• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.55-64
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• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.477-483
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• 2011

This article is concerned with a class of threshold-asymmetric GARCH models both for stationary case and for non-stationary case. We investigate large sample properties of estimators from QML(quasi-maximum likelihood) and QL(quasilikelihood) methods. Asymptotic distributions are derived and it is interesting to note for non-stationary case that both QML and QL give asymptotic normal distributions.

• Journal of the Korean Statistical Society
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• 제26권4호
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• pp.467-476
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• 1997

The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

• 대한수학회지
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• 제42권3호
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• pp.543-553
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• 2005

In this paper, we prove the existence of nonconstant bounded harmonic maps on a Cartan-Hadamard manifold of pinched negative curvature by solving the asymptotic Dirichlet problem. To be precise, given any continuous data f on the boundary at infinity with image within a ball in the normal range, we prove that there exists a unique harmonic map from the manifold into the ball with boundary value f.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.251-269
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• 1994

In this paper we extend Kim and Pollard's cube root asymptotics to other rates of convergence, to establish an asymptotic theory for a multidimensional mode estimator based on uniform kernel with shrinking bandwidths. We obtain rates of convergence depending on shrinking rates of bandwidth and non-normal limit distributions. Optimal decreasing rates of bandwidth are discussed.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.13-32
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• 1994

Let A(n) and B(n) be sequences of $m \times m$ random matrices with a joint asymptotic distribution as $n \to \infty$. The asymptotic distribution of the ordered roots of $$\mid$A(n) - f B(n)$\mid$ = 0$ depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.

• 응용통계연구
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• 제22권1호
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• pp.171-179
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• 2009

본 논문에서는 정규확률변수의 곱과 그의 합으로 표현되는 통계량의 분포에 대한 효과적인 근사법을 다루었다. 이차 형식에 대한 안장점근사에 기초한 이 방법은 기존의 정규근사에 비해 매우 정확한 결과를 제공한다. 또한 이에 대한 응용으로 FSK 통신에서 발생하는 문제를 제시하고, 그 해결책으로 본 논문에서 제안한 안장점근사법을 사용하였다. 모의실험을 통해 제안된 근사법이 중심영역은 물론, 통신이론에서 주요 관심 영역인, 극단 꼬리부분의 확률 근사에도 매우 유용한 방법임을 확인하였다.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.333-343
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• 2010

The asymptotic behavior of solutions of higher order differential equations with deviating argument $$(py^{(n-1)}(t))'\;+\;\sum\limits_{i=1}^{n-1}ci(t)y^{(i-1)}(t)\;=\;f\[t,\;y(t),\;y'(t),\;{\ldots},\;y^{(n-1)}(t),\;y(\phi(t)),\;y'(\phi(t)),\;{\ldots},\;y^{(n-1)}\;(\phi(t))\]\;\;\;\;(1)$$ $t\;{\in}\;[0,\;\infty)$ is studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1) have some asymptotic behavior.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.137-145
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• 2001

There are many situations in which the well-known tests such as log-rank test and Gehan-Wilcoxon test fail to detect the survival differences. Assuming large samples, these tests are developed asymptotically normal properties. Thus, they shall be called asymptotic tests in this paper, Several asymptotic tests sensitive to some specific types of survival differences have been recently proposed. This paper compares by simulations the test levels and the powers of the conventional asymptotic tests and their random permutation versions. Simulation studies show that the random permutation tests possess competitive powers compared to the corresponding asymptotic tests, keeping exact test levels even in the small sample case. It also provides the guidelines for choosing the valid and most powerful test under the given situation.