Weighted Approximations of Tail Copula Processes with Application to Testing the Bivariate Extreme Value Condition

Weighted Approximations of Tail Copula Processes with Application to Testing the Bivariate Extreme Value Condition

Consider n i.i.d. random vectors on ${\Bbb R}^{2}$ , with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value conditio...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 34(2006), 4, Seite 1987-2014
1. Verfasser: Einmahl, John H. J. (VerfasserIn)
Weitere Verfasser: de Haan, Laurens, Li, Deyuan
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2006
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Dependence structure Goodness-of-fit test Bivariate extreme value theory Tail copula process Weighted approximation Mathematics Philosophy
LEADER 01000caa a22002652 4500
001 JST008992266
003 DE-627
005 20240619180936.0
007 cr uuu---uuuuu
008 150323s2006 xx |||||o 00| ||eng c
035 |a (DE-627)JST008992266 
035 |a (JST)25463491 
040 |a DE-627  |b ger  |c DE-627  |e rakwb 
041 |a eng 
084 |a 62G32  |2 MSC 
084 |a 62G30  |2 MSC 
084 |a 62G10  |2 MSC 
084 |a 60G70  |2 MSC 
084 |a 60F17  |2 MSC 
100 1 |a Einmahl, John H. J.  |e verfasserin  |4 aut 
245 1 0 |a Weighted Approximations of Tail Copula Processes with Application to Testing the Bivariate Extreme Value Condition 
264 1 |c 2006 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
520 |a Consider n i.i.d. random vectors on ${\Bbb R}^{2}$ , with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented. 
540 |a Copyright 2006 The Institute of Mathematical Statistics 
650 4 |a Dependence structure 
650 4 |a Goodness-of-fit test 
650 4 |a Bivariate extreme value theory 
650 4 |a Tail copula process 
650 4 |a Weighted approximation 
650 4 |a Mathematics  |x Mathematical procedures  |x Approximation 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Inferential statistics  |x Statistical estimation  |x Estimation methods  |x Estimators 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Probabilities 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions  |x Continuous probability distributions  |x Cauchy Lorentz distribution 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics 
650 4 |a Philosophy  |x Applied philosophy  |x Philosophy of science  |x Scientific method  |x Hypothesis testing  |x Null hypothesis 
650 4 |a Mathematics  |x Mathematical values  |x Mathematical variables  |x Mathematical independent variables 
650 4 |a Philosophy  |x Logic  |x Logical topics  |x Formal logic  |x Mathematical logic  |x Mathematical set theory  |x Mathematical sets  |x Borel sets 
650 4 |a Mathematics  |x Mathematical procedures  |x Approximation 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Inferential statistics  |x Statistical estimation  |x Estimation methods  |x Estimators 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Probabilities 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions  |x Continuous probability distributions  |x Cauchy Lorentz distribution 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics 
650 4 |a Philosophy  |x Applied philosophy  |x Philosophy of science  |x Scientific method  |x Hypothesis testing  |x Null hypothesis 
650 4 |a Mathematics  |x Mathematical values  |x Mathematical variables  |x Mathematical independent variables 
650 4 |a Philosophy  |x Logic  |x Logical topics  |x Formal logic  |x Mathematical logic  |x Mathematical set theory  |x Mathematical sets  |x Borel sets  |x Statistics and Extreme Values 
655 4 |a research-article 
700 1 |a de Haan, Laurens  |e verfasserin  |4 aut 
700 1 |a Li, Deyuan  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t The Annals of Statistics  |d Institute of Mathematical Statistics  |g 34(2006), 4, Seite 1987-2014  |w (DE-627)270129162  |w (DE-600)1476670-X  |x 00905364  |7 nnns 
773 1 8 |g volume:34  |g year:2006  |g number:4  |g pages:1987-2014 
856 4 0 |u https://www.jstor.org/stable/25463491  |3 Volltext 
912 |a GBV_USEFLAG_A 
912 |a SYSFLAG_A 
912 |a GBV_JST 
912 |a GBV_ILN_11 
912 |a GBV_ILN_20 
912 |a GBV_ILN_22 
912 |a GBV_ILN_23 
912 |a GBV_ILN_24 
912 |a GBV_ILN_31 
912 |a GBV_ILN_32 
912 |a GBV_ILN_39 
912 |a GBV_ILN_40 
912 |a GBV_ILN_60 
912 |a GBV_ILN_62 
912 |a GBV_ILN_63 
912 |a GBV_ILN_69 
912 |a GBV_ILN_70 
912 |a GBV_ILN_73 
912 |a GBV_ILN_90 
912 |a GBV_ILN_95 
912 |a GBV_ILN_100 
912 |a GBV_ILN_105 
912 |a GBV_ILN_110 
912 |a GBV_ILN_120 
912 |a GBV_ILN_151 
912 |a GBV_ILN_161 
912 |a GBV_ILN_170 
912 |a GBV_ILN_213 
912 |a GBV_ILN_230 
912 |a GBV_ILN_285 
912 |a GBV_ILN_293 
912 |a GBV_ILN_370 
912 |a GBV_ILN_374 
912 |a GBV_ILN_602 
912 |a GBV_ILN_702 
912 |a GBV_ILN_2001 
912 |a GBV_ILN_2003 
912 |a GBV_ILN_2005 
912 |a GBV_ILN_2006 
912 |a GBV_ILN_2007 
912 |a GBV_ILN_2008 
912 |a GBV_ILN_2009 
912 |a GBV_ILN_2010 
912 |a GBV_ILN_2011 
912 |a GBV_ILN_2014 
912 |a GBV_ILN_2015 
912 |a GBV_ILN_2018 
912 |a GBV_ILN_2020 
912 |a GBV_ILN_2021 
912 |a GBV_ILN_2026 
912 |a GBV_ILN_2027 
912 |a GBV_ILN_2044 
912 |a GBV_ILN_2050 
912 |a GBV_ILN_2056 
912 |a GBV_ILN_2057 
912 |a GBV_ILN_2061 
912 |a GBV_ILN_2088 
912 |a GBV_ILN_2107 
912 |a GBV_ILN_2110 
912 |a GBV_ILN_2111 
912 |a GBV_ILN_2190 
912 |a GBV_ILN_2932 
912 |a GBV_ILN_2947 
912 |a GBV_ILN_2949 
912 |a GBV_ILN_2950 
912 |a GBV_ILN_4012 
912 |a GBV_ILN_4035 
912 |a GBV_ILN_4037 
912 |a GBV_ILN_4046 
912 |a GBV_ILN_4112 
912 |a GBV_ILN_4125 
912 |a GBV_ILN_4126 
912 |a GBV_ILN_4242 
912 |a GBV_ILN_4249 
912 |a GBV_ILN_4251 
912 |a GBV_ILN_4305 
912 |a GBV_ILN_4306 
912 |a GBV_ILN_4307 
912 |a GBV_ILN_4313 
912 |a GBV_ILN_4322 
912 |a GBV_ILN_4323 
912 |a GBV_ILN_4324 
912 |a GBV_ILN_4325 
912 |a GBV_ILN_4326 
912 |a GBV_ILN_4335 
912 |a GBV_ILN_4338 
912 |a GBV_ILN_4346 
912 |a GBV_ILN_4367 
912 |a GBV_ILN_4393 
912 |a GBV_ILN_4700 
951 |a AR 
952 |d 34  |j 2006  |e 4  |h 1987-2014