• Korean Journal of Optics and Photonics
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• v.13 no.6
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• pp.537-542
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• 2002

Null tests using two different kinds of null corrector have been discussed. A parabolic mirror was used as a surface under test. After designing, encoding, and fabricating the CGH (computer generated hologram), the null CGH test was performed. An autocollimation test was also performed using a flat mirror. The reliability of the null CGH test has been discussed by comparing the result obtained by both null tests.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.483-497
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• 2001

When one fits a parametric density function to a data set, it is usually advisable to test the goodness of the postulated model. In this paper we study the nonparametric tests for testing the null hypothesis against general alternatives, when the null hypothesis specifies the density function up to unknown parameters. We modify the test statistic which was proposed by the first author and his colleagues. Asymptotic distribution of the modified statistic is derived and its performance is compared with some other tests through simulation.

• Korean Journal of Optics and Photonics
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• v.12 no.5
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• pp.352-355
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• 2001

A null lens is designed for testing the hyperbolic mirror which is the first mirror of the off-axis three mirror anastigmat(TMA) designed as a high resolution camera for remote sensing. To choose a better null lens system for the hyperbolic surface under test, both autostigmatic and mixed type null lenses are designed and analysed for sensitivity with respect to change of each surface parameter such as the radius of curvature and the thickness.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1059-1072
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• 2009

In the analysis of microarray data with a small number of arrays, the most important task is the detection of differentially expressed genes by a significance test. For this purpose, one needs to construct a null distribution based on a large number of genes and one of the best way for constructing the null distribution for a small number of arrays is by means of permutation methods. In this paper we propose simple test statistics and permutation methods that are appropriate in constructing the null distribution. In a simulation study, we compare the null distributions generated by the proposed test statistics and permutation methods with the previous ones. With an example microarray data, differentially expressed genes are determined by applying these methods.

• Proceedings of the Optical Society of Korea Conference
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• 2003.07a
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• pp.150-151
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• 2003

비구면은 점광원에서 출발한 광이 측정면에서 반사한 후 다시 한 점으로 모이지 않아 일반적인 간섭계로 측정하는데 어려움이 있다. 이 때 비구면이 만들어내는 파면과 반대되는 파면을 생성하는 null compensator를 설치하여 null test를 수행할 수 있다. CGH는 렌즈나 거울과 같은 기계적인 가공을 하지 않고, 이론상 수식적으로 표현이 가능한 모든 파면을 만들 수 있으므로 많이 사용되어 왔다. (중략)

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.787-793
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• 1997

It is well known that the assumption of independence is ofter not valid for real data. This phenomenon has been observed empirically by many prominent scientists. In this article the sensitivity of dependence on Bayes test of a sharp null hypothesis is considered. The robustness is considered with respect to the significant level and the prior probability on the null hypothesis.

• Journal of Korean Society for Quality Management
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• v.30 no.3
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• pp.195-202
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• 2002

The problem of trend change in the mean residual life is great Interest in the reliability and survival analysis. In this paper, a new test statistic for testing whether or not the mean residual life changes its trend Is developed. It is assumed that neither the change point nor the proportion at which the trend change occurs is known. The asymptotic null distribution of test statistic is established and asymptotic critical values of the asymptotic null distribution is obtained. Monte Carlo simulation is used to compare the proposed test with previously known tests.

• Journal of Korean Society for Quality Management
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• v.30 no.4
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• pp.78-85
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• 2002

The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, a new test statistic for testing whether or not the mean residual life changes its trend is developed. It is assumed that neither the change point nor the proportion at which the trend change occurs is known. The asymptotic null distribution of test statistic is established and asymptotic critical values of the asymptotic null distribution is obtained. Monte Carlo simulation is used to compare the proposed test with previously known tests.