• 응용통계연구
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• 제23권4호
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• pp.759-765
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• 2010

In this paper, two new inverse regression methods are introduced. One is a distance based method, and the other is a likelihood based method. While a model is fitted by minimizing the sum of squared prediction errors of y's and x's in the classical and inverse methods, respectively. In the new distance based method, we simultaneously minimize the sum of both squared prediction errors. In the likelihood based method, we propose an inverse regression with Arnold-Beaver Skew Normal(ABSN) error distribution. Using the cross validation method with an asymmetric real data set, two new and two existing methods are studied based on the relative prediction bias(RBP) criteria.

• 응용통계연구
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• 제34권6호
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• pp.957-968
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• 2021

역중도절단확률가중(inverse censoring probability weighting, ICPW)은 생존분석에서 흔히 사용되는 방법이다. 중도절단 회귀모형과 같은 ICPW 방법의 응용에 있어서 중도절단 확률의 정확한 추정은 핵심적인 요소라고 할 수 있다. 본 논문에서는 중도절단 확률의 추정이 ICPW 기반 중도절단 회귀모형의 성능에 어떠한 영향을 주는지 모의실험을 통하여 알아보았다. 모의실험에서는 Kaplan-Meier 추정량, Cox 비례위험(proportional hazard) 모형 추정량, 그리고 국소 Kaplan-Meier 추정량 세 가지를 비교하였다. 국소 KM 추정량에 대해서는 차원의 저주를 피하기 위해 공변량의 차원축소 방법을 추가적으로 적용하였다. 차원축소 방법으로는 흔히 사용되는 주성분분석(principal component analysis, PCA)과 절단역회귀(sliced inverse regression)방법을 고려하였다. 그 결과 Cox 비례위험 추정량이 평균 및 중위수 중도절단 회귀모형 모두에서 중도절단 확률을 추정하는 데 가장 좋은 성능을 보여주었다.

• Communications for Statistical Applications and Methods
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• 제24권1호
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• pp.97-113
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• 2017

This paper proposes a method for sufficient dimension reduction (SDR) of mixture data. We consider mixture data containing more than one component that have distinct central subspaces. We adopt an approach of a model-based sliced inverse regression (MSIR) to the mixture data in a simple and intuitive manner. We employed mixture probabilistic principal component analysis (MPPCA) to estimate each central subspaces and cluster the data points. The results from simulation studies and a real data set show that our method is satisfactory to catch appropriate central spaces and is also robust regardless of the number of slices chosen. Discussions about root selection, estimation accuracy, and classification with initial value issues of MPPCA and its related simulation results are also provided.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권10호
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• pp.3482-3497
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• 2021

Artificial intelligence has emerged as the core of the 4th industrial revolution, and large amounts of data processing, such as big data technology and rapid data analysis, are inevitable. The most fundamental and universal data interpretation technique is an analysis of information through regression, which is also the basis of machine learning. Ridge regression is a technique of regression that decreases sensitivity to unique or outlier information. The time-consuming calculation portion of the matrix computation, however, basically includes the introduction of an inverse matrix. As the size of the matrix expands, the matrix solution method becomes a major challenge. In this paper, a new algorithm is introduced to enhance the speed of ridge regression estimator calculation through series expansion and computation recycle without adopting an inverse matrix in the calculation process or other factorization methods. In addition, the performances of the proposed algorithm and the existing algorithm were compared according to the matrix size. Overall, excellent speed-up of the proposed algorithm with good accuracy was demonstrated.

• 응용통계연구
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• 제18권2호
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• pp.381-393
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• 2005

회귀모형에서 필요한 설명변수들의 선형결합들을 탐색하기 위한 방법 중의 하나로 분할역회귀모형을 들 수 있다. 이러한 분할역회귀모형에서 모형에 필요한 설명변수들의 선형결합의 수, 즉 차원을 결정하기 위한 여러 가지의 검정법들이 소개 되었으나 설명변수들의 정규성 가정을 필요로 하거나 다른 제약이 있다. 본 논문에서는 주성분분석에 대한 확률모형을 이 용하여 정규성가정을 필요로하지 않으며 분할의 수에 로버스트한 검정법을 소개하고 모의실험과 실제자료에 대한 적용결과를 통하여 기존의 검정법과 비교하였다.

• Geomechanics and Engineering
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• 제16권6호
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• pp.577-588
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• 2018

A major concern in deep excavation project in soft clay deposits is the potential for adjacent buildings to be damaged as a result of the associated excessive ground movements. In order to accurately determine the wall deflections using a numerical procedure such as the finite element method, it is critical to use the correct soil parameters such as the stiffness/strength properties. This can be carried out by performing an inverse analysis using the measured wall deflections. This paper firstly presents the results of extensive plane strain finite element analyses of braced diaphragm walls to examine the influence of various parameters such as the excavation geometry, soil properties and wall stiffness on the wall deflections. Based on these results, a multivariate adaptive regression splines (MARS) model was developed for inverse parameter identification of the soil relative stiffness ratio. A second MARS model was also developed for inverse parameter estimation of the wall system stiffness, to enable designers to determine the appropriate wall size during the preliminary design phase. Soil relative stiffness ratios and system stiffness values derived via these two different MARS models were found to compare favourably with a number of field and published records.

• Archives of Pharmacal Research
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• 제11권2호
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• pp.99-113
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• 1988

Quantitation of ethenzamide, isopropylantipyrine and caffeine takes about 41 hrs by conventional GC method. Quantitation of allylisoprorylacetylurea takes about 40 hrs by conventional UV method. But quantitation of them takes about 6 hrs by DRIFT developing method. Each standard and sample sieved, powdered and acquired DRIFT spectrum. Out of them peak of each component was selected and ratio of each peak to standard peak was acquired, and then linear stepwise multiple regression was performed with these data and concentration. Reflectance value, Kubelka-Munk equation and Inverse-Kubelka-Munk equation were modified by us. Inverse-Kubelka-Munk equation completed the deficit of Kubelka-Munk equation. Correlation coefficients acquired by conventioanl GC and UV against DRIFT were more than 0.95.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.553-562
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• 2021

Directional regression (DR; Li and Wang, 2007) is well-known as an exhaustive sufficient dimension reduction method, and performs well in complex regression models to have linear and nonlinear trends. However, the extension of DR is not well-done upto date, so we will extend DR to accommodate multivariate regression and large p-small n regression. We propose three versions of DR for multivariate regression and discuss how DR is applicable for the latter regression case. Numerical studies confirm that DR is robust to the number of clusters and the choice of hierarchical-clustering or pooled DR.

• 생태와환경
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• 제54권2호
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• pp.102-107
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• 2021

The distribution pattern of species richness was determined by temperature. To examine the relationship between hemipteran richness and temperature, hemipteran species were collected using pitfall traps at six different oak forest sites with different annual mean temperatures in South Korea. Multiple linear regression analyses were conducted with mean annual temperature (MAT) and plant richness to evaluate differences in hemipteran richness. The influences of MAT and plant richness of study sites on hemipteran richness were examined by comparing three models (plant richness+MAT+MAT², plant richness+MAT, and MAT) or two models (plant richness+MAT and MAT). Hemipteran richness showed an inverse diversity pattern as a function of temperature, with higher species richness at lower temperature sites. Meanwhile, Aphididae showed a bell-shaped diversity pattern with the highest value at low medium temperatures. The regression analysis showed that hemipteran richness was affected by temperature and plant richness in their habitats.

• Communications for Statistical Applications and Methods
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• 제31권2호
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• pp.247-262
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• 2024

In this paper, we explore nonlinear sufficient dimension reduction (SDR) methods, with a primary focus on establishing a foundational framework that integrates various nonlinear SDR methods. We illustrate the generalized sliced inverse regression (GSIR) and the generalized sliced average variance estimation (GSAVE) which are fitted by the framework. Further, we delve into nonlinear extensions of inverse moments through the kernel trick, specifically examining the kernel sliced inverse regression (KSIR) and kernel canonical correlation analysis (KCCA), and explore their relationships within the established framework. We also briefly explain the nonlinear SDR for functional data. In addition, we present practical aspects such as algorithmic implementations. This paper concludes with remarks on the dimensionality problem of the target function class.