N(∙) kdv iqfiqiWh vxssruW/ Biτ is qr Orqjhu d Odj WuxqfdWirq sdUdPhWhUι Dqguhzv ghuiyhs
wkh rswlpdo nhuqho wkh TV nhuqho/ wkdw plqlpl}hv dq dv|pswrwlf PVH> kh dovr sursrvhv
d SdUdPhWuif “sOxjoiq” gdWdoguiyhq edqgzigWk fkrifh iru Biτ = Edshg rq Dqguhzs (1991),
SkiOOiss dqg Prrq (1999, Si 1084) sursrshg d KDF hsWipdWru by taking Wkh dyhudjh ri lʌ
ryhu l=
• n
•
l l j liA =
i=l
SkiOOiss dqg Prrq +4<<<, yhuifihg Wkh frqsisthqfy ri l by dssxpiqg Biτ, q>W $ 4 zitk
EiT@W $ f = Qhzhy dqg ZhsW +4<<7, sursrsh d qrqsdudPhWuif “sOxgoiq” gdWdoguiyhq fkrifh
ri Eiτ iru Wkhiu EduWOhWW khuqhOobdshg hsWipdWru l,χw∙ Dqguhzs dqg Pdqdkdq (1<<2, ixuWkhu
sursrsh d suhzkiWhqiqg khuqhO hsWipdWru
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+2143,
1 Λ /'τ)∖ ∙ nil 1 1 T T i Λ j TA ∙ ∕IΓA∙∏∖ ∙ j∙ C Гт T ∕x∏∖ 1
zkhuh Ai (β) is d fiOWhu bdshg rq d YhfWru DxWrUguhssirq (∖'.∖U∣ dssur{iPdWirq iru {Yi(β) j
dqg f,+ ( o ) = W T-ɪ Sll+1Y +( β) Y+_,( βe)' > l ` 0 > 1 >...>W - 1 >
'τ' 1 T-* S +1YJ+λβ)Y(ββ)'> l ` -1.....-(T -1)
is Wkh sdPsOh dxWrfryduidqfh ixqfWirq ri Wkh YDU uhsigxdO Vi(ββ)i
H{Whqsiyh sipxOdWirq h{shuiphqWs iq Wkh OiWhudWxuh skrz WkdW khuqhO hsWipdWrus shuirup
srruOy iq qiWh sdpsOhs zkhq Wkhuh is sWurqg dxWrfruuhOdWirq1 Wkhy riWhq Ohdg Wr sWurqg
ryhuuhmhfWirq iq WhsWiqg dqg Wrr qduurz frqghqfh iqWhuydOs iq hsWipdWirq1 Wkis is Wuxh hyhq
ii Wkh +iqihdsibOh, qiWh sdpsOh rsWipdO bdqgzigWk sdudphWhu is xshg1 LW dsshdus WkdW iW is
Wkh yhuy qdWxuh ri Wkh khuqhO phWkrg/ udWkhu Wkdq Wkh fkrifh ri d bdqgzigWk ru d khuqhO/ WkdW
dWWuibxWhs iWs srru shuirupdqfh iq qiWh sdpsOhs zkhq Wkh gdWd gissOdy sWurqg ghshqghqfh1
Lq rxu rsiqirq/ Wkh pdiq uhdsrq iru Wkh srru shuirupdqfh ri Wkh khuqhO hsWipdWrus is WkdW
Wkh sshfWudO ghqsiWy kds d shdk dW iuhtxhqfy 3 zkhq Wkhuh h{isWs sWurqg dxWrfruuhOdWirq/ bxW
Wkh khuqhO phWkrg/ ds d OrfdO dyhudgiqg phWkrg/ Whqgs Wr xqghuhsWipdWh Wkh shdk1 Dqguhzs
dqg Prqdkdq*s +4<<2, suhzkiWhqiqg surfhgxuh dOOhyidWhs Wkis grzqzdug bids sxbsWdqWidOOy
dqg Wkxs giyhs bhWWhu WhsW si}hs1 Krzhyhu/ iW dOsr iqdWhs Wkh yduidqfh dqg Wkxs pdy qrW
grpiqdWh Wkh sdph surfhgxuh dssOihg Wr Wkh ruigiqdO shuihs iq Whups ri PVH fuiWhuid1 EhOrz
zh sWxgy Wkh qiWh sdpsOh surshuWihs ri Wkh yduirxs KDF hsWipdWrus iq Wkh sdqhO frqWh{W1
61 PRQWH FDUOR HYLGHQFH
Zh qrz frpsduh Wkh qiWh sdpsOh shuirupdqfhs ri Wkuhh KDF fryduidqfh pdWui{ hs0
WipdWrus= qrqsdudphWuif khuqhO0bdshg ziWk dqg ziWkrxW suhzkiWhqiqg hsWipdWrus dqg Wkh