• Kyungpook Mathematical Journal
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• v.49 no.1
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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.

• Journal of the Korean Data and Information Science Society
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• v.24 no.2
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• pp.333-339
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• 2013

This paper discusses a method for getting a basis set of estimable functions of less than full rank linear model. Since model parameters are not estimable estimable functions should be identified for making inferences proper about them. So, it suggests a method of using full rank factorization of model matrix to find estimable functions in easy way. Although they might be obtained in many different ways of using model matrix, the suggested full rank factorization technique could be one of much easier methods. It also discusses how to use projection matrix to identify estimable functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.517-523
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• 2002

The closed from of sums and weighted sums of the score functions of the locally optimum rank detectors are obtained in this paper. When we consider the asymptotic performance characteristics of a detector based on rank and sign statistics, the sums and weighted sums of the score functions have to be prepared. The efficacy of a detector can be obtained from the sums and weighted sums of the score functions. Score functions based on rank statistics, as well as those based on magnitude rank and sign statistics, have also been considered, which includes most score functions presented in the literature.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.837-842
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• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.223-241
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• 2005

Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.12
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• pp.4604-4623
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• 2014

Authentication mechanisms coupled with strong encryption techniques are used for network security purposes; however, given sufficient time, well-equipped intruders are successful for compromising system security. The authentication protocols often fail when they are analysed critically. Formal approaches have emerged to analyse protocol failures. In this study, Communicating Sequential Processes (CSP) which is an abstract language designed especially for the description of communication patterns is employed. Rank functions are also used for verification and analysis which are helpful to establish that some critical information is not available to the intruder. In order to establish this, by assigning a value or rank to each critical information, it is shown that all the critical information that can be generated within the network have a particular characterizing property. This paper presents an application of rank functions approach to an authentication protocol that combines delaying the decryption process with timed authentication while keys are dynamically renewed under pseudo-secure situations. The analysis and verification of authentication properties and results are presented and discussed.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.183-193
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• 1999

In the problem of estimating estimable functions in classification linear models, we propose a method of obtaining least squares estimators of estimable functions. This method is based on the hierarchical Bayesian approach for estimating a vector of unknown parameters. Also, we verify that estimators obtained by our method are identical to least squares estimators of estimable functions obtained by using either generalized inverses or full rank reparametrization of the models. Some examples are given which illustrate our results.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.41-54
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• 2015

In this article, we propose nonconcave penalties on a reduced-rank regression model to select variables and estimate coefficients simultaneously. We apply HARD (hard thresholding) and SCAD (smoothly clipped absolute deviation) symmetric penalty functions with singularities at the origin, and bounded by a constant to reduce bias. In our simulation study and real data analysis, the new method is compared with an existing variable selection method using $L_1$ penalty that exhibits competitive performance in prediction and variable selection. Instead of using only one type of penalty function, we use two or three penalty functions simultaneously and take advantages of various types of penalty functions together to select relevant predictors and estimation to improve the overall performance of model fitting.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.279-293
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• 2000

This article suggests two change-point estimators which are modifications of Carlstein(1988) change-point estimators with rank functions and mean functions where there is one change-point in a mean function. A comparison study of Carlstein(1988) estimators and proposed estimators is done by simulation on the mean, the MSE, and the proportion of matching true change-point.