• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.203-212
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under two non-normal distributions.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under a non-normal distribution.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.182-184
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• 2005

In this study, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. A simulation study is conducted to study the accuracy, in finite samples, of the limiting distribution of the test statistic under spherical symmetry. The power of our test is compared with those of other tests for spherical symmetry in various alternative distributions via simulation.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.99-113
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• 2005

In this article, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. The limiting distribution of the test statistic is derived under spherical symmetry and its accuracy, in finite samples, is studied via simulation. Also, a simulation study is conducted in which the power of our test is compared with those of other tests for spherical symmetry in various alternative distributions. Finally, an illustrative example of application to a real data is provided.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.81-90
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• 2002

The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.117-133
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• 2019

In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.217-234
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• 2018

Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.

• Radiation Oncology Journal
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• v.19 no.1
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• pp.21-26
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• 2001

Purpose : This study was peformed to evaluate the cosmetic outcome of conservative treatment for early breast cancer and to analyze the factors influencing cosmetic outcome. Materials and Methods : From February 1992 through January 1997, 120 patients with early breast cancer were treated with conservative surgery and postoperative radiotherapy. The types of conservative surgery were quadrantectomy and axillary node dissection for 108 patients $(90\%)$ and lumpectomy or excisional biopsy for 10 patients $(8.3\%)$. Forty six patients $(38\%)$ received adjuvant chemotherapy (CMF or CAF). Cosmetic result evaluation was carried out between 16 and 74 months (median, 33 months) after surgery. The cosmetic results were classified into four categories, i.e., excellent, good, fair, and poor. The appearances of the patients' breasts were also analyzed for symmetry using the differences in distances from the sternal notch to right and left nipples. A logistic regression analysis was performed to identify independent variables influencing the cosmetic outcome. Results : Cosmetic score was excellent or good in $76\%$ (91/120), fair in $19\%$ (23/120) and poor in $5\%$ (6/120) of the patients. Univariate analysis showed that tumor size (T1 versus T2) (p=0.04), axillary node status (N0 versus N1) (p=0.0002), extent of surgery (quadrantectomy versus lumpectomy or excisional biopsy) (p=0.02), axillary node irradiation (p=0.0005) and chemotherapy (p=0.0001) affected cosmetic score. Multivariate analysis revealed that extent of surgery (p=0.04) and chemotherapy (p=0.0002) were significant factors. For breast symmetry, univariate analysis confirmed exactly the same factors as above. Multivariate analysis revealed that tumor size (p=0.003) and lymph node status (p=0.007) affected breast symmetry. Conclusion : Conservative surgery and postoperative radiotherapy resulted in excellent or good cosmetic outcome in a large portion of the patients. Better cosmetic results were achieved generally in the group of patients with smaller tumor size, without axillary node metastasis and treated with less extensive surgery without chemotherapy.