• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.205-215
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• 2021

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2009.06a
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• pp.186-186
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• 2009

The characterization strategy of fracture networks are classified into a deterministic or statistical characterization according to the type of required information. A deterministic characterization is most efficient for a sparsely fractured system, while the statistics are sufficient for densely fractured rock. In this study, the ensemble mean and variability of the effective connectivity is systematically analyzed with various density values for different network structures of a power law size distribution. The results of high resolution Monte Carlo analyses show that statistical characteristics can be a necessary information to determine the transport properties of a fracture system when fracture density is greater than a percolation threshold. When the percolation probability (II) approaches unity with increasing fracture density, the effective connectivity of the network can be safely estimated using statistics only (sufficient condition). It is inferred from conditional simulations that deterministic information for main pathways can reduce the uncertainty in estimation of system properties when the network becomes denser. Overall results imply that most pathways need to be identified when II < 0.5 statistics are sufficient when II $\rightarrow$ 1 and statistics are necessary and the identification of main pathways can significantly reduce the uncertainty in estimation of transport properties when 0.5$\ll$1. It is suggested that the proper estimation of the percolation probability of a fracture network is a prerequisite for an appropriate conceptualization and further characterization.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.115-125
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• 2001

We consider the threshold autoregressive moving average(TARMA) process and find a sufficient condition for strict stationarity of the proces. Given region for stationarity of TARMA(p,q) model is the same as that of TAR(p) model given by Chan and Tong(1985), which shows that the moving average part of TARMA(p,q) process does not affect the stationarity of the process. We find also a sufficient condition for the existence of kth moments(k$\geq$1) of the process with respect to the stationary distribution.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.7 no.2
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• pp.55-58
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• 1982

An useful method for evaluating the threshold of the optimum detector can be used if sufficient statistics exists. This was done by giving examples. The design of the suboptimum detector can be carried out by finding the threshold of the appropriate test statistics. The results are conformed with the existing theory and the method given above is applicable in extensive area of designing the detectors.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.519-526
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• 2019

Response dimension reduction in a sufficient dimension reduction (SDR) context has been widely ignored until Yoo and Cook (Computational Statistics and Data Analysis, 53, 334-343, 2008) founded theories for it and developed an estimation approach. Recent research in SDR shows that a semi-parametric approach can outperform conventional non-parametric SDR methods. Yoo (Statistics: A Journal of Theoretical and Applied Statistics, 52, 409-425, 2018) developed a semi-parametric approach for response reduction in Yoo and Cook (2008) context, and Yoo (Journal of the Korean Statistical Society, 2019) completes the semi-parametric approach by proposing an unstructured method. This paper theoretically discusses and provides insightful remarks on three versions of semi-parametric approaches that can be useful for statistical practitioners. It is also possible to avoid numerical instability by presenting the results for an orthogonal transformation of the response variables.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.285-294
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• 2015

A permutation test is the popular and attractive alternative to derive asymptotic distributions of dimension test statistics in sufficient dimension reduction methodologies; however, recent studies show that a bootstrapping technique also can be used. We consider two types of bootstrapping dimension determination, which are partial and whole bootstrapping procedures. Numerical studies compare the permutation test and the two bootstrapping procedures; subsequently, real data application is presented. Considering two additional bootstrapping procedures to the existing permutation test, one has more supporting evidence for the dimension estimation of the central subspace that allow it to be determined more convincingly.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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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.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.245-259
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• 2003

The 2-way balanced one-level rotation design has been discussed (Park et al., 2001), where the 2-way balancing is done on interview time in monthly sample and rotation group. We extend it to 3-way balanced multi-level design to obtain more information of the same sample unit for one or more previous months. The 3-way balancing is accomplished not only on interview time in monthly sample and rotation group but also on recall time as well. The 3-way balancing eliminates or reduces any bias arising from unbalanced interview time, rotation group and recall time, and all rotation groups are equally represented in the monthly sample. We present the rule and rotation algorithm which guarantee the 3-way balancing. In particular, we specify the necessary and sufficient condition for the 3-way balanced multi-level rotation design.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.15-22
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• 2013

We find a sufficient condition for optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields studied by Nourdin and Peccati (2009b).