k1
M* (kl ) = TT!n,,X^^ - lnX'-Λ+ 1У and (20)
kI i=1
k1
ξ* (k1 ) = 1 У lnX* i -lnX* k T (21)
n x 1 / i n1 ,i nj,kj+ 1 ` '
k1 i=1
Then find kl 0 (n1 ), i.e. the value of k1, which minimizes the AMSE (19):
k*1,o (n1 ) = argmin Q (n1, k1 ) (22)
= (n1 )/n yields k**O (n2 ) .
(23)
A second step completely analogous to the first one but with a smaller sample size n2
Next calculate
lnn -lnkj o(n )
k (n)= (k*,o(n1l> I (lnk(n1))2 ɔ lnn1
0 k(n2Ц(2lnn1 -lnk*o(n1 ))2 y
This allows to calculate the reciprocal tail index estimator:
^
^ 1 ko
^ n I ko I = ɪ У lnXι,j
× × k i=1
o0
ln X
*
n1,ko+1
(24)
This estimation procedure for k depends on two parameters, the number of bootstrap resamples, l, and the sample
size, n1. The number of resamples is in general determined by the available computational facilities. The application
presented in section 4 utilizes 10000 repetitions giving very stable results. Evaluation and optimization of n1,
necessitates a further step. Calculate the ratio
jQ(n μ (Q(nirt,o))2
R(n1)=Жх!
(25)
and determine n1 = argmin R (n1 ) numerically. If n * differs from the initial choice n 1, the previous steps should be
repeated. Remember that the quantile estimates derived from EVT are only valid for the tails of the profit-and-loss-
distribution. To allow inferences about quantiles in the interior of the distribution, Danielsson and de Vries (2000)
propose to link the tail estimator with the empirical distribution function at the threshold Xk+1. Thus the particular
advantages of the EVT and the HS are combined.
More intriguing information
1. Institutions, Social Norms, and Bargaining Power: An Analysis of Individual Leisure Time in Couple Households2. Recognizability of Individual Creative Style Within and Across Domains: Preliminary Studies
3. Endogenous Determination of FDI Growth and Economic Growth:The OECD Case
4. Imitation in location choice
5. The name is absent
6. On the Real Exchange Rate Effects of Higher Electricity Prices in South Africa
7. The name is absent
8. Developments and Development Directions of Electronic Trade Platforms in US and European Agri-Food Markets: Impact on Sector Organization
9. CONSIDERATIONS CONCERNING THE ROLE OF ACCOUNTING AS INFORMATIONAL SYSTEM AND ASSISTANCE OF DECISION
10. The Role of State Trading Enterprises and Their Impact on Agricultural Development and Economic Growth in Developing Countries