Inverse Prediction Using Empirical Likelihood Ratio

홍창곤,정미영 한국자료분석학회 2006 Journal of the Korean Data Analysis Society Vol.8 No.5

The (interval) prediction of ratio-type quantity needs special technique called Fieller's method. In regression analysis the F statistic based inverse prediction works only if the normality assumption on the error terms is valid. Without the normality assumption, a nonparametric method which does not need the distributional assumption will be preferred. The nonparametric construction of confidence region using empirical likelihood ratio was developed by Owen(1991). In the inverse prediction problem, we suggest a new profile empirical likelihood ratio statistic, which is simpler than but as efficient as the Owen's. We prove an asymptotic theorem on the suggested statistic and check the efficiency via simulation.

On optimal number of lags in variogram estimation in spatial data analysis

홍창곤,김영화 한국자료분석학회 2004 Journal of the Korean Data Analysis Society Vol.6 No.1

In the analysis of spatial data, the 'variogram' plays an important role. Nonparametric estimator of the variogram is severely influenced by the number of lags, say , which plays the role of a smoothing parameter. This means that could cause a severe influence on both Least squares estimator and the kriging predictor. Therefore, it is very important to choose the proper value of but few theoretical studies have been done on the choice of . In applications, is now being quite subjectively chosen. In this paper we have shown that under infill asymptotics very small value (1 or 2) of gives best result even for very large number of sample size. The optimal order of under mixed-increasing domain asymptotics is also obtained. The data-driven choice of using cross-validation criterion is considered and the performance of this selection procedure is checked through simulation under several variogram models.

The Asymptotic Properties of Mean-centered Binned Kernel Density Estimator

홍창곤,윤미숙 한국자료분석학회 2009 Journal of the Korean Data Analysis Society Vol.11 No.4

With the massive data set the kernel density estimator has the deficiency of huge computation time. In this situation, the reduction of the computation time is of crucial interest and hence the development of the binned kernel estimator is required. The general framework for binning rule and the resulting binned kernel estimator have been studied by some authors. In this paper we deal with another kind of binning rule, mean-centered binning, which is not included in the general framework for binning. We investigate the asymptotic properties of the mean-centered binned kernel density estimator. We also do the simulation study for the comparison with simple binned kernel estimator.

Discrete Approximation to the Optimal Density in Moment Problems

Chang Kon Hong(홍창곤) 한국통계학회 1994 응용통계연구 Vol.7 No.2

본 논문에서는 주어진 n개의 적률을 갖는 최적의 확률 밀도 함수를 찾는 문제와 관련된 몇가지 근사 정리들을 제안하고 증명한다. 또한, 이 근사 정리들이 예를 통하여 수행될 것이다. In this paper we present some approximation theorems related to the problem of finding optimal densities with prescribed moments. The implementation of the approximation theorems is to be done in some examples.

Test Using Profile Empirical Likelihood Ratio with the Least Squares Estimator

이상진,홍창곤 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.1

In regression analysis the test and interval estimation using the F statistic works only if the normality assumption on the error terms is valid. Without the normality assumption, a nonparametric method which does not need the distributional assumption will be preferred. The nonparametric construction of confidence region using empirical likelihood ratio was developed by Owen (1991). Hong, Jung (2006) proposed a profile empirical likelihood ratio statistic, which is simpler than but as efficient as the Owen's. In this paper, we suggest a new test statistic using a profile empirical likelihood ratio for general testing problem in linear models and derive the asymptotic distribution of the statistic. We compare and the suggested statistic with the statistic in Hong, Jung (2006) via simulation study. The simulation results show that the new test statistic has higher rejection ratios than that of Hong, Jung (2006) and also show that the corresponding confidence intervals are narrower.

일반화 최소제곱추정량을 이용한 프로파일 경험적가능도비에 대한 연구

조영우,홍창곤 한국자료분석학회 2015 Journal of the Korean Data Analysis Society Vol.17 No.1

Empirical likelihood ratio method was suggested as a device for constructing nonparametric confidence regions for statistical functions by Owen (1988). Owen shows that it is also useful for nonparametric hypothesis testing. Hong, Jung (2006), Lee, Hong (2013) have studied a different method of constructing a profile empirical likelihood ratio using least squares estimators. They show that the suggested profile empirical likelihood ratios are easier to compute and as useful as Owen's. First, Hong, Jung (2006) suggests a profile empirical likelihood ratio instead using least squares estimator under null hypothesis. And Lee, Hong (2013) also suggests another profile empirical likelihood ratio using least squares estimator without restriction. In this paper, when variance-covariance matrix of the error term vector is a general positive-definite matrix we suggest a profile empirical likelihood ratio using generalized least squares estimator and study the property of the statistic. Via simulation study, we compare the performance of the suggested statistic and those of the existing statistics. The simulation also includes the problem of inverse prediction. Owen(1988)에 의하여 제안되고 연구된 경험적 가능도비는 통계적 함수에 대한 비모수적 신뢰구간의 구축이나 비모수적 가설검정에 아주 유용하게 사용된다. Hong, Jung(2006), Lee, Hong (2013)은 경험적 가능도비 대신 보다 간단히 계산하면서도 비슷한 정도의 유효성을 보이는 또 다른 경험적 가능도비에 대한 연구를 수행하여 왔다. 우선, 귀무가설 하에서의 최소제곱추정량을 이용한 프로파일 경험적 가능도비를 제안하고 그 성질에 대한 연구를 하였으며, 그 다음으로 아무 제약조건 없는 최소제곱추정량을 이용한 프로파일 경험적 가능도비에 대한 연구도 수행하였다. 본 논문에서는 일반적인 선형모형에서 오차항 벡터가 일반적인 분산-공분산 행렬을 가질 경우, 일반화 최소제곱추정량을 이용한 프로파일 경험적 가능도비를 제안하고, 그 성질에 대한 연구를 수행한다. 또한, 다양한 시뮬레이션 연구를 통하여 제안된 통계량과 기존의 통계량과의 비교연구를 수행하고자 한다. 시뮬레이션은, 등분산을 가지지 않는 자료를 생성한 다음 기존의 프로파일 경험적 가능도비와 새로 제안된 프로파일 경험적 가능도비에 이용해 계산되는 신뢰구간과 검정결과를 구하여 비교한다. 또한 역예측 문제에 대하여도 시뮬레이션 연구를 수행한다.

Robust Estimation in Generalized Linear Model Using Density Power Divergence

이상진,홍창곤 한국자료분석학회 2019 Journal of the Korean Data Analysis Society Vol.21 No.1

In parametric density estimation, the maximum likelihood estimator (MLE) is known to be asymptotically efficient but not robust with respect to both model misspecification and outliers. Basu et al. (1998) suggest a family of divergence measures called `density power divergences'. Each measure in this family depends on a single tuning parameter alpha, which controls the trade-off between the efficiency and the robustness of the estimators. The Kullback-Leibler divergence (Kullback, Leibler, 1951) and L_2-distance belong to this family. With a selected tuning parameter the density power divergence can be used a criterion for estimation. The minimizer of this divergence is called a minimum density power divergence estimator (MDPDE). In this paper, we will apply the power divergence idea to the regression data. We will generalize the definition of density power divergence for generalized linear model and derive the estimating criterion for the parameters. The resulting minimum density power divergence estimators (MDPDE) of the regression parameters are expected to be robust with respect to the outliers. The robustness of the MDPDE will be investigated via simulation study.

Accuracy of Mean-centered Binned Kernel Density Estimator as an Approximation to the Ordinary Kernel Estimator

윤미숙,홍창곤 한국자료분석학회 2011 Journal of the Korean Data Analysis Society Vol.13 No.4

When the data set is very large it takes huge computation time to obtain the kernel density estimator. In this case it is of crucial interest to reduce the computation time. One of the efficient way to achieve this goal is to use the binned kernel density estimator. Several binning rules and the resulting binned kernel estimator have been studied by some authors. In this paper we study, the accuracy of the mean-centered binned kernel estimator as a practical substitute for the original kernel density estimator. We investigate the asymptotic mean integrated squared difference between the mean-centered binned kernel density estimator and the original kernel estimator. We also do the simulation study for checking the accuracy.

The Asymptotic Properties of Automatically Selected Tuning Parameter in the Minimum Density Power Divergence Estimator

김재선,홍창곤 한국자료분석학회 2016 Journal of the Korean Data Analysis Society Vol.18 No.6

A family of density-based divergence measures called `density power divergences' was suggested by Basu et al. (1998). This is a family of measures indexed by single tuning parameter alpha. The tuning parameter controls the trade-off between robustness and asymptotic efficiency of the estimators. This family includes the Kullback-Leibler divergence (Kullback, Leibler, 1951) and L_2-distance. With a suitably chosen tuning parameter, a minimum density power divergence estimator (MDPDE) can be obtained. For 0<alpha<1, the estimator is in between MLE (efficient-but-nonrobust) and minimum L_2-distance estimator L_2E (robust-but- inefficient). Hong, Kim (2001) suggest a data-driven selection of this tuning parameter. They study the efficiency and the robustness of the MDPDE with this data-drivenly selected tuning parameter via simulation study. In this paper, we will study the asymptotic properties of MDPDE with the automatically selected tuning parameter alpha. The asymptotic optimality of the MDPDE with the automatically selected alpha for uncontaminated data will be also proved.

한국인 성인 남자에서 흡연이 신체구성 지표에 미치는 영향

이혜정,박소영,이상진,홍창곤 한국자료분석학회 2019 Journal of the Korean Data Analysis Society Vol.21 No.1

The aim of the study was to analyze the body composition and age parameters in relation to cigarette smoking. The study enrolled 308 healthy adult men working in H company in B city, South Korea. The first part of the study assessed body composition (weight, skeletal muscle mass, body fat mass, body mass index, basal metabolic rate) according to their smoking habits (smokers or non-smokers). The second part of the study analyzed body composition according to smoking habits in three groups of ages (20-49, 50-59, 60-69 years old). The body composition did not differ significantly between the groups of smokers and non-smokers. However, in men from 50 to 59 years old, weight and body fat mass of body composition were significantly lower than that of non-smokers. For from 50 to 59 year old men, smoking might have an effect on decreasing weight and body fat mass. The results suggest that smoking might be related to lipid metabolism, especially fifties. 흡연과 신체구성 지표와의 상관관계에 대한 연구는 다양한 측면에서 많은 연구가 선행되어 왔다. 그러나 그 상관관계의 분석은 여전히 많은 논란이 있다. 본 연구에서는 한국인 성인 남자에서 흡연이 신체구성 지표에 어떠한 영향을 주는지 분석하여, 그 분석 결과에 따른 의미를 해석해 보고자 하였다. 건강증진 프로그램에 참여한 20-69세 남자 308명을 대상으로 흡연 군과 비흡연 군으로 나누었으며, 연령대는 49세 이하, 50-59세, 60세 이상 세 군으로 분류하였다. 신체구성 지표는 체중, 골격근량, 체지방량, 체지방률, 체질량지수, 기초대사량을 측정하였다. 분석 결과, 전체 연령 군을 대상으로 실시한 흡연 군과 비흡연 군 간의 신체구성 지표에는 의미 있는 차이를 보이지 않았다. 연령대에 따라 나눈 세 군에서 신체구성 지표를 분석한 결과 49세 이하, 60세 이상 군에서는 흡연과 비흡연의 차이를 보이지 않았지만, 50-59세 연령대에서 체중과 체지방량이 흡연 군에서 의미 있게 감소하는 것을 관찰하였다. 이러한 결과는 다른 연령대보다 50대에서 흡연이 체중 및 체지방량에 중요한 요인으로 작용함을 시사한다. 성인병 발병률이 높아지는 50대에서 이러한 영향에 대한 심층 연구가 필요할 것으로 사료된다.