1
1726-4057
Iranian Statistical Society
172
60: Probability theory and stochastic processes
Wavelet Linear Density Estimation for a GARCH Model under Various Dependence Structures
Chesneau
Christophe
Doosti
Hassan
1
3
2012
11
1
1
21
03
03
2012
12
09
2015
We consider n observations from the GARCH-type model:
S = σ2Z, where σ2 and Z are independent random variables. We develop
a new wavelet linear estimator of the unknown density of σ2 under
four different dependence structures: the strong mixing case, the β-
mixing case, the pairwise positive quadrant case and the ρ-mixing case.
Its asymptotic mean integrated squared error properties are explored.
In each case, we prove that it attains a fast rate of convergence.
174
60: Probability theory and stochastic processes
Prediction in a Trivariate Normal Distribution via Two Order Statistics
Arabpour
Alireza
Mahmood Molaiey
Mahsa
Jamalizadeh
Ahad
1
3
2012
11
1
39
56
03
03
2012
12
09
2015
In this paper, assuming that (X, Y1, Y2)T has a trivariate
normal distribution, we derive the exact joint distribution of (
X, Y(1),
Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T .
We show that this joint distribution is a mixture of truncated trivariate
normal distributions and then use this mixture representation to derive
the best (nonlinear) predictiors of X in terms of (
Y(1), Y(2))^T. We also
predict Y(1) in terms of (
X, Y(2) )^T , and Y(2) in terms of (
X, Y(1))^T. Finally
illustrate the usefulness of these results by using real-life data.
175
60: Probability theory and stochastic processes
Asymptotic Cost of Cutting Down Random Free Trees
Zohoorian Azad
Elahe
1
3
2012
11
1
57
73
03
03
2012
12
09
2015
In this work, we calculate the limit distribution of the total
cost incurred by splitting a tree selected at random from the set of all
finite free trees. This total cost is considered to be an additive functional
induced by a toll equal to the square of the size of tree. The main
tools used are the recent results connecting the asymptotics of generating
functions with the asymptotics of their Hadamard product, and the
method of moments.
176
60: Probability theory and stochastic processes
Estimation of the Entropy Rate of ErgodicMarkov Chains
Yari
Gholam Hosein
Nikooravesh
Zohre
1
3
2012
11
1
75
85
03
03
2012
12
09
2015
In this paper an approximation for entropy rate of an ergodic
Markov chain via sample path simulation is calculated. Although there
is an explicit form of the entropy rate here, the exact computational
method is laborious to apply. It is demonstrated that the estimated
entropy rate of Markov chain via sample path not only converges to the
correct entropy rate but also does it exponentially fast.
177
60: Probability theory and stochastic processes
An Identity of Jack Polynomials
D´ıaz-Garc´ıa
Jos´e A.
Guti´errez-J´aimez
Ram´on
1
3
2012
11
1
87
92
03
03
2012
12
09
2015
In this work we give an alterative proof of one of basic
properties of zonal polynomials and generalised it for Jack polynomials