• Communications for Statistical Applications and Methods
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• 제5권3호
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• pp.591-597
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• 1998

We prove (at least empirically) that some forms of the scaled residuals calculated from i.i.d. multivariate normal random vectors are ancillary. We further show that, if the scaled residuals are ancillary, then they have the same distribution whatever form of rotation is rosed to remove sample correlations.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.385-392
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• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.361-375
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• 2015

A measure of skewness and kurtosis is proposed to test multivariate normality. It is based on an empirical standardization using the scaled residuals of the observations. First, we consider the statistics that take the skewness or the kurtosis for each coordinate of the scaled residuals. The null distributions of the statistics converge very slowly to the asymptotic distributions; therefore, we apply a transformation of the skewness or the kurtosis to univariate normality for each coordinate. Size and power are investigated through simulation; consequently, the null distributions of the statistics from the transformed ones are quite well approximated to asymptotic distributions. A simulation study also shows that the combined statistics of skewness and kurtosis have moderate sensitivity of all alternatives under study, and they might be candidates for an omnibus test.

• Communications for Statistical Applications and Methods
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• 제30권4호
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• pp.423-435
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• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Journal of Gastric Cancer
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• 제15권4호
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• pp.238-245
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• 2015

Purpose: This study aimed to identify time-dependent prognostic factors and demonstrate the time-dependent effects of important prognostic factors in patients with advanced gastric cancer (AGC). Materials and Methods: We retrospectively evaluated 3,653 patients with AGC who underwent curative standard gastrectomy between 1991 and 2005 at the Korea Cancer Center Hospital. Multivariate survival analysis with Cox proportional hazards regression was used in the analysis. A non-proportionality test based on the Schoenfeld residuals (also known as partial residuals) was performed, and scaled Schoenfeld residuals were plotted over time for each covariate. Results: The multivariate analysis revealed that sex, depth of invasion, metastatic lymph node (LN) ratio, tumor size, and chemotherapy were time-dependent covariates violating the proportional hazards assumption. The prognostic effects (i.e., log of hazard ratio [LHR]) of the time-dependent covariates changed over time during follow-up, and the effects generally diminished with low slope (e.g., depth of invasion and tumor size), with gentle slope (e.g., metastatic LN ratio), or with steep slope (e.g., chemotherapy). Meanwhile, the LHR functions of some covariates (e.g., sex) crossed the zero reference line from positive (i.e., bad prognosis) to negative (i.e., good prognosis). Conclusions: The time-dependent effects of the prognostic factors of AGC are clearly demonstrated in this study. We can suggest that time-dependent effects are not an uncommon phenomenon among prognostic factors of AGC.

• 한국정보통신학회논문지
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• 제4권3호
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• pp.697-703
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• 2000

임팩트이온화현상은 소자의 크기가 점점 작아지면서, 높은 에너지에 있는 hot carrier 전송 을 해석하기 위해 매우 중요하므로 소자의 시뮬레이션에 정확한 임팩트이온화모델이 필수적이다. 털 연구에서는 의사포텐셜방법을 사용하여 풀밴드모델을 구하고, 임팩트이온화율은 수정된 Keldysh 공식을 이용하여 유도하였다. 본 연구에서는 Gahs 임팩트이은화의 온도의존특성을 조사하기 위하여 Monte Carlo 시뮬레이터를 제작하여 임팩트이온화계수를 구하였다. 결과적으로, 임팩트이온화계수는 300K에서 실험값과 잘 일치하였다. 또한 에너지는 전계가 증가할수록 증가하고, 높은 온도에서는 포논 산란의 emission mode가 높기 때문에 에너지가 감소함을 알 수 있었다. 임팩트이온화의 대수 fitting 함수 식은 온도와 전계에 대해 2차식으로 표현하였다. 대수 fitting 함수의 오차는 대부분 5%이내에 머물렀다. 그러므로 대수식으로 표현된 임팩트 이온화계수는 온도에 의존함을 알았고, 임팩트이온화계수를 구하는데 시간을 절약할 수 있다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2000년도 춘계종합학술대회
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• pp.460-464
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• 2000

임팩트이온화현상은 소자의 크기가 점점 작아지면서, 높은 에너지에 있는 hot carrier 전송을 해석하기 위해 매우 중요하므로 소자의 시뮬레이션에 정확한 임팩트이온화모델이 필수적이다. 본 연구에서는 의사포텐셜방법을 사용하여 full 밴드모델을 구하고, 임팩트이온화율은 수정된 Keldysh 공식을 이용하여 유도하였다. 본 연구에서는 GaAs 임팩트이온화의 온도와 전계에 대한 의존특성을 조사하기 위하여 Monte Carlo 시뮬레이터를 제작하여 임팩트이온화계수를 구하였다. 결과적으로, 임팩트이온화계수는 300K에서 실험 값과 잘 일치하였다. 또한 에너지는 전계가 증가할수륵 증가하고, 높은 온도에서는 포논산란의 emission mode가 높기 때문에 에너지가 감소함을 알 수 있었다. 임팩트 이온화의 대수 fitting 함수 식은 온도와 전계에 대해 2차 식으로 표현하였다. 대수 fitting 함수의 오차는 대부분 5%이내에 머물렀다. 그러므로 대수 식으로 표현된 임팩트이온화계수는 온도와 전계에 의존함을 알았고, 온도와 전계에 의존하는 임팩트이온화계수를 구하는데 시간을 절약할 수 있다