ait| ulh ˇl? | l?@* 5)44i|h) ? a 4i 5ih it l i*t · 2019-04-08 · ait| ulh ˇl?_ | l?@* 5)44i|h)...

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Page 1: Ait| uLh ˇL? | L?@* 5)44i|h) ? A 4i 5ih it L i*t · 2019-04-08 · Ait| uLh ˇL?_ | L?@* 5)44i|h) ? A 4i 5ih it L_i*t at@? @ _ 5ihi?@} h}t|2Sc†bbH Devwudfw Wkh dvvxpswlrq ri frqglwlrqdo

� Ait| uLh �L?_�|�L?@* 5)44i|h) �? A�4i 5ih�it�L_i*t�

a�t�@? �@� _ 5ihi?@ �} h

��}�t| 2Sc �bbH

Devwudfw

Wkh dvvxpswlrq ri frqglwlrqdo v|pphwu| lv riwhq lqyrnhg wr ydolgdwh dgdswlyhhvwlpdwlrq dqg frqvlvwhqw hvwlpdwlrq ri DUFK2JDUFK prghov e| txdvl pd{lpxpolnholkrrg1 Lpsrvlqj frqglwlrqdo v|pphwu| fdq lqfuhdvh wkh h�flhqf| ri errwvwudsvli wkh v|pphwu| dvvxpswlrq lv ydolg1 Wklv sdshu sursrvhv d surfhgxuh iru whvwlqjfrqglwlrqdo v|pphwu|1 Wkh sursrvhg whvw grhv qrw uhtxluh wkh gdwd wr eh vwdwlrqdu|ru l=l=g=/ dqg wkh glphqvlrq ri wkh frqglwlrqdo yduldeohv frxog eh lq�qlwh1 Wkh vl}hdqg srzhu ri wkh whvw duh vdwlvidfwru| hyhq iru vpdoo vdpsohv1 Lq dgglwlrq/ wkhsursrvhg whvw lv vkrzq wr kdyh qrq0wulyldo srzhu djdlqvw urrw0W orfdo dowhuqdwlyhv1Dsso|lqj wkh whvw wr ydulrxv wlph vhulhv/ zh uhmhfw frqglwlrqdo v|pphwu| lq lq�dwlrq/h{fkdqjh udwh dqg vwrfn uhwxuqv1 Dprqj wkh qrq0�qdqfldo wlph vhulhv frqvlghuhg/ zh�qg wkdw lqyhvwphqw/ wkh frqvxpswlrq ri gxudeohv/ dqg pdqxidfwxulqj hpsor|phqwdovr uhmhfw frqglwlrqdo v|pphwu|1 Lqwhuhvwlqjo|/ wkhvh duh vhulhv zkrvh g|qdplfv duheholhyhg wr eh d�hfwhg e| �{hg frvwv ri dgmxvwphqwv1

MHO Fodvvl�fdwlrq= F45> F551

Nh| Zrugv dqg Skudvhv= frqglwlrqdo v|pphwu|/ hpslulfdo glvwulexwlrq ixqfwlrq/nhuqho hvwlpdwlrq/ Eurzqldq prwlrq/ DUFK2JDUFK/ qrqolqhdu wlph vhulhv1

�Zh wkdqn vhplqdu sduwlflsdqwv dw wkh Fdps Hfrqrphwulfv iru xvhixo frpphqwv1 Wklv sdshu lv dovrsuhsduhg iru wkh QEHU2QVI Wlph Vhulhv Vhplqdu wr eh khog lq Fklfdjr lq Vhswhpehu/ 4<<;1 Wkh �uvwdxwkru dfnqrzohgjhv �qdqfldo vxssruw iurp wkh Qdwlrqdo Vflhqfh Irxqgdwlrq xqghu Judqw VEU0<:3<83;1

|Ghsduwphqw ri Hfrqrplfv/ Ervwrq Froohjh/ Hpdlo= mxvkdq1edlCef1hgx1}Ghsduwphqw ri Hfrqrplfv/ Ervwrq Froohjh1 Hpdlo= vhuhqd1qjCef1hgx

Fruuhvsrqghqfh= Mxvkdq Edl/ Ghsduwphqw ri Hfrqrplfv/ Ervwrq Froohjh/ Fkhvwqxw Kloo/ PD/ 3579:1

Page 2: Ait| uLh ˇL? | L?@* 5)44i|h) ? A 4i 5ih it L i*t · 2019-04-08 · Ait| uLh ˇL?_ | L?@* 5)44i|h) ? A 4i 5ih it L_i*t at@? @ _ 5ihi?@} h}t|2Sc†bbH Devwudfw Wkh dvvxpswlrq ri frqglwlrqdo

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Page 32: Ait| uLh ˇL? | L?@* 5)44i|h) ? A 4i 5ih it L i*t · 2019-04-08 · Ait| uLh ˇL?_ | L?@* 5)44i|h) ? A 4i 5ih it L_i*t at@? @ _ 5ihi?@} h}t|2Sc†bbH Devwudfw Wkh dvvxpswlrq ri frqglwlrqdo

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Page 33: Ait| uLh ˇL? | L?@* 5)44i|h) ? A 4i 5ih it L i*t · 2019-04-08 · Ait| uLh ˇL?_ | L?@* 5)44i|h) ? A 4i 5ih it L_i*t at@? @ _ 5ihi?@} h}t|2Sc†bbH Devwudfw Wkh dvvxpswlrq ri frqglwlrqdo

Figure 1: Test of Symmetry for Simulated Normal Observations. Dashed line: WT (x). Solidline: ST (x). Light-solid line: WT (x). Two horizontal lines: the 95% con�dence band.

(a)

0 50 100 150 200

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12

3

(b)

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Page 34: Ait| uLh ˇL? | L?@* 5)44i|h) ? A 4i 5ih it L i*t · 2019-04-08 · Ait| uLh ˇL?_ | L?@* 5)44i|h) ? A 4i 5ih it L_i*t at@? @ _ 5ihi?@} h}t|2Sc†bbH Devwudfw Wkh dvvxpswlrq ri frqglwlrqdo

Figure 2: Test of Symmetry for Simulated Chi-Square Observations. Dashed line: WT (x).Solid line: ST (x). Light-solid line: WT (x). Two horizontal lines: the 95% con�dence band.

(a)

0 50 100 150 200

-20

24

(b)

0 50 100 150 200

-20

24