Journal of the Iranian Statistical Society
http://jirss@irstat.ir
Journal of The Iranian Statistical Society - Journal articles for year 2012, Volume 11, Number 1Yektaweb Collection - https://yektaweb.comen2012/3/11Wavelet Linear Density Estimation for a GARCH Model under Various Dependence Structures
http://jirss.irstat.ir/browse.php?a_id=172&sid=1&slc_lang=en
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.
Christophe ChesneauPrediction in a Trivariate Normal Distribution via Two Order Statistics
http://jirss.irstat.ir/browse.php?a_id=174&sid=1&slc_lang=en
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.
Alireza ArabpourAsymptotic Cost of Cutting Down Random Free Trees
http://jirss.irstat.ir/browse.php?a_id=175&sid=1&slc_lang=en
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.
Elahe Zohoorian AzadEstimation of the Entropy Rate of ErgodicMarkov Chains
http://jirss.irstat.ir/browse.php?a_id=176&sid=1&slc_lang=en
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.
Gholam Hosein YariAn Identity of Jack Polynomials
http://jirss.irstat.ir/browse.php?a_id=177&sid=1&slc_lang=en
In this work we give an alterative proof of one of basic
properties of zonal polynomials and generalised it for Jack polynomials
Jos´e A. D´ıaz-Garc´ıa