• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.657-663
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• 2005

Under the minimum risk point estimation formulation of Robbins(1959), we consider the sequential point estimation problem for normal population $N({\theta},\;{\theta})$ with unknown parameter ${\theta}$. In the case of completely unknown ${\theta}$, Stein's(1945) two-stage procedure is known to enjoy the consistency property, but it is not even first-order efficient. In the case when ${\theta}>{\theta}_L\;where\;{\theta}_L(>0)$ is known, the revised two-stage procedure is shown to enjoy all the usual second-order properties.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.260-279
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• 2015

In this paper, we investigate physical layer security for multiple decode-and-forward (DF) relaying underlay cognitive radio networks (CRNs) with fixed transmit power at the secondary network against passive eavesdropping attacks. We propose a simple relay selection scheme to improve wireless transmission security based on the instantaneous channel information of all legitimate users and the statistical information about the eavesdropper channels. The closed-form expressions of the probability of non-zero secrecy capacity and the secrecy outage probability (SOP) are derived over independent and non-identically distributed Rayleigh fading environments. Furthermore, we conduct the asymptotic analysis to evaluate the secrecy diversity order performance and prove that full diversity is achieved by using the proposed relay selection. Finally, numerical results are presented to verify the theoretical analysis and depict that primary interference constrain has a significant impact on the secure performance and a proper transmit power for the second transmitters is preferred to be energy-efficient and improve the secure performance.