• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.29-37
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• 2001

In this paper, we consider the second order probability matching criterion for the ratio of the variance components under the one-way random effect model. It turns out that among all of the reference priors given in Ye(1994), the only one reference prior satisfies the second order matching criterion. Similar results are also obtained for the intraclass correlation as well.

• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.699-709
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• 2000

The constrained maximum likelihood estimation of the number of trials in several binomial populations under order restriction, such as simple order, is discussed. The estimation procedure is based on, so called, pool adjacent violators algorithm. Three handy estimators are given and their performances are compared using an artificial example.

• Journal of the Korean Statistical Society
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• 제26권4호
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• pp.521-530
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• 1997

The new Laplace autoregressive model of order 2-NLAR92) studied by Dewald and Lewis (1985) is extended to the p-th order model-NLAR(p). A necessary and sufficient condition for the existence of an innovation sequence and a stationary ergodic NLAR(p) model is obtained. It is shown that the distribution of the innovation sequence is given by the probabilistic mixture of independent Laplace distributions and a degenrate distribution.

• Journal of the Korean Statistical Society
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• 제7권2호
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• pp.109-119
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• 1978

When a response surface by a seconde order polynomial regression model, the stationary point is obtained by solving simultaneous linear equations. But the point is a function of random variables. We can find a confidence region for this point as Box and Hunter provided. However, the confidence region is often too large to be useful for the experiments, and it is necessary to augment additional design points in order to obtain a satisfactory confidence region for the stationary point. In this note, the author suggests a method how to augment design points "eficiently", and shows the change of the confidence region of the estimated stationary point in a response surface.e surface.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2002년도 봄 학술발표논문집 Vol.29 No.1 (B)
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• pp.289-291
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• 2002

Host of source separation methods focus on stationary sources so higher-order statistics is necessary In this paler we consider a problem of source separation when sources are second-order nonstationary stochastic processes . We employ the natural gradient method and develop learning algorithms for both 1inear feedback and feedforward neural networks. Thus our algorithms possess equivariant property Local stabi1iffy analysis shows that separating solutions are always locally stable stationary points of the proposed algorithms, regardless of probability distributions of

• 대한수학회보
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• 제58권6호
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• pp.1495-1506
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• 2021

The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

• 대한수학회보
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• 제59권1호
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• pp.203-212
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• 2022

A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order 12p³ for any prime number p.

• 응용통계연구
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• 제33권2호
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• pp.147-160
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• 2020

본 논문은 시계열 일반화 선형 모형의 하나인 계수형 시계열 모형에서 중요한 역할을 하는 과거 관측값과 조건부 평균값의 차수를 자동으로 결정하는 알고리즘을 연구한다. 본 알고리즘은 ARIMA 모형의 차수를 기반으로 시계열 일반화 선형 모형의 차수 후보군을 만들고, 차수 후보군의 조합을 이용하여 정보량 기준으로 최종 모형으로 선택한다. 제안된 알고리즘을 평가하기 위하여, 내재적 모형 및 내재적 시계열의 종류에 따른 시뮬레이션 및 실증 분석을 수행하고 예측력을 ARIMA 모형과 비교한다. 예측 성능 평가 결과, 계수형 시계열 분석에서 ARIMA 모형에 비해 시계열 일반화 선형 모형의 예측 성능이 우수함을 확인할 수 있다. 또한 실증분석으로서, 살인사건 발생 건수의 예측결과 ARIMA 모형보다 중기 및 장기 예측에서 우수한 성능을 나타내는 것을 확인할 수 있다.

• Wind and Structures
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• 제36권6호
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• pp.393-404
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• 2023

Skewness and kurtosis are important higher-order statistics for simulating non-Gaussian wind pressure series on low-rise buildings, but their predictions are less studied in comparison with those of the low order statistics as mean and rms. The distribution gradients of skewness and kurtosis on roofs are evidently higher than those of mean and rms, which increases their prediction difficulty. The conventional artificial neural networks (ANNs) used for predicting mean and rms show unsatisfactory accuracy in predicting skewness and kurtosis owing to the limited capacity of shallow learning of ANNs. In this work, the deep neural networks (DNNs) model with the ability of deep learning is introduced to predict the skewness and kurtosis on a low-rise building. For obtaining the optimal generalization of the DNNs model, the hyper parameters are automatically determined by Bayesian Optimization (BO). Moreover, for providing a benchmark for future studies on predicting higher order statistics, the data sets for training and testing the DNNs model are extracted from the internationally open NIST-UWO database, and the prediction errors of all taps are comprehensively quantified by various error metrices. The results show that the prediction accuracy in this study is apparently better than that in the literature, since the correlation coefficient between the predicted and experimental results is 0.99 and 0.75 in this paper and the literature respectively. In the untrained cornering wind direction, the distributions of skewness and kurtosis are well captured by DNNs on the whole building including the roof corner with strong non-normality, and the correlation coefficients between the predicted and experimental results are 0.99 and 0.95 for skewness and kurtosis respectively.