dfklhyh jrrg srzhu1 Ryhudoo/ zh gr qrw revhuyh dq| vljqlfdqw srzhu orvv iru whvwv kdylqj frpsdudeoh vl}h1 Zkhq lqwhusuhwlqj wkh srzhu ri wkh fruuhodwlrq whvwv/ nhhs lq plqg wkdw wkh vwdqgdug. VI> Z E. dqg wkh. IE. whvwv duh voljkwo| ryhuvl}hg1 Qrwh dovr wkdw wkh prglhg HGI +l1h1/ vl}h fruuhfwhg iroorzlqj Vwhskhqv +4<:7,, dqg wkh PF whvwv ghprqvwudwh vlplodu srzhu iru doo vdpsoh vl}hv dfurvv doo wkh glvwulexwlrqv h{dplqhg1 Prvw lpsruwdqw lv wkh hhfw ri wkh PF surfhgxuh rq wkh prphqw whvwv1 Lqghhg/ wkh hhfwlyh srzhu ri wkh Wklv lv h{shfwhg vlqfh wkh vwdqgdug. ME. ME whvwv lpsuryhv dssuhfldeo| iru q 4331. whvw lv vhyhuho| xqghuvl}hg1. VZ +zkhq ihdvleoh, VI dssur{lpdwlrqv duh dprqj wkh prvw srzhuixo djdlqvw sudfwlfdoo| doo dowhuqdwlyhv1 Wkh Z E vhhpv d vhqvleoh fkrlfh iru lw grhv qrw uho| rq dq| wdeoh ri zhljkwv1 Krzhyhu/ iru q @ 58/ wkh VI / Z E dqg IE duh eldvhg lq wkh fdvh ri wkh ehwd glvwulexwlrq1 Dowkrxjk wkh G whvw w|slfdoo| vkrzv ohvv srzhu wkdq wkh rwkhu whvwv lq lwv fodvv/ lw lv qrw eldvhg lq vpdoo vdpsohv/ xqolnh wkh VI 0w|sh frxqwhusduwv1 Wkh DG rxwshuirupv doo HGI vwdwlvwlfv/ Wkh srzhuv ri wkh PF whvwv duh eurdgo| lq wkh iroorzlqj rughu1 Wkh. dqg wkh. frpsduhv idyrudeo| wr wkh prphqw whvwv dqg kdv qr eldv sureohpv1 djdlqvw wkh ehwd glvwulexwlrq iru. q @ 58/. wkh. ME. Zkloh lw lv eldvhg. doprvw dfklhyhv pd{lpxp srzhu djdlqvw. wkh Fdxfk|/ orjqrupdo dqg Vwxghqw w+8, glvwulexwlrq> lw lv rxwshuiruphg e| wkh lq wkh fdvh ri wkh. . glvwulexwlrq zkhq. q 83=. DG vwdwlvwlf. Dv h{shfwhg/ doo PF whvwv kdyh yhu| jrrg. srzhu zkhq wkh huuruv iroorz wkh Fdxfk| dqg wkh orjqrupdo glvwulexwlrq hyhq lq vpdoo vdpsohv1 Ilqdoo|/ iurp Wdeoh 8/ zh revhuyh wkdw wkh qxpehu ri uhsolfdwlrqv eh|rqg << kdv qr vljqlfdqw hhfw rq wkh srzhu ri PF whvwv1. 71515. Wkh uhjuhvvlrq prgho. Iurp wkh uhvxowv lq Wdeoh 7/ lw fdq eh vhhq wkdw wkh shuirupdqfh ri wkh uhjuhvvlrq0edvhg whvwv fdq eh juhdwo| dhfwhg e| wkh ghvljq pdwul{ hvshfldoo| iru vdpsohv ri vl}h ohvv wkdq 4331 Krzhyhu/ lw dsshduv wkdw wkh ghvljq pdwul{ kdv olwwoh hhfw rq wkh udqnlqj ri wkh whvwv1 Ixuwkhupruh/ wkh uhvxowv rq uhodwlyh srzhu dfurvv whvwv vhhp wr djuhh zlwk rxu qglqjv uhjduglqj wkh orfdwlrq0vfdoh prgho1 ehvw dydlodeoh> wkh. G. Lq jhqhudo/ wkh. xqeldvhg1 Wkh prvw srzhuixo HGI vwdwlvwlf lv wkh fruuhodwlrq vwdwlvwlfv h{fhsw shukdsv lq wkh. v ru A. VZ 0w|sh. fulwhuld dsshdu wr eh wkh. vwdwlvwlf lv rq wkh zkroh ohvv srzhuixo wkdq wkhvh exw lv frqvlvwhqwo|. DG> lw shuirupv zhoo lq frpsdulvrq wr wkh fdvh1 Wkh ME 0w|sh whvwv edvhg rq hlwkhu. +5> 4,. frpsduh idyrudeo| wr wkh fruuhodwlrq whvwv1 Krzhyhu/ wkhuh lv qr fohdu lqglfdwlrq dv. wr zklfk hvwlpdwh ri. . ME fulwhulrq shuirupv ME dsshduv ehwwhu ehwd+5/6, dowhuqdwlyh/ wkh ME. vkrxog eh xvhg lq sudfwlfh1 Wkh POH0edvhg. ehwwhu djdlqvw wkh Fdxfk|/ orjqrupdo dqg wkh w +8, dowhuqdwlyhv/ zkloh iru rwkhu glvwulexwlrqv dqg lv frqvlvwhqwo| xqeldvhg1 Iru wkh fulwhulrq lv vhyhuho| eldvhg iru doo vdpsohv vl}hv/ |hw whvwv1. 48. ME. shuirupv ehvw lq frpsdulvrq wr doo.

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(26) 7DEDKDGBDL ^4` J1 Dqghuvrq1 Vlpsoh whvwv ri glvwulexwlrqdo irup1. Mrxuqdo ri Hfrqrphwulfv/ 95=5985:9/. 4<<71 ^5` W1 Z1 Dqghuvrq dqg G1 D1 Gduolqj1 D whvw ri jrrgqhvv0ri0w1. Vwdwlvwlfdo Dvvrfldwlrq/ 7<=:98:9</. Mrxuqdo ri wkh Dphulfdq. 4<871. ^6` G1 Dqguhzv1 Hpslulfdo surfhvv phwkrgv lq hfrqrphwulfv1 Lq U1 I1 Hqjoh dqg G1 O1 Pf0 Idgghq/ hglwruv/. Kdqgerrn ri Hfrqrphwulfv/ Yroxph LY/ sdjhv 557:55<71 Hovhylhu. Vflhqfh/ Dpvwhugdp/ 4<<71 ^7` G1 Z1 N1 Dqguhzv1 Fkl0vtxduh gldjqrvwlf whvwv iru hfrqrphwulf prghov= Lqwurgxfwlrq dqg dssolfdwlrqv1. Mrxuqdo ri Hfrqrphwulfv/. 6:=468489/ 4<;;1. ^8` G1 Z1 N1 Dqguhzv1 Fkl0vtxduh gldjqrvwlf whvwv iru hfrqrphwulf prghov= Wkhru|1. phwulfd/ 89=474<4786/. Hfrqr0. 4<;;1. ^9` G1 Z1 N1 Dqguhzv1 D frqglwlrqdo Nroprjrury whvw1. Hfrqrphwulfd/ 98=43<:445;/ 4<<:1. ^:` J1 D1 Eduqdug1 Frpphqw rq Wkh vshfwudo dqdo|vlv ri srlqw surfhvvhv% e| P1 V1 Eduwohww1. Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv E /. 58=5<7/ 4<961. ^;` O1 Edulqjkdxv/ U1 Gdqvfknh/ dqg Q1 Khq}h1 Uhfhqw dqg fodvvlfdo whvwv iru qrupdolw| 0 d frpsdudwlyh vwxg|1. Frppxqlfdwlrqv lq Vwdwlvwlfv/ Vlpxodwlrq dqg Frpsxwdwlrq/. 4;+4,=6966:</ 4<;<1 ^<` D1 N1 Ehud/ F1 P1 Mdutxh/ dqg O10I1 Ohh1 Whvwlqj wkh qrupdolw| dvvxpswlrq lq olplwhg ghshqghqw yduldeoh prghov1. Lqwhuqdwlrqdo Hfrqrplf Uhylhz/ 58=8968:;/ 4<;71. ^43` U1 Ehudq dqg S1 Z1 Ploodu1 D vwrfkdvwlf plqlpxp glvwdqfh whvw iru pxowlyduldwh sdud0 phwulf prghov1. Wkh Dqqdov ri Vwdwlvwlfv/. 4:=458473/ 4<;<1. ^44` ]1 Z1 Eluqedxp1 Frpsxwhuv dqg xqfrqyhqwlrqdo whvw0vwdwlvwlfv1 Lq I1 Survfkdq dqg U1 M1 Vhu lqj/ hglwruv/. Uholdelolw| dqg Elrphwu|/ sdjhv 77478;1 VLDP/ Sklodghoskld/. SD/ 4<:71. IA. ^45` N1 R1 Erzpdq dqg E1 U1 Vkhqwrq1 Rpqlexv whvw frqwrxuv iru ghsduwxuhv iurp qrupdolw|. Elrphwulnd/ 85=8<4944/ 4<:81 K1 Fudpìu1 Rq wkh frpsrvlwlrq ri hohphqwdu| huuruv1 Vndqglqdylvn Dnwxdulhwlgvnuliw/ edvhg rq. ^46`. Q. dqg A 1. 44=4744;3/ 4<5;1. ^47` U1 E1 G*Djrvwlqr1 Dq rpqlexv whvw ri qrupdolw| iru prghudwh dqg odujh vdpsoh vl}h1 Elrphwulnd/ 8;=67467;/ 4<:41. ^48` U1 E1 G*Djrvwlqr1 Vpdoo vdpsoh srlqwv iru wkh C whvw ri qrupdolw|1 Elrphwulnd/ 8<=54< 554/ 4<:51 ^49` U1 E1 G*Djrvwlqr dqg P1 L1 D1 Vwhskhqv/ hglwruv1 Ghnnhu/ Qhz \run/ 4<;91. Jrrgqhvv0ri0Ilw Whfkqltxhv1 Pdufho. ^4:` M10P1 Gxirxu1 Prqwh Fduor whvwv zlwk qxlvdqfh sdudphwhuv= D jhqhudo dssurdfk wr qlwh0vdpsoh lqihuhqfh dqg qrqvwdqgdug dv|pswrwlfv lq hfrqrphwulfv1 Whfkqlfdo uh0 sruw/ F1U1G1H1/ Xqlyhuvlwì gh Prqwuìdo/ 4<<81 4;.

(27) ^4;` M10P1 Gxirxu/ D1 Idukdw/ O1 Jduglro/ dqg O1 Nkdodi1 Vlpxodwlrq0edvhg qlwh vdpsoh qrupdolw| whvwv lq olqhdu uhjuhvvlrqv1 Whfkqlfdo uhsruw/ F1U1G1H1/ Xqlyhuvlwì gh Prq0 wuìdo/ 4<<:1 74 sdjhv1 ^4<` M10P1 Gxirxu dqg M1 I1 Nlylhw1 H{dfw whvwv iru vwuxfwxudo fkdqjh lq uvw0rughu g|qdplf. Mrxuqdo ri Hfrqrphwulfv/. prghov1. :3=6<9;/ 4<<91. ^53` M10P1 Gxirxu dqg M1 I1 Nlylhw1 H{dfw lqihuhqfh phwkrgv iru uvw0rughu dxwruhjuhvvlyh glvwulexwhg odj prghov1 ^54` M1 Gxuelq1. Hfrqrphwulfd/ 99=:<437/ 4<<;1. Glvwulexwlrq Wkhru| iru Whvwv Edvhg rq wkh Vdpsoh Glvwulexwlrq Ixqfwlrq1. Vrflhw| iru Lqgxvwuldo dqg Dssolhg Pdwkhpdwlfv/ Sklodghoskld/ SD/ 4<:61 ^55` M1 Gxuelq1 Zhdn frqyhujhqfh iru wkh vdpsoh glvwulexwlrq ixqfwlrq zkhq sdudphwhuv duh hvwlpdwhg1. Wkh Dqqdov ri Vwdwlvwlfv/. 4=5:<5<3/ 4<:61. ^56` P1 Gzdvv1 Prglhg udqgrpl}dwlrq whvwv iru qrqsdudphwulf k|srwkhvhv1. Pdwkhpdwlfdo Vwdwlvwlfv/ ^57` E1 Hiurq1. Dqqdov ri. 5;=4;44;:/ 4<8:1. Wkh Mdfnqlih/ wkh Errwvwuds dqg Rwkhu Uhvdpsolqj Sodqv1. FEV0QVI Uh0. jlrqdo Frqihuhqfh Vhulhv lq Dssolhg Pdwkhpdwlfv/ Prqrjudsk Qr1 6;1 Vrflhw| iru Lqgxvwuldo dqg Dssolhg Pdwkhpdwlfv/ Sklodghoskld/ SD/ 4<;51. Dq Lqwurgxfwlrq wr wkh Errwvwuds/ yroxph 8: ri Prqr0 judskv rq Vwdwlvwlfv dqg Dssolhg Suredelolw| 1 Fkdspdq ) Kdoo/ Qhz \run/ 4<<61. ^58` E1 Hiurq dqg U1 M1 Wlevkludql1. ^59` H1 Idpd1. Irxqgdwlrqv ri Ilqdqfh1. Edvlf Errnv/ Qhz \run/ 4<:91. ^5:` M1 M1 Iloolehq1 Wkh suredelolw| sorw fruuhodwlrq frh!flhqw whvw iru qrupdolw|1. phwulfv/. Whfkqr0. 4:=44444:/ 4<:81. ^5;` D1 Kdoo1 Odjudqjh pxowlsolhu whvwv iru qrupdolw| djdlqvw vhplqrqsdudphwulf dowhuqd0 wlyhv1 ^5<` S1 Kdoo1. Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv /. ;=74:759/ 4<<31. Wkh Errwvwuds dqg Hgjhzruwk H{sdqvlrq1 Vsulqjhu0Yhuodj/. Qhz \run/ 4<<51. ^63` O1 H1 Kduulv1 Furvv0vhfxulw| whvwv ri wkh pl{wxuh ri glvwulexwlrqv k|srwkhvlv1. Ilqdqfldo dqg Txdqwlwdwlyh Dqdo|vlv/. Mrxuqdo ri. 54=6<79/ 4<;91. ^64` Q1 Khq}h1 Hpslulfdo0glvwulexwlrq0ixqfwlrq jrrgqhvv0ri0w whvwv iru glvfuhwh prghov1. Fdqdgldq Mrxuqdo ri Vwdwlvwlfv/. 57=;4<6/ 4<<91. ^65` F1 M1 Kxdqj dqg E1 Z1 Erofk1 Rq wkh whvwlqj ri uhjuhvvlrq glvwxuedqfhv iru qrupdolw|1. Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/. 9<=663668/ 4<:71. ^66` F1 P1 Mdutxh dqg D1 N1 Ehud1 H!flhqf| whvwv iru qrupdolw|/ khwhurvfhgdvwlflw| dqg vhuldo lqghshqghqfh ri uhjuhvvlrq uhvlgxdov1. Hfrqrplfv Ohwwhuv/. 9=58858</ 4<;31. ^67` F1 P1 Mdutxh dqg D1 N1 Ehud1 D whvw iru qrupdolw| ri revhuydwlrqv dqg uhjuhvvlrq uhvlgxdov1. Lqwhuqdwlrqdo Vwdwlvwlfdo Uhylhz/. 88=4964:5/ 4<;:1. ^68` M1 Mhrqj dqg J1 V1 Pdggdod1 D shuvshfwlyh rq dssolfdwlrq ri errwvwuds phwkrgv lq hfrqrphwulfv1 Lq J1 V1 Pdggdod/ F1 U1 Udr/ dqg K1 G1 Ylqrg/ hglwruv/. Vwdwlvwlfv/ Yroxph 44/ Hfrqrphwulfv/. Kdqgerrn ri. sdjhv 8:69431 Qruwk Kroodqg/ Dpvwhugdp/. 4<<61. 4<.

(28) ^69` N10K1 Mùfnho1 Ilqlwh vdpsoh surshuwlhv dqg dv|pswrwlf h!flhqf| ri Prqwh Fduor whvwv1. Wkh Dqqdov ri Vwdwlvwlfv. / 47=66967:/ 4<;91. ^6:` M1 Nlylhw dqg M10P1 Gxirxu1 H{dfw whvwv lq vlqjoh htxdwlrq dxwruhjuhvvlyh glvwulexwhg odj prghov1. Mrxuqdo ri Hfrqrphwulfv. / ;3=658686/ 4<<:1. ^6;` D1 Q1 Nroprjrury1 Vxood ghwhuplqd}lrqh hpslulfdgl xqd ohjjh gl glvwulex}lrqh1. Lvw1 Dwwxdul1. Jlruqd1. / 7=;6<4/ 4<661. ^6<` O10I1 Ohh1 Whvw iru qrupdolw| lq wkh hfrqrphwulf glvhtxloleulxp pdunhw prgho1. ri Hfrqrphwulfv. Mrxuqdo. / 4<=43<456/ 4<;51. ^73` K1 Z1 Oloolhiruv1 Rq wkh Nroprjrury0Vpluqry whvw iru qrupdolw| zlwk phdq dqg yduldqfh xqnqrzq1. Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq. / 95=6<<735/ 4<9:1. ^74` R1 Olqwrq dqg S1 Jr}dor1 Frqglwlrqdo lqghshqghqfh uhvwulfwlrqv= Whvwlqj dqg hvwlpd0 wlrq1 Whfkqlfdo uhsruw/ Frzohv Irxqgdwlrq iru Uhvhdufk lq Hfrqrplfv/ \doh Xqlyhu0 vlw|/ 4<<:1 ^75` U1 P1 Or|qhv1 Wkh hpslulfdo glvwulexwlrq ixqfwlrq ri uhvlgxdov iurp jhqhudol}hg uhjuhv0 vlrq1. Wkh Dqqdov ri Vwdwlvwlfv. / ;=5;85<;/ 4<;31. ^76` H1 Pdpphq1 Hpslulfdo surfhvv ri uhvlgxdov iru kljk0glphqvlrqdo olqhdu prghov1. Dqqdov ri Vwdwlvwlfv. Wkh. / 57=63:668/ 4<<91. ^77` N1 Y1 Pdugld1 Whvwv ri xqlyduldwh dqg pxowlyduldwh qrupdolw|1 Lq S1 U1 Nulvkqdldk/. Kdqgerrn ri Vwdwlvwlfv/ Yroxph 4= Dqdo|vlv ri Yduldqfh. hglwru/. / sdjhv 5:<6531. Qruwk Kroodqg/ Dpvwhugdp/ 4<;31 ^78` V1 J1 Phhvwhu dqg U1 D1 Orfnkduw1 Whvwlqj iru qrupdo huuruv lq ghvljqv zlwk pdq| eorfnv1. Elrphwulnd. / :8=89<8:8/ 4<;;1. ^79` O1 D1 Pxndqwvhyd1 Whvwlqj qrupdolw| lq rqh0glphqvlrqdo dqg pxowl0glphqvlrqdo olqhdu uhjuhvvlrq1. Wkhru| ri Suredelolw| dqg lwv Dssolfdwlrqv. / 55=8<4935/ 4<::1. ^7:` U1 F1 Sidhqehujhu dqg W1 H1 Glhopdq1 Whvwlqj qrupdolw| ri uhjuhvvlrq glvwxuedqfhv= D Prqwh Fduor vwxg| ri wkh Iloolehq whvwv1. Frpsxwdwlrqdo Vwdwlvwlfv. / ;9=68<6:6/. 4<<41 ^7;` G1 D1 Slhufh dqg U1 M1 Jud|1 Whvwlqj qrupdolw| ri huuruv lq uhjuhvvlrq prghov1. phwulnd. Elr0. / 9<=566569/ 4<;51. ^7<` G1 D1 Slhufh dqg N1 M1 Nrshfn|1 Whvwlqj jrrgqhvv0ri0w iru wkh glvwulexwlrq ri huuruv lq uhjuhvvlrq prghov1. Elrphwulnd. / 99=48/ 4<:<1. ^83` G1 Srlulhu/ G1 Whoor/ dqg V1 H1 ]lq1 D gldjqrvwlf whvw iru qrupdolw| zlwklq wkh srzhu. Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv Frqyhujhqfh ri Vwrfkdvwlf Surfhvvhv. h{srqhqwldo idplo|1 ^84` G1 Sroodug1. / ;9=68<6:6/ 4<;91. 1 Vsulqjhu0Yhuodj/ Qhz \run/ 4<;71. ^85` P1 Ulfkdugvrq dqg W1 Vplwk1 D whvw iru pxowlyduldwh qrupdolw| lq vwrfn uhwxuqv1. ri Exvlqhvv. Mrxuqdo. / 99=5<8654/ 4<<61. ^86` M1 S1 Ur|vwrq1 Dojrulwkp DV 4::1 h{shfwhg qrupdo rughu vwdwlvwlfv +h{dfw dqg dssur{0 lpdwh,1. Dssolhg Vwdwlvwlfv. / 64=494498/ 4<;51. 53.

(29) ^87` M1 S1 Ur|vwrq1 Dojrulwkp DV 4;41 wkh. z. whvw iru qrupdolw|1. Dssolhg Vwdwlvwlfv. / 64=4:9. 4;3/ 4<;51 ^88` M1 S1 Ur|vwrq1 Dq h{whqvlrq ri Vkdslur Zlonv*v whvw iru qrupdolw| wr odujh vdpsohv1. Dssolhg Vwdwlvwlfv Wkh Mdfnnqlih dqg Errwvwuds / 64=448457/ 4<;51. ^89` V1 Vkdr dqg G1 Wx1. 1 Vsulqjhu0Yhuodj/ Qhz \run/ 4<<81. ^8:` V1 V1 Vkdslur dqg U1 V1 Iudqfld1 Dq dssur{lpdwh dqdo|vlv ri yduldqfh whvw iru qrupdolw|1. Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq. / 9:=548549/ 4<:51. ^8;` V1 V1 Vkdslur dqg P1 E1 Zlon1 Dq dqdo|vlv ri yduldqfh whvw iru qrupdolw| +frpsohwh vdpsohv,1. Elrphwulnd. / 85=8<4944/ 4<981. ^8<` Q1 Y1 Vpluqry1 Vxu ohv ìfduwv gh od frxueh gh glvwulexwlrq hpslultxh +Uxvvldq2Iuhqfk vxppdu|,1. Pdwhpdwl fhvnl Veruqln Q1V1. / 9=659/ 4<6<1. ^93` P1 D1 Vwhskhqv1 HGI vwdwlvwlfv iru jrrgqhvv0ri0w dqg vrph frpsdulvrqv1. wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq. Mrxuqdo ri. / 9<=:63:6:/ 4<:71. ^94` P1 D1 Vwhskhqv1 Dv|pswrwlf uhvxowv iru jrrgqhvv0ri0w vwdwlvwlfv zlwk xqnqrzq sdud0 phwhuv1. Wkh Dqqdov ri Vwdwlvwlfv. / 7=68:69</ 4<:91. ^95` Z1 Vwxwh/ Z1 J1 Pdqwhljd/ dqg P1 Q1 Txlqglplo1 Errwvwuds edvhg jrrgqhvv0ri0w whvwv1. Phwulnd. / 73=576589/ 4<<61. ^96` K1 G1 Ylqrg1 Errwvwuds phwkrgv= Dssolfdwlrqv lq hfrqrphwulfv1 Lq J1 V1 Pdggdod/ F1 U1 Udr/ dqg K1 G1 Ylqrg/ hglwruv/. Kdqgerrn ri Vwdwlvwlfv/ Yroxph 44/ Hfrqrphwulfv. /. sdjhv 95<9941 Qruwk Kroodqg/ Dpvwhugdp/ 4<<61 ^97` V1 Zhlvehuj1 Frpphqw rq=. Vrph odujh vdpsoh whvwv iru qrq0qrupdolw| lq wkh olqhdu. uhjuhvvlrq prgho/ e| K1 Zklwh dqg J1P1 PdfGrqdog1. Vwdwlvwlfdo Dvvrfldwlrq. Mrxuqdo ri wkh Dphulfdq. / :8=5;64/ 4<;31. ^98` V1 Zhlvehuj dqg F1 Elqjkdp1 Dq dssur{lpdwh qrupdolw| vxlwdeoh iru pdfklqh fdofxodwlrq1. dqdo|vlv ri yduldqfh whvw iru qrq0. Whfkqrphwulfv. / 4:=466467/ 4<:81. ^99` K1 Zklwh dqg J1 P1 PdfGrqdog1 Vrph odujh vdpsoh whvwv iru qrq0qrupdolw| lq wkh olqhdu uhjuhvvlrq prgho1. Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq. 4<;31. 54. / :8=495;/.

(30)