• 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.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.291-300
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• 2013

In this paper, we propose method-free permutation predictor hypothesis tests in the context of sufficient dimension reduction. Different from an existing method-free bootstrap approach, predictor hypotheses are evaluated based on p-values; therefore, usual statistical practitioners should have a potential preference. Numerical studies validate the developed theories, and real data application is provided.

• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.303-315
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• 2017

Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the $x^2$ test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

• 응용통계연구
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• 제23권5호
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• pp.813-822
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• 2010

차원 축소(dimension reduction) 기법은 주로 횡단면 자료 분석에서 널리 이용되어 왔으며 시계열 분석 분야에서의 적용은 상대적으로 미진한 실정이다. 본 논문에서는 부분-수량화를 통한 주성분분석 방법을 계절형 시계열에 적용시켜 시계열 자료의 차원 축소를 시도하고자 한다. 분석 방법론을 단계별로 제시하였으며 월별 실업률 자료 분석을 통해 설명하였다.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.497-506
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• 2019

Forecasting the U.S. employment level is made using machine learning methods of the artificial neural network: deep neural network, long short term memory (LSTM), gated recurrent unit (GRU). We consider the big data of the federal reserve economic data among which 105 important macroeconomic variables chosen by McCracken and Ng (Journal of Business and Economic Statistics, 34, 574-589, 2016) are considered as predictors. We investigate the influence of the two statistical issues of the dimension reduction and time series differencing on the machine learning forecast. An out-of-sample forecast comparison shows that (LSTM, GRU) with differencing performs better than the autoregressive model and the dimension reduction improves long-term forecasts and some short-term forecasts.

• Communications for Statistical Applications and Methods
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• 제29권5호
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• pp.615-627
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• 2022

Principal Fitted Component (PFC) is a semi-parametric sufficient dimension reduction (SDR) method, which is originally proposed in Cook (2007). According to Cook (2007), the PFC has a connection with other usual non-parametric SDR methods. The connection is limited to sliced inverse regression (Li, 1991) and ordinary least squares. Since there is no direct comparison between the two approaches in various forward regressions up to date, a practical guidance between the two approaches is necessary for usual statistical practitioners. To fill this practical necessity, in this paper, we newly derive a connection of the PFC to covariance methods (Yin and Cook, 2002), which is one of the most popular SDR methods. Also, intensive numerical studies have done closely to examine and compare the estimation performances of the semi- and non-parametric SDR methods for various forward regressions. The founding from the numerical studies are confirmed in a real data example.

• Communications for Statistical Applications and Methods
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• 제30권2호
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• pp.179-189
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• 2023

Hybrid sufficient dimension reduction (SDR) methods to a weighted mean of kernel matrices of two different SDR methods by Ye and Weiss (2003) require heavy computation and time consumption due to bootstrapping. To avoid this, Park et al. (2022) recently develop the so-called cross-distance selection (CDS) algorithm. In this paper, two variations of the original CDS algorithm are proposed depending on how well and equally the covk-SAVE is treated in the selection procedure. In one variation, which is called the larger CDS algorithm, the covk-SAVE is equally and fairly utilized with the other two candiates of SIR-SAVE and covk-DR. But, for the final selection, a random selection should be necessary. On the other hand, SIR-SAVE and covk-DR are utilized with completely ruling covk-SAVE out, which is called the smaller CDS algorithm. Numerical studies confirm that the original CDS algorithm is better than or compete quite well to the two proposed variations. A real data example is presented to compare and interpret the decisions by the three CDS algorithms in practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권1호
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.107-115
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• 2012

본 논문에서는 Yoo와 Cook (2007)에 의하여 제시된 다변량 회귀의 조건부 평균에 대한 최소 불일치 함수 접근법을 통한 최적 차원축소 부분공간의 추정에서 차원의 수가 추정된 선형결합들과 설명력 등에 어떤 영향을 미치는 지를 시뮬레이션 자료를 통하여 알아보았다. 그 결과 추정에 사용된 차원수에 따른 여러 결과들을 차원결정을 위한 검정과 함께 활용하면 모형에 필요한 차원수를 탐색하는데 매우 효과적임을 알 수 있었다.

• 정보처리학회논문지D
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• 제19D권2호
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• pp.147-150
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• 2012

클래스들 간의 거리를 최대화시키는 사영 방향을 구하는 감독차원감소 방법인 선형판별분석법(LDA)은 클래스 정보를 가진 데이터의 수가 매우 적을 때 성능이 급격히 저하되는 경향이 있다. 이러한 경우 상대적으로 저렴한 비용으로 얻을 수 있는 클래스 라벨 정보가 없는 데이터를 활용할 수 있는 반감독 차원 감소법이 사용될 수 있다. 그러나 통계적 차원 감소법에서 흔히 사용되는 행렬연산은 많은 양의 데이터를 사용하는데 메모리와 처리시간에서 한계가 있고, 적은 수의 라벨드 데이터(labeled data)에 비해 너무나 많은 언라벨드 데이터(unlabeled data)의 사용은 처리 시간의 증가에 비해 오히려 성능감소를 가져올 수 있다. 이러한 문제들을 극복하기 위해 앙상블 접근법을 이용한 반감독 차원 감소 방법을 제안한다. 문서분류 문제에서의 실험결과를 통해 제안한 방법의 성능을 입증한다.