Bootstrap Method for k-Spatial Medians

Jhun, Myoung-Shic The Korean Statistical Society 1986 Journal of the Korean Statistical Society Vol.15 No.1

The k-medians clustering method is considered to partition observations into k clusters. Consistency and advantage of bootstrap confidence sets of k optimal cluster centers are discussed. The k-medians and k-means clustering methods are compared by using actual data sets.

On the Use of Adaptive Weights for the F_∞-Norm Support Vector Machine

Bang, Sung-Wan,Jhun, Myoung-Shic The Korean Statistical Society 2012 응용통계연구 Vol.25 No.5

When the input features are generated by factors in a classification problem, it is more meaningful to identify important factors, rather than individual features. The $F_{\infty}$-norm support vector machine(SVM) has been developed to perform automatic factor selection in classification. However, the $F_{\infty}$-norm SVM may suffer from estimation inefficiency and model selection inconsistency because it applies the same amount of shrinkage to each factor without assessing its relative importance. To overcome such a limitation, we propose the adaptive $F_{\infty}$-norm ($AF_{\infty}$-norm) SVM, which penalizes the empirical hinge loss by the sum of the adaptively weighted factor-wise $L_{\infty}$-norm penalty. The $AF_{\infty}$-norm SVM computes the weights by the 2-norm SVM estimator and can be formulated as a linear programming(LP) problem which is similar to the one of the $F_{\infty}$-norm SVM. The simulation studies show that the proposed $AF_{\infty}$-norm SVM improves upon the $F_{\infty}$-norm SVM in terms of classification accuracy and factor selection performance.

로버스트 회귀모형을 이용한 자료결합방법

전명식,정시송,박혜진,Jhun, Myoung-Shic,Jung, Ji-Song,Park, Hye-Jin 한국통계학회 2008 응용통계연구 Vol.21 No.6

Statistical matching techniques whose aim is to achieve a complete data file from different sources. Since the statistical matching method proposed by Rubin (1986) assumes the multivariate normality for data, using this method to data which violates the assumption would involve some problems. This research proposed the statistical matching method using robust regression as an alternative to the linear regression. Furthermore, we carried out a simulation study to compare the performance of the robust regression model and the linear regression model for the statistical matching. 서로 다른 출처로부터 얻어진 데이터 파일들을 하나의 데이터 파일로 만드는 통계적 자료결합방법은 공통변수와 서로 다른 고유변수를 포함하여 변수들 간에 존재하는 관련성에 대해 살펴볼 수 있다. Robin (1986)이 제안한 일반회귀모형의 예측값을 이용한 통계적 결합방법은 자료에 대한 다변량 정규성을 가정하기 때문에 이 가정을 위반하는 자료를 이용하는 것은 많은 문제를 수반한다. 본 연구는 제공파일의 고유변수에 모분포를 반영하지 못하는 특이점이 존재하는 경우, 일반회귀모형을 이용한 통계적 결합방법의 대안으로 로러스트 회귀추정방법을 이용한 자료결합방법을 제안하였다. 나아가 로버스트 회귀모형을 이용한 결합방법과 일반회귀모형을 이용한 결합방법에서의 상관관계 및 결정계수 보존에 관한 성능을 비교하기 위하여 모의실험을 수행하였다.

이변량 음이항 모형에서 붓스트랩 방법을 이용한 과대산포에 대한 검정

전명식,정병철,Jhun, Myoung-Shic,Jung, Byoung-Cheol 한국통계학회 2008 응용통계연구 Vol.21 No.2

본 연구에서는 이변량 음이항 분포에서 과대산포와 "내재적 상"의 존재유무에 대한 가설검정 문제를 다루었다. 과대산포에 대한 스코어 검정의 표준정규분포 근사는 명목 유의수준을 과소추정한 반면 "내재적 상"에 대한 스코어 검정은 명목유의수준을 과대 추정하고 있음을 보였다. 본 연구에서는 이와 같은 스코어 검정의 표준정규분포 근사의 문제점을 해결하기 위하여 붓스트랩 방법을 제안하였다. 스코어 검정에 대한 붓스트랩 방법은 두 검정에서 명목유의수준을 제대로 유지하고 검정력도 높게 나타나 스코어 검정의 표준정규분포 근사에 존재하는 문제를 해결하는 효율적인 대안으로 판단된다. The bootstrap method for the score test statistic is proposed in a bivariate negative binomial distribution. The Monte Carlo study shows that the score test for testing overdispersion underestimates the nominal significance level, while the score test for "intrinsic correlation" overestimates the nominal one. To overcome this problem, we propose a bootstrap method for the score test. We find that bootstrap methods keep the significance level close to the nominal significance level for testing the hypothesis. An empirical example is provided to illustrate the results.

Adaptive Nearest Neighbors를 활용한 판별분류방법

전명식,최인경,Jhun, Myoung-Shic,Choi, In-Kyung 한국통계학회 2009 응용통계연구 Vol.22 No.3

비모수적 판별분류방법으로 널리 사용되는 ${\kappa}$-Nearest Neighbors Classification(KNNC) 방법은 자료의 국소적 특징을 고려하지 않고 전체 자료에 대해 고정된 이웃의 개수 ${\kappa}$를 사용하여 개체를 분류하는 방법이다. 본 연구에서는 KNNC의 대안으로 자료의 국소적 특징을 고려하는 Adaptive Nearest Neighbors Classificaion(ANNC) 방법을 제안하였다. 제안된 방법의 특징을 규명하기 위하여 실제 자료에 대한 분석을 통하여 제안된 방법의 응용 가능성을 제시하였으며, 나아가 모의실험을 통하여 기존의 방법과의 효율성을 비교하였다. The ${\kappa}$-Nearest Neighbors Classification(KNNC) is a popular non-parametric classification method which assigns a fixed number ${\kappa}$ of neighbors to every observation without consideration of the local feature of the each observation. In this paper, we propose an Adaptive Nearest Neighbors Classification(ANNC) as an alternative to KNNC. The proposed ANNC method adapts the number of neighbors according to the local feature of the observation such as density of data. To verify characteristics of ANNC, we compare the number of misclassified observation with KNNC by Monte Carlo study and confirm the potential performance of ANNC method.

A Robust Approach of Regression-Based Statistical Matching for Continuous Data

Sohn, Soon-Cheol,Jhun, Myoung-Shic The Korean Statistical Society 2012 응용통계연구 Vol.25 No.2

Statistical matching is a methodology used to merge microdata from two (or more) files into a single matched file, the variants of which have been extensively studied. Among existing studies, we focused on Moriarity and Scheuren's (2001) method, which is a representative method of statistical matching for continuous data. We examined this method and proposed a revision to it by using a robust approach in the regression step of the procedure. We evaluated the efficiency of our revised method through simulation studies using both simulated and real data, which showed that the proposed method has distinct advantages over existing alternatives.

ESTIMATING THE SIMULTANEOUS CONFIDENCE LEVELS FOR THE DIFFERENCE OF PROPORTIONS FROM MULTIVARIATE BINOMIAL DISTRIBUTIONS

Jeong, Hyeong-Chul,Jhun, Myoung-Shic,Lee, Jae-Won The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.3

For the two groups data from multivariate binomial distribution, we consider a bootstrap approach to inferring the simultaneous confidence level and its standard error of a collection of the dependent confidence intervals for the difference of proportions with an experimentwise error rate at the a level are presented. The bootstrap method is used to estimate the simultaneous confidence probability for the difference of proportions.

A Robust Approach of Regression-Based Statistical Matching for Continuous Data

Soon Cheol Sohn,Myoung Shic Jhun 한국통계학회 2012 응용통계연구 Vol.25 No.2

Statistical matching is a methodology used to merge microdata from two (or more) files into a single matched file, the variants of which have been extensively studied. Among existing studies, we focused on Moriarity and Scheuren``s (2001) method, which is a representative method of statistical matching for continuous data. We examined this method and proposed a revision to it by using a robust approach in the regression step of the procedure. We evaluated the efficiency of our revised method through simulation studies using both simulated and real data, which showed that the proposed method has distinct advantages over existing alternatives.

κ-공간중위 군집방법을 활용한 층화방법

손순철,전명식,Son, Soon-Chul,Jhun, Myoung-Shic 한국통계학회 2009 응용통계연구 Vol.22 No.4

Stratification of population is widely used to improve the efficiency of the estimation in a sample survey. However, it causes several problems when there are some variables containing outliers. To overcome these problems, Park and Yun (2008) proposed a rather subjective method, which finds outliers before $\kappa$-means clustering for stratification. In this study, we propose the $\kappa$-spatial medians clustering method which is more robust than $\kappa$-means clustering method and also does not need the process of finding outliers in advance. We investigate the characteristics of the proposed method through a case study used in Park and Yun (2008) and confirm the efficiency of the proposed method. 표본조사에서 널리 쓰이는 모집단의 층화는 추정의 효율을 높이는 방법 중의 하나지만, 이상점을 포함하는 변수가 있는 경우에 여러 가지 문제점을 유발시킬 수 있다. 특히, 이상점이 존재하는 다변량 자료의 경우, 층화를 위한 $\kappa$-평균 군집방법은 이상점에 매우 민감하여 추정의 효율을 떨어뜨릴 수 있다. 본 연구에서는 이상점이 존재하는 다변량 자료의 층화를 위해 $\kappa$-평균 군집방법보다 강건하며 이상점을 따로 식별하는 과정이 배제된 $\kappa$-공간중위수 군집방법을 제안한다. 기존 관련연구인 박진우와 윤석훈 (2008)과 동일한 자료에 대한 사례분석을 통해 층화과정들을 비교, 검토하였으며 이들의 효율성을 추정량의 분산을 통해 비교하였다.

A Study for Obtaining Weights in Pairwise Comparison Matrix in AHP

Jeong, Hyeong-Chul,Lee, Jong-Chan,Jhun, Myoung-Shic 한국통계학회 2012 응용통계연구 Vol.25 No.3

In this study, we consider various methods to estimate the weights of a pairwise comparison matrix in the Analytic Hierarchy Process widely applied in various decision-making fields. This paper uses a data dependent simulation to evaluate the statistical accuracy, minimum violation and minimum norm of the obtaining weight methods from a reciprocal symmetric matrix. No method dominates others in all criteria. Least squares methods perform best in point of mean squared errors; however, the eigenvectors method has an advantage in the minimum norm.