• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.291-303
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• 2003

This work is proposed an alternative identification method of outlying cell which is one of important issues in categorical data analysis. One finds that there is a strong relationship between the location of an outlying cell and the corresponding parameter estimates of the well-fitted log-linear model. Among parameters of log-linear model, an outlying cell is affected by interaction terms rather than main effect terms. Hence one could identify an outlying cell by investigating of parameter estimates in an appropriate log-linear model.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.487-496
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• 1996

Let f(z) be an entire function. Then the order $\rho(f)$ of f is defined by $$ \rho(f) = \overline{lim}_r\to\infty \frac{log r}{log^+ T(r,f)} = \overline{lim}_r\to\infty \frac{log r}{log^+ log^+ M(r,f)}, $$ where T(r,f) is the Nevanlinna characteristic of f (see [4]), $M(r,f) = max_{$\mid$z$\mid$=r} $\mid$f(z)$\mid$$ and $log^+ t = max(log t, 0)$.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.293-307
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• 2024

In this paper, we give a general method to compute the linear independence measure of 1, log(1 - 1/r), log(1 + 1/s) for infinitely many integers r and s. We also give improvements for the special cases when r = s, for example, ν(1, log 3/4, log 5/4) ≤ 9.197.

• East Asian mathematical journal
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• v.26 no.1
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• pp.9-23
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• 2010

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.1-11
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• 2012

We present methods to study the log-density ratio of the conditional densities of the predictors given the response variable in the logistic regression model. This allows us to select which predictors are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. A simulation study shows that the linear and log terms are required in general. If the conditional distributions of xjy for the two groups overlap significantly, we need both the linear and log terms; however, only the linear or log term is needed in the model if they are well separated.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.242-251
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• 2004

Several statistical methods are introduced 1=o analyze the accelerated failure time data. Most frequently used method is the log-linear approach with parametric assumption. Since the accelerated failure time experiments are exposed to many environmental restrictions, parametric log-linear relationship might not be working properly to analyze the resulting data. The models proposed by Buckley and James(1979) and Stute(1993) could be useful in the situation where parametric log-linear method could not be applicable. Those methods are introduced in accelerated experimental situation under the thermal acceleration and discussed through an illustrated example.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.357-366
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• 1999

Let us assume that two different log-linear models are selected by various model selection methods. When these are non-hierarchical it is not easy to choose one of these models. In this paper the well-known Cox's statistic is applied to compare these non-hierarchical log-linear models. Since it is impossible to obtain the analytic solution about the problem we proposed a alternative method by extending Pesaran and pesaran's (1993) simulation approach. We find that the values of proposed test statistic and the estimates are very much stable with some empirical results.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.519-527
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• 2004

Relationship between the partial likelihood ratio statistics for logisitic models and the partial goodness-of-fit statistics for corresponding log-linear models is discussed. This paper shows how definitions of suppression in logistic model can be adapted for log-linear model and how they are related to confounding in terms of collapsibility for categorical data. Several $2{times}2{times}2$ contingency tables are illustrated.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.755-764
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• 2006

Most graphical methods for categorical data can describe the structure of data and represent a measure of association among categorical variables. Among them the polyhedron plot represents sequential relationships among hierarchical log-linear models for a multidimensional contingency table. This kind of plot could be explored to describe the differences among sequential models. In this paper we suggest graphical methods, containing all the information, that reflect the relationship among all log-linear models in a certain hierarchical structure. We use the ideas of a correlation diagram.

• East Asian mathematical journal
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• v.29 no.3
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• pp.279-292
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• 2013

It is well known that each kernel function defines a primal-dual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has ${\mathcal{O}}((log\;p){\sqrt{n}}\;log\;n\;log\;{\frac{n}{\epsilon}})$ and ${\mathcal{O}}((q\;log\;p)^{\frac{3}{2}}{\sqrt{n}}\;log\;{\frac{n}{\epsilon}})$ iteration bound for large- and small-update methods, respectively. These are currently the best known complexity results.