Hill, B. (1975) A Simple General Approach to Inference About the Tail of a Distribution. Ann. Statist. 3(5), 1163-1174. Home/Search Document Not in Database Summary Related Articles Check |
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Financial Risk and Heavy Tails - Bradley, Taqqu (2002) (1 citation) (Correct)
....so that fixing q = FX (x) one gets x = VaR q (X) The value of q should be large, namely, q = FX (x) F (X ) 1 k n. This yields VaR q (X) X q) 44) We obtained an estimator for VaR but it depends on k through X , on the sample size n and #. To estimate #, Hill [Hil75] proposed the following estimator # which is also dependent on the order statistics and sample size: # 1 . 45) The consistency and asymptotic normality properties of this # estimator are known in the i.i.d. case and for certain stationary processes. There are ....
B.M. Hill. A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3(5):1163--1174, 1975.
Delay Distributions on Fixed Internet Paths - Hoohiemstra, Van Mienhem (Correct)
....tail parameter . D.2 The Hill estimator. A reliable method to estimate the tail index in the presence of a heavy tail is the Hill estimator. Suppose again that the tail of the Internet delay density l (t) satisfies (13) The extreme vMue index = 1 , can be estimated with the Hill estimator [12]: v = 1og log , i=1 20 0 1 2 3 4 5 delay t [in ms] Fig. 12. Mean excess for 20 simulations of a Pareto distribution (12) with c = 1.25 and = 0.27 in dotted line and the data in bold line. The insert shows mean excess of the data versus delay t. The linear fit satisfies ....
B.M. Hill, "A simple general approach to inference about the tail of a distribution", Annals of Statistics, vol. 3, pp 1163-1174, 1975.
Long-Range Dependence and Heavy-Tail Modeling for.. - Cappe, Moulines.. (2002) (3 citations) (Correct)
....tail index, #, from a finite stretch of data (X 1 , X 2 , X n ) 6.1 Hill Plot Let X 1,n X 2,n # # X n,n be the order statistics of the sample X 1 , X n , which consist of the samples of the process, placed in increasing order. For some k n, we define the Hill estimator [17] to be the di#erence between the logarithm of the k th largest observation and the average of the logarithm of the k largest observations, i.e. # 1 k,n = k 1 log(X n k j,n X n k,n ) When 1#j#n is an i.i.d. sample of a Pareto distribution (see eq. 4) then the Hill estimator ....
B. M. Hill, "A simple general approach to inference about the tail of a distribution", Annals of Statistics, vol.3, pp. 11631174, 1975.
Markovian Modeling of Real Data Traffic: Heuristic phase.. - Horváth, Telek (Correct)
....to the server 0.5 1 1.5 2 2.5 3 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 estimate k Hill estimator qq estimator Fig. 2. The Hill and the dynamic qq plot for the EPA trace Hill estimator A possible approach to estimate the index of the tail behavior is the Hill estimator [20]. This estimator provides the index as a function of the k largest elements of the dataset and is de ned as n;k = k 1 log X (n i) log X (n k) 1 (3) where X (1) X (n) denotes the order statistics of the dataset. In practice, the estimator given in (3) is plotted against k ....
B. M. Hill. A simple general approach to inference about the tail of a distribution. The Annals of Statistics, 3:1163-1174, 1975.
Nonlinear Time Series, Complexity Theory, And Finance - Brock, de Lima (1995) (1 citation) (Correct)
....of the maximal moment exponent, ff = sup q 0 E j X q j 1, for a group of stock market and exchange returns. The parameter ff is estimated using the procedure 6 See Zolatarev (1986) for an extensive survey and Samorodnitsky and Taqqu (1994) for some recent developments. 21 developed by Hill (1975) and Hall (1982) Let X 1 ; X 2 ; XN be a sample of independent observations on a distribution with (asymptotically) Paretotype tails. Let XN;1 ; XN;2 ; XN;N represent the ordered sample values. The maximal moment exponent can then be consistently estimated by ff s = 0 s ....
Hill, B. (1975),"A simple general approach to inference about the tail of a distribution, " Annals of Mathematical Statistics 3, 1163-1174.
Sample Conditioned Inference - Corradi, Swanson (2000) (Correct)
....memory under both hypotheses. Proposition 6: H 0000 0 implies that 1 T P T t=1 X 2 t a.s ##, and H 0000 A implies that 1 T P T t=1 X 2 t a.s #M #. Classical hypothesis tests for the null of # = # 0 against the alternative of # 6= # 0 are available (e.g. using the Hill estimator (Hill 1975)) 13 ,usingthen T (where n T ##at a proper rate as T ##) largest values of # t . In this example, we observe X t , but not # t . To the b est o f our knowledge, there are no tests available based on observations on X t rather than # t . The primary reason for assessing #, and equivalently ....
Hill, B.M., (1975), A Simple General Approach to Inference About the Tail of a Distribution, 22 Annals of Statistics, 3, 1163-1174.
The Effect of TCP on the Self-Similarity of Network Traffic - Sikdar, Vastola (2001) (1 citation) (Correct)
....the OFF times for various window sizes for the traces for Italy and the heavy tailed nature of each is clearly evident. A statistically more rigorous method for estimating the slope of the tails and thus ff as compared to the eyeballing method associated with plotting ccdfs is the Hill s estimator [6]. The presence of heavy tails is indicated by a straight line behavior of the Hill s estimate ff n as the number of samples used in the calculation of the estimate increases while a steadily decreasing pattern is a strong indication of the data being not from a heavy tailed distribution. Fig. 2 ....
B. M. Hill, "A simple general approach to inference about the tail of a distribution," Annals of Statistics, vol. 3, pp. 11631174, 1975.
On the Contribution of TCP to the Self-Similarity of Network.. - Sikdar, Vastola (2001) (Correct)
....solid evidence for or against the presence of heavy tails, an eyeballing method is statistically unsatisfactory and the rough estimates of ff obtained from these plots may be unreliable. A statistically more rigorous method for estimating the slope of the tails and thus ff is the Hill s estimator [8]. The presence of heavy tails is indicated by a straight line behavior of the Hill s estimate ff n as the number of samples used in the calculation of the estimate increases while a steadily decreasing pattern is a strong indication of the data being not from a heavy tailed distribution. Figs. 3 ....
Hill, B. M.: A simple general approach to inference about the tail of a distribution. Annals of Statistics. 3 (1975) 1163-1174
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Hill, B.M., (1975), A simple general approach to inference about the tail of a distribution, The Annals of Statistics, 3, 1163-1174.
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Hill, B. (1975) A Simple General Approach to Inference About the Tail of a Distribution. Ann. Statist. 3(5), 1163-1174.
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B. M. Hill. A simple general approach to inference about the tail of a distribution. The Annals of Statistics, 3:1163--1174, 1975.
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Hill, B. (1975) A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163--1173.
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Hill, B. (1975) A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163--1173.
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B. Hill (1975) A simple general approach to inference about the tail of a distribution. Ann. Statist., 3, no. 5, 1163--1173.
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Hill, B (1975) A simple general approach to inference about the tail of a distribution. Ann. Statist. 3, no. 5, 1163--1173.
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B. M. Hill, "A simple general approach to inference about the tail of a distribution", Annals of Statistics, Vol.3:1163-1174, 1975.
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B. M. HILL, A simple general approach to inference about the tail of a distribution, The Annals of Statistics, 3 (1975), pp. 1163--1174.
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B. Hill, A simple general approach to inference about the tail of a distribution, Ann. Math. Statist. 3 (1975) 1163--1174.
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Hill,B. M., A simple general approach to inference about the tail of a distribution, Ann. Statist.3 1163-1174(1975)
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Hill, B. A simple general approach to inference about the tail of a distribution. The Annals of Statistics, 3, 5, 11631174, (1975).
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B. Hill, \A Simple General Approach to Inference about the Tail of a Distribution, " Annals of Statistics, vol. 3, no. 5, pp. 1163-1174, 1975.
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Hill, B. M., (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163--1174.
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Hill, B.M., (1975), A Simple General Approach to Inference About the Tail of a Distribution, Annals of Statistics, vol 3, 1163-1179.
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Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1174.
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Hill, B.M., (1975), A Simple General Approach to Inference About the Tail of a Distribution, Annals of Statistics, vol 3, 1163-1179.
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