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ROC curve estimation based on local smoothing

2001, Journal of Statistical Computation and Simulation

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1.15 .006 ¹ ¹ ¹ 50 .003 0 ´ 1 ½ RASE ¹ ¹ 50 .012 1.06 1.03 RASE 0 RASE 1.15 ASE .5 ASE ASE ASE .5 Ãm=10 1.2 Ãm=20 1.15 Ãm=50 Ãm=30 Ãm=40 1.1 ´ 1.05 0 10 µ 20 ¶ 30 Än (h) · 40 ¸ 1 50 ´ 0 10 µ 20 ¶ 30 n (i) · 40 ¸ 50 ÅMÆ@Ç,ÈfÉ Ê^Ë>ÌaÍ>ÎÐÏÑ0ÒDÓ%ÔMՄÏ>×D Ö ØXÙ ×¥ØXÙÒݚÏgÞVÒ¥Ó%ÔM՟Ï`× Ö ØXÙ ×¥ØXÙÒݚÏáÒ¥Ó%ÔM՟Ï`×¥ Ö ØXÙ ×¥ØXÙÒ'ãÓ%ÔMՄÏ>× Ö ØXÙ ×¥ØXÙÒÝ ß Øà Û ß Øà Û ÚÜÛ ÚâÛ ÏäÒÐÓ%ÔM՟Ï`å Ö æ å ÒݝÏgÊZÒ«Ó%ÔMՄÏ`å— Ö çèoé å ÒݝÏgêÒÐÓ%ÔMՄÏhå Ö æ å Ò'ãÓ%ÔMՄÏfå% Ö çèoé å ÒݝÏgÇ`ÒӗÔmՄÏ0ë— Ö ì ë±ÒݝÏíÒ Û Û Û Û Û Ó%ÔMՄÏ0ë% Ö î ë±ÒݔÏÆOÒ#Ó%ÔMՄÏ`ë— Ö ì ë±Ò'ãÓ%ÔMՄÏ>ë% Ö î ë±ÒÌ Û Û Û ï Í 1.5 RASE 1.2 1.3 1.4 0.03 0 1 ð a2 (a) ó 3 ô 4 1.1 ö 0 ÷ õ2 úa (b) 1 ø 3 ù 1.0 ò 0.0 0.01 ASE 0.02 0.03 ASE 0.02 0.01 0.0 ñ 4 ö 0 1 ÷ õ 2a (c) û®üLý,þfÿ      !   " #$    %'&( )  "* +  ø 3 ù 4 50 30 n (l) 0.9 1.0 0 10 20 m=5 m=10 m=20 m=30 m=40 m=50 1.1 1.2 1.3 50 40 30 0.9 1.0 0 10 20 n (k) m=5 m=10 m=20 m=30 m=40 m=50 1.1 1.2 1.3 50 40 30 n (j) 0.9 1.0 0 10 20 m=5 m=10 m=20 m=30 m=40 m=50 1.1 1.2 1.3 1.4 50 30 0.9 1.0 1.1 1.2 1.3 1.4 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (i) 40 50 40 30 n (e) 10 0.9 1.0 1.1 1.2 1.3 1.4 0.9 1.0 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (a) 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 0 RASE 1.1 1.4 50 30 20 10 0 0.9 1.0 1.1 1.2 1.3 1.4 RASE 1.2 n (f) 40 m=5 m=10 m=20 m=30 m=40 m=50 n (b) 0.9 1.0 1.1 1.2 0 10 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 RASE 50 RASE 1.3 1.4 50 40 30 20 10 0 0.9 1.0 1.1 1.2 1.3 1.4 RASE 1.3 n (g) m=5 m=10 m=20 m=30 m=40 m=50 n (c) 0.9 1.0 1.1 1.2 1.3 1.4 0 10 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 RASE 50 RASE 1.4 40 50 30 20 0.9 1.0 1.1 1.2 1.3 1.4 0 10 m=5 m=10 m=20 m=30 m=40 m=50 10 0 0.9 1.0 1.1 1.2 1.3 1.4 RASE 1.4 n (h) 40 50 n (d) 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 RASE 50 RASE RASE RASE ,-/.10324657983:!; <=!> @ ? 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E*B@C7F> G CIHKJMLN> OQPRBTS$CUVWJMLX> OQBTS$CYI>ZCIHKJ\[]D_^ 5*`aOQPRU V\JbLX> OQBTS$CY%> c$C]HdJfe]=g`hSiPRUVjJkLN> OQBTS$CYl> mnCoHpJb=qerOQPRUsVfJqLX> OQBTS$CYl>4tCoHuJbLX> OQPRBTS$CU VvJq[]D_^ 5Y>wC HxJq[oD_^ VqJ‚[]D_^ 5Yƒ> -„ClH 5`yOQPRUVMJz[]D_^ 5QY>.)C HxJve]={`|SiPRU}VvJk[oD_^ JaLX> OQPRBTS$CUVzJke]=‚`‚SiY>†ClH‡Jˆ[]D_^ 5Y%> ~nCH€J=zeNOQPRU 5]`XOQPRUnVkJkeo=‚`ˆSiY>‰ŠClH‡Jkeo=‚`ˆSiPRU V‹J‹e]=h`hSiYŒ> -„CHJ|=|erOQPRUŽVjJeo=h`gSiYn~3424I[q-’‘G”“–•—mŠ-’‘'˜'2™-’Zš03˜-/›1œ6iGi2™-’GiZšž’4Io-/˜~ =j-’‘G_œ£4¥¤Q¦›1œŠ4Tœ ˜-’G_žƒmŠ-’‘'˜'2™-’Zš03˜-/›1œ§¨Gi2™-©GiZšž/4 o-/˜~£ª”4TG_œ«Si7 S¥8 Ÿ–¡ ¢b5!G_œŠm 50 30 n (l) 20 0.8 0.9 0 10 m=5 m=10 m=20 m=30 m=40 m=50 1.0 1.1 1.2 1.3 50 30 0.8 0.9 1.0 1.1 1.2 1.3 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (k) 40 50 40 30 50 40 30 0.8 0.9 1.0 1.1 1.2 1.3 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (j) 40 30 50 40 30 0.8 0.9 1.0 1.1 1.2 1.3 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (i) 40 30 n (e) 20 0.8 0.9 1.0 1.1 1.2 1.3 0.8 0.9 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (a) RASE 1.0 0 10 m=5 m=10 m=20 m=30 m=40 m=50 30 40 50 RASE 1.1 n (f) 10 0 0.8 0.9 1.0 1.1 1.2 1.3 0.8 0.9 1.1 1.0 RASE 50 RASE 1.2 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (b) 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 50 RASE 1.2 n (g) 10 0 0.8 0.9 1.0 1.1 1.2 1.3 0.8 0.9 1.0 1.1 1.2 1.3 0 10 m=5 m=10 m=20 m=30 m=40 m=50 20 n (c) 20 30 40 m=5 m=10 m=20 m=30 m=40 m=50 RASE 50 RASE 1.3 40 50 20 0.8 0.9 0 10 m=5 m=10 m=20 m=30 m=40 m=50 1.0 1.1 1.2 1.3 RASE 1.3 n (h) 30 40 50 40 30 n (d) 20 0.8 0.9 0 10 m=5 m=10 m=20 m=30 m=40 m=50 1.1 1.2 1.3 1.0 RASE 50 RASE RASE RASE ¬­/®1¯3°±6²³´µ!¶ ·¸!¹ » º ¼%½»¾'¿(¶ ·¸!¹» º À*½»¾³F¹ Á ¾IÂKÃMÄN¹ÆÅiÇ´½TÅ$¾ÈÉWÃMÄX¹ ÊQ½TÅ$¾ËI¹Ì¾IÂKÃ\Í]¿_Î ²*ÏkÅiÇ´È É\ÃbÄX¹ ÊQ½TÅ$¾Ë%¹ Ð$¾]ÂdÃfÑ]¸gÏÓÒÇ´ÈÉjÃkÄN¹ ÊQ½TÅ$¾Ël¹ Ôn¾oÂpÃb¸{ÏÓÊQÇ´ÈsÉfÃqÄX¹ ÊQ½TÅ$¾Ël¹±t¾oÂuÃbÄX¹ÆÅiÇ´½TÅ$¾È ÉvÃqÍ]¿_Î ²Ë¹Õ¾ ÂxÃqÍo¿_Î ÉqÂÍ]¿_Î ²˃¹ ­„¾l ²Ï{ÅiÇ´ÈÉMÃzÍ]¿_Î ²Q˹®)¾ ÂxÃvÑ]¸{ψÒÇ´È}ÉvÃkÍo¿_Î ÃaÄX¹ÆÅiÇ´½TÅ$¾ÈÉzÃkÑ]¸‚Ï‚Åi˹׾l‡ÈÍ]¿_Î ²Ë%¹ Ön¾€Á¸|ςÊQÇ´È ²]ψÅiÇ´ÈnÉkÃkÑo¸‚ψÅi˹؊¾l‡ÃkÑo¸‚ÏNÒÇ´È É‹Ã‹Ñ]¸hÏhÅiˌ¹ ­„¾Ã|¸aÏÓÊQÇ´ȎÉjÁÑo¸hÏgÅiËnÙÖ3±°±IÍq­’ÚÁ”Û–Ü—ÔŠ­’Ú'Ý'°™­’Ìš¯3Ý­/Þ1ß6àiÁi°™­’Ái̚ᒱIÙo­/ÝÖ ¸j­’ÚÁ_ߣ±¥åQæÞ1ߊ±Tß Ý­’Á_áƒÔŠ­’Ú'Ý'°™­’Ìš¯3Ý­/Þ1ߧà¨Ái°™­©Ái̚á/± Ùo­/Ý֣由TÁ_ß«Åi³ ÅT´ â–ã äb²!Á_ßŠÔ ì 2.25 8 êHarrell-Davis Method ë Empirical Method RSE 4 SE 6 1.75 é 1.25 2 0.75 0 é é é 0.0 é 0.2 é 0.4 é è 0.6 0.8 0.25 é 1.0 é 0.0 é 0.2 s (a) è 0.8 1.0 í íKernel Fit (2.4) ëKernel Fit (2.4) 0.03 ëEmpirical Fit (1.4) Empirical Fit (1.4) 0.01 0.10 SE 0.02 0.20 é 0.6 s (b) é 0.0 0.0 SE é 0.4 0.0 é 0.2 é 0.4 é è 0.6 é 0.8 é 1.0 0.0 é 0.2 s (c) îï/ð1ñ3òóõôö÷øù ú û]ü]ýŠóþÿñŠúiòó óò™ò_ò™þ*ùû é 0.4 é è 0.6 é 0.8 1.0 s (d) ýŠó úiòòóúï’þÿ)ñšú ï’óIóTþï”ú_òú ý3óónï/ò™ïú  ÿñŠú ï!/ó%óTþï”ú_ò#"ý3ó$ý3ó%&'šï’þ'óTú_þ'ó$( šñ©úï)&šï’þ'ò™ï)*nñï)&ï©þ,+%- . ô(/10243Iú $57698:'; ù<*û=ý3ó ò™úï)> ?ý3ó@'A Bý3óC úiòòó) úï©þ ÿ)ñŠú Dï/ólóTþï”ú_òEFýŠó%G Bý3ó%ónï/ò™ïú )ÿ)ñŠú Dï/óóTþï§ú_ò; ùH$ûIý3ó'Jiú ’ñ3óTþ LKMONgú PKM>QR"oý3óSý3óO&'šï’þ'óTú_þ'óT( šñ’úï&UŠï©þ'ò™ï)*šñï)&§ï’þI+@- . ô/V0243W;ùHnû M K N ú B KM Q "oýŠóAý3óL&'Šï©þ'óTú_þ'óA( šñ’úï&7Šï©þ'ò™ï)*šñï)& ï’þF+@- . ôO/V:'243ö ü]ý3ó Šï’þóTú_þ'óY( šñ’úï&Tšï’þ'ò™ï)*nñï)&§ï©þ+%- . ô ú YZ[6\576X8:”ïSB) þ*ùH$û%ú  ùHnûö ý3óU'X¨ú ’ñŠóTþ> 0T÷ View publication stats