• 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.

• 한국컴퓨터정보학회논문지
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• 제10권6호
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• pp.17-26
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• 2005

본 논문에서는 통계학의 선형순위통계량(linear rank statistics)에 기초한 3가지 비모수 검정법 즉. Wilcoxon 검정법, Median 검정법 그리고 Van der Waerden 검정법을 이용하여 에지를 검출하고자 한다. 5$\times$5 윈도우상에서 중심픽셀의 에지여부는 에지-높이 모수(edge-height parameter)를 사용한 모형 하에서 두 영역간의 유의한 차이가 있는지를 검정함으로서 결정한다. 영상실험에서 통계적 방법들 간의 에지검출 성능은 에지맵(edge map)을 통한 정성적인 비교와 객관적인 척도 하에서 정량적인 비교를 통하여 분석하였다.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.319-332
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• 1997

The application of multivariate linear rank statistics to data with item nonresponse is considered. Only a modest extension of the complete data techniques is required when the missing data may be thought of as a random sample, and an appropriate modification of the covariances is derived. A proof of the asymptotic multivariate normality is given. A review of some related results in the literature is presented and applications including longitudinal and repeated measures designs are discussed.

• 품질경영학회지
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• 제21권1호
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• pp.136-143
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• 1993

Tests associated with the linear signed rank statistics are considered for testing the symmetry of a continuous distribution about an unknown median. The results of Monte Carlo study show that the proposed tests are reasonably good in level control and powers.

• 응용통계연구
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• 제24권1호
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• pp.137-143
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• 2011

The classification of subjects with unknown distribution in a small sample size often involves order-restricted constraints in multivariate parameter setups. Those problems make the optimality of a conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Multivariate linear rank statistics along with that principle, yield a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in a small sample. Applications of this method are illustrated in a real microarray data example (Lobenhofer et al., 2002).

• 대한수학회지
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• 제54권4호
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• pp.1317-1329
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• 2017

A Boolean rank one matrix can be factored as $\text{uv}^t$ for vectors u and v of appropriate orders. The perimeter of this Boolean rank one matrix is the number of nonzero entries in u plus the number of nonzero entries in v. A Boolean matrix of Boolean rank k is the sum of k Boolean rank one matrices, a rank one decomposition. The perimeter of a Boolean matrix A of Boolean rank k is the minimum over all Boolean rank one decompositions of A of the sums of perimeters of the Boolean rank one matrices. The arctic rank of a Boolean matrix is one half the perimeter. In this article we characterize the linear operators that preserve the symmetric arctic rank of symmetric Boolean matrices.

• 대한수학회지
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• 제41권2호
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• pp.397-406
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• 2004

For a Boolean rank-l matrix $A\;=\;ab^{t}$, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-l matrices.

• 대한수학회지
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• 제52권3호
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• pp.625-636
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• 2015

The Boolean rank of a nonzero $m{\times}n$ Boolean matrix A is the least integer k such that there are an $m{\times}k$ Boolean matrix B and a $k{\times}n$ Boolean matrix C with A = BC. We investigate the structure of linear transformations T : $\mathbb{M}_{m,n}{\rightarrow}\mathbb{M}_{p,q}$ which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, $2{\leq}k{\leq}$ min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.

• 대한수학회지
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• 제51권1호
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.