• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.385-407
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• 2010

To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.

• Journal of the Korea Institute of Military Science and Technology
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• v.3 no.2
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• pp.140-148
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• 2000

This paper presents a fault detection and isolation(FDI) method based on Generalized Likelihood Ratio(GLR) test for the tightly coupled SDINS/CPS system. The GLR test is known to have the capability of detecting an assumed change while estimating its occurrence time and magnitude, and isolating the changing part. Once a fault is detected even if we don't know if the fault occurrs at either INS or GPS, multi-hypothesized GLR scheme performs the fault isolation between INS and GPS, and find which satellite malfunctions. However, in the INS faulty case, it turned out to fail to accomodate the fault isolation between accelerometer and gyroscope due to the coupling effects and a poor observability of the system. Hence, to isolate the INS fault, it needs to change the attitude of the vehicle resulting in enhancing the degree of observability.

• Journal of Korean Society for Quality Management
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• v.26 no.4
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• pp.79-87
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• 1998

This paper considers the problem of testing a one-sided hypothesis under the generalized sampling plan which is defined by a sequence of independent Bernoulli trials. A certain lexicographic order is defined for the boundary points of the sampling plan. It is shown that the family of probability mass function defined on the boundary points has monotone likelihood ratio, and that the test function is uniformly most powerful.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.297-307
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• 2006

Most methods for describing the relationship among random variables require specific probability distributions and some assumptions of random variables. The mutual information based on the entropy to measure the dependency among random variables does not need any specific assumptions. And the redundancy which is a analogous version of the mutual information was also proposed. In this paper, the redundancy and mutual information are explored to multi-dimensional categorical data. It is found that the redundancy for categorical data could be expressed as the function of the generalized likelihood ratio statistic under several kinds of independent log-linear models, so that the redundancy could also be used to analyze contingency tables. Whereas the generalized likelihood ratio statistic to test the goodness-of-fit of the log-linear models is sensitive to the sample size, the redundancy for categorical data does not depend on sample size but its cell probabilities itself.

• International Journal of Reliability and Applications
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• v.2 no.4
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• pp.263-268
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• 2001

Shanmugam(1991) generalized the Poisson distribution to capture a restriction on the incidence rate $\theta$ (i.e. $\theta$ ＜ $\beta$, an unknown upper limit), and named it incidence rate restricted Poisson (IRRP) distribution. Using Neyman's C($\alpha$) concept, Shanmugam then devised a hypothesis testing procedure for $\beta$ when $\theta$ remains unknown nuisance parameter. Shanmugam's C ($\alpha$) based .results involve inverse moments which are not easy tools, This article presents an alternate testing procedure based on likelihood ratio concept. It turns out that likelihood ratio test statistic offers more power than the C($\alpha$) test statistic. Numerical examples are included.

• Journal of Communications and Networks
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• v.14 no.5
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• pp.471-480
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• 2012

Reliable detection of primary user activity increases the opportunity to access temporarily unused bands and prevents harmful interference to the primary system. By extracting a global decision from local sensing results, cooperative sensing achieves high reliability against multipath fading. For the effective combining of sensing results, which is generalized by a likelihood ratio test, the fusion center should learn some parameters, such as the probabilities of primary transmission, false alarm, and detection at the local sensors. During the training period in supervised learning, the on/off log of primary transmission serves as the output label of decision statistics from the local sensor. In this paper, we extend unsupervised learning techniques with an expectation maximization algorithm for cooperative spectrum sensing, which does not require an external primary transmission log. Local sensors report binary hard decisions to the fusion center and adjust their operating points to enhance learning performance. Increasing the number of sensors, the joint-expectation step makes a confident classification on the primary transmission as in the supervised learning. Thereby, the proposed scheme provides accurate parameter estimates and a fast convergence rate even in low signal-to-noise ratio regimes, where the primary signal is dominated by the noise at the local sensors.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1661-1671
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• 2016

Risk analysis is a systematic study of uncertainties and risks we encounter in business, engineering, public policy, and many other areas. Value at Risk (VaR) is one of the most widely used risk measurements in risk management. In this paper, the Korean Composite Stock Price Index data has been utilized to model the VaR employing the classical ARMA (1,1)-GARCH (1,1) models with normal, t, generalized hyperbolic, and generalized pareto distributed errors. The aim of this paper is to compare the performance of each model in estimating the VaR. The performance of models were compared in terms of the number of VaR violations and Kupiec exceedance test. The GARCH-GPD likelihood ratio unconditional test statistic has been found to have the smallest value among the models.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.112-121
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• 1995

Let $p_1$ and $p_2$ be the proportions of two populations. To test the hypothesis $H_0 : p_1 = p_2$, we usually use the $x^2$ statistic, the large sample binomial statistic Z, and the Generalized Likelihood Ratio statistic-2log $\lambda$developed based on different mathematical rationale, respectively. Since testing the above hypothesis is equivalent to testing whether two populations follow the common Bernoulli distribution, one may also test the hypothesis by comparing 1 with the ratio of each density estimate and the hypothesized common density estimate, called comparison density, which was devised by Parzen(1988). We show that the above traditional test statistics ate actually estimating the measure of distance between the true densities and the common density under $H_0$ by representing them with the comparison density.

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.337-346
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• 2004

The Pearson chi-square goodness-of-fit test and the likelihood ratio tests are usually used for testing independence in two-way contingency tables under random sampling. But both of these tests may provide false results for the contingency table with clustered observations. In this case we consider the generalized linear mixed model which includes random effects of clustering in addition to the fixed effects of covariates. Both the heterogeneity between clusters and the dependency within a cluster can be explained via generalized linear mixed model. In this paper we introduce several types of generalized linear mixed model for testing independence in contingency tables with clustered observations. We also discuss the fitting of these models through a real dataset.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.11
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• pp.943-951
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• 2012

In this paper, we propose a novel spectrum sensing scheme based on the order statistic for cooperative cognitive radio network in non-Gaussian noise environments. Specifically, we model the ambient noise as the bivariate isotropic symmetric ${\alpha}$-stable random variable, and then, propose a cooperative spectrum sensing scheme based on the order of observations and the generalized likelihood ratio test. From numerical results, it is confirmed that the proposed scheme offers a substantial performance improvement over the conventional scheme in non-Gaussian noise environments.