• Communications for Statistical Applications and Methods
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• 제10권3호
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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.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

• 한국컴퓨터정보학회논문지
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• 제19권8호
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• pp.27-34
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• 2014

이 논문에서는 hybrid projection 함수와 rank order 필터를 이용하여 눈동자를 검출하는 방법을 제안한다. 눈썹을 눈동자로 검출하는 오류를 줄이기 위하여, hybrid projection 함수를 이용하여 얼굴 영역에서 눈썹을 검출하고 눈썹이 포함되지 않도록 눈 영역을 설정한다. 눈 영역에서 rank order 필터를 사용하여 눈동자 후보점을 찾고 위치를 보정한다. 두 눈동자 후보점을 기하학적인 제약조건을 기반으로 쌍으로 묶고 각 쌍의 두 눈에 대한 유사도를 정합을 이용하여 측정하여가장작은값을 갖는 쌍을 최종눈동자로 결정한다. BioID 얼굴데이터베이스의 얼굴 영상 700개에 대한 실험 결과 92.4%의 검출율을 얻었으며 기존 방법보다 약 21.5% 개선된 결과를 얻었다.

• 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.

• 충청수학회지
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• 제27권4호
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• pp.553-562
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• 2014

In this paper we study of densities of the 4-rank of narrow ideal class groups of real quadratic function fields over the rational function field $\mathbb{F}_q(T)$ when $q{\equiv}3$ mod 4.

• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.791-802
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• 2020

We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.183-193
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• 2009

Pseudo-rank functions on Rickart *-rings are introduced and their properties are studied.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.425-437
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• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• 대한수학회논문집
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• 제31권3호
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• pp.585-590
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• 2016

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.