• Communications for Statistical Applications and Methods
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• 제11권2호
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• pp.275-285
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• 2004

We explore classification analysis using graphical methods such as sliced inverse regression and sliced average variance estimation based on dimension reduction. Some useful information about classification analysis are obtained by sliced inverse regression and sliced average variance estimation through dimension reduction. Two examples are illustrated, and classification rates by sliced inverse regression and sliced average variance estimation are compared with those by discriminant analysis and logistic regression.

• 응용통계연구
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• 제31권6호
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• pp.835-842
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• 2018

충분차원축소의 대표적 방법론 중 하나인 sliced average variance estimation (SAVE)은 슬라이스라고 불리우는 반응변수의 범주화의 총 수에 민감하다고 알려져 있다. 이러한 점을 극복하기 위한 방법으로 최근에 다양한 수의 슬라이스로부터 얻어진 SAVE의 정보를 결합하는 fused SAVE (FSAVE)가 개발되었다. 본 논문에서는 소위 large p-small n 자료라고 불리우는 자료의 수가 변수의 수보다 적은 자료에서 FASVE가 어떻게 실제적으로 사용될 수 있을지에 대해 실증적 분석을 하고자 한다. 이를 위해 근적외분광분석을 통해 얻어진 비스킷 자료를 이용할 것이고, 이러한 자료분석에서 FASVE에 의한 차원축소에 의해 분석된 결과가 기존의 방법론에 비해 우수함을 보고자 한다.

• Journal of the Korean Data Analysis Society
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• 제20권6호
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• pp.2733-2746
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• 2018

The two inverse regression estimation methods, SIR and SAVE to estimate the central space are computationally easy and are widely used. However, SIR and SAVE may have poor performance in finite samples and need strong assumptions (linearity and/or constant covariance conditions) on predictors. The two non-parametric estimation methods, MAVE and dMAVE have much better performance for finite samples than SIR and SAVE. MAVE and dMAVE need no strong requirements on predictors or on the response variable. MAVE is focused on estimating the central mean subspace, but dMAVE is to estimate the central space. This paper explores and compares four methods to explain the dimension reduction. Each algorithm of these four methods is reviewed. Empirical study for simulated data shows that MAVE and dMAVE has relatively better performance than SIR and SAVE, regardless of not only different models but also different distributional assumptions of predictors. However, real data example with the binary response demonstrates that SAVE is better than other methods.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.213-217
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• 2003

In this paper we discuss graphical and diagnostic methods for logistic regression, in which the response is the number of successes in a fixed number of trials.

• 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.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.105-117
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• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.