• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1089-1099
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• 2012

We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.393-406
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• 2020

We analyze a posteriori error estimator for the conforming P2 finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming P1 finite element proposed in [4]. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.107-117
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• 1989

A stronger result than that of Park and Marron (1994) is proved here on the asymptotic distribution of the plug-in bandwidth selector. The new result is that the plug-in bandwidth selector may have the rate of convergence ($n^{-4/13}$ with less smoothness conditions on the unknown density functions than as described in Park and Marron's paper. Together with this, a class of various plug-in bandwidth selectors are considered and their asymptotic distributions are given. Finally, some ideas of possible improvements on those plug-in bandwidth selectors are provided.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.193-205
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• 1999

An approximate Bayes criterion for Behrens-Fisher problem (testing equality of means of two normal populations with unequal variances) is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approachintroduced by Spiegelhalter and Smith (1982). The proposed criterion is designed to develop a Bayesian test criterion having a closed form, so that it provides an alternative test to those based upon asymptotic sampling theory (such as Welch's t test). For the suggested Bayes criterion, numerical study gives comparisons with a couple of asymptotic classical test criteria.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.111-117
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• 1997

The ordinary least squares estimator $S^2$ for the variance of the disturbances is considered in the linear regression model with sutocorrelated disturbances. It is proved that the OLS-estimator of disturbance variance is asymptotically unbiased and weakly consistent, when the distrubances are generated by an MA(q) process. In particular, the asymptotic unbiasedness and consistency of $S^2$ is satisfied without any restriction on the regressor matrix.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1007-1015
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• 2003

In this paper we introduced a new score generating function for the rank dispersion function in a general linear model. Based on the new score function, we derived the null asymptotic theory of the rank-based hypothesis testing in a linear model. In essence we showed that several rank test statistics, which are primarily focused on our new score generating function and new dispersion function, are mainly distribution free and asymptotically converges to a chi-square distribution.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.49-58
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• 2004

In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.123-133
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• 2015

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

• Journal of the Korean Data and Information Science Society
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• v.6 no.2
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• pp.65-76
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• 1995

The importance of left truncated and right censoring cases has considered for better information in medical follow-up and engineering life testing studies. We propose some estimation procedure for the mean residual life function with consistency and asymptotic normality on the left truncated and right censoring model. And then, the comparision with Kaplan-Meier estimator ignoring the left truncated effect and the small sample properities are investigated by asymptotic biases and M.S.E.'s thresh Monte Carlo study.