• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.363-381
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• 2012

Shortfall risk is considered by taking some exposed risks because the superhedging price is too expensive to be used in practice. Minimizing shortfall risk can be reduced to the problem of finding a randomized test ${\psi}$ in the static problem. The optimization problem can be solved via the classical Neyman-Pearson theory, and can be also explained in terms of hypothesis testing. We introduce the classical Neyman-Pearson lemma expressed in terms of mathematics and see how it is applied to shortfall risk in finance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.3
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• pp.219-231
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• 1991

In this paper, various results on Iocally optimum detection of signals are reviewed concisely, which are easlily apphcable to weak signal detection problems. In addition, locally optmum rank detection schemes for weak signals are reviewed, which are nonparametric counterparts of the locally optimum detecturs. Examples of practical applications, problems in implementation dnd performance characteristecs of the locally optimum detectors are also discussed, Finally, a fuzzy extension of the generalized Neyman Pearson lemma is briefly discussd.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.8
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• pp.789-795
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• 1992

The generalized Neyman-Pearson lemma Is reformulated In the framework of the fuzzy set theory. Based on the result, we define the locally optimum fuzzy test and derive the locally optimum fuzzy test function. As a pratical application of the locally optimum fuzzy test, detection of weak deterministic signals corrupted by purely-adative noise Is considered, which Is an important problem In statistical signal processing. Comparisons between the locally optimum and the locally optimum fuzzy tests are also made.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.987-1000
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• 2011

We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where $\tilde{\psi}$ is a randomized test in the static problem. Coherent risk measure is used as risk measure in the $L^{\infty}$ random variable spaces. The paper is written in expository style to some degree. We use an average risk of measure(AVaR), which is a special coherent risk measure, to see how to hedge the modified claim in a complete market model.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1991.10a
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• pp.107-110
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• 1991

When the noise has both additive and signal-dependent components, locally optimum detector test statistics are obtained for detection of weak composite signals using the generalized Neyman-Pearson lemma. In order to consider the non-additive noise as well as purely-additive noise, a generalized observation model is used in this paper. The locally optimum detector test statistics are derived for several different cases according to the relative strengths of the known signal component, the random signal component, and the signal-dependent noise component. Schematic diagrams of the locally optimum detector structures are also included.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.8C
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• pp.709-712
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• 2010

In this paper, the two sample locally optimum rank detector is obtained in the weakly dependent noise with non-zero temporal correlation between noise observations. The test statistic of the locally optimum rank detector is derived from the Neyman-Pearson lemma suitable for the two sample observation models, where it is assumed that reference observations are available in addition to regular observations. Two-sample locally optimum rank detecter shows the same performance with the one-sample locally optimum rank detector asymptotically. The structure of the two-sample rank detector is simpler than that of the one-sample rank detector because the sign statistic is not processed separately.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38B no.10
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• pp.832-842
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• 2013

Cognitive Radio has attracted intensive interests of the researchers, recently. The data rate always increases in the emerging technologies. The increased data rate poses mainly two challenges for spectrum sensing. One is that the state of primary user (PU) is fast and alternatively varying between "on/off" in a spectrum sensing window. The other is that the asynchronicity among the reports in a cooperative spectrum sensing setting becomes more apparent. Both of them would deteriorate the spectrum sensing performance. Thus, we propose an asynchronous cooperative spectrum sensing method to cope with these two challenges. A likelihood ratio test based spectrum sensing is developed for a single cooperator. The likelihood ratio is obtained in the setting of fast varying PU state. The likelihood ratio test is uniformly powerful according to the Neyman-pearson lemma. Furthermore, the asynchronicity among the cooperators are studied. Two sets of fusion weights are discussed for the asynchronous time among cooperators. One is designed based on the condition probability of the PU state variation and the other one is designed based on the queueing theory. The simulation results are provided with different fusion methods. The performance improvements are demonstrated.