• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Journal of the Korean Statistical Society
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• 제17권2호
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• pp.121-133
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• 1988

In this paper a class of mixture designs for estimating the slope of second order Scheffe polynomial response surfaces for mixture experiments with q components is presented. The variance of the estimated directional slope at a point is a function of the direction of the slope and the design. If the variance is averaged over all possible directions in the (q-1)-dimensional simplex, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the centroid point. This property is called "slope-rotatability over al directions in the simplex", and the necessary and sufficient conditions for mixture design to have this property are given and proved. The class of designs with this property is compared with other mixture designs and discussed.discussed.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.393-408
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• 2024

The sparse linear discriminant analysis can be incorporated into the penalized linear regression framework, but most studies have been limited to specific convex penalties, including the least absolute selection and shrinkage operator and its variants. Within this framework, concave penalties can serve as natural counterparts of the convex penalties. Implementing the concave penalized direction vector of discrimination appears to be straightforward, but developing its theoretical properties remains challenging. In this paper, we explore a class of concave penalties that covers the smoothly clipped absolute deviation and minimax concave penalties as examples. We prove that employing concave penalties guarantees an oracle property uniformly within this penalty class, even for high-dimensional samples. Here, the oracle property implies that an ideal direction vector of discrimination can be exactly recovered through concave penalized least squares estimation. Numerical studies confirm that the theoretical results hold with finite samples.

• Journal of the Korean Statistical Society
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• 제29권1호
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• pp.9-16
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• 2000

This article addresses the problem of maximum likelihood estimation in ARCH regression with lagged dependent variables. Some topics in asymptotics of the model such as uniform expansion of likelihood function and construction of a class of MLE are discussed, and the regularity property of MLE is obtained. The error process here is possibly non-Gaussian.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.141-146
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• 2007

In this paper, we consider a Box-Cox transformed threshold GARCH(1,1) process and find a sufficient condition under which the process is geometrically ergodic and has the ${\beta}$-mixing property with an exponential decay rate.

• Journal of the Korean Statistical Society
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• 제35권1호
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• pp.79-90
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• 2006

We consider the subdiagonal bilinear model and ARMA model with subdiagonal bilinear errors. Sufficient conditions for geometric ergodicity of associated Markov chains are derived by using results on generalized random coefficient autoregressive models and then strict stationarity and ,a-mixing property with exponential decay rates for given processes are obtained.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.959-966
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• 2000

A dimensionality assessment procedure DETECT uses the property of being near zero of conditional covariances as an indication of unidimensionality .This study provides the convergent properties to zero of conditional covariances when the dta is unidimensional, with which DETECT extends its theoretical grounds.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.285-290
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• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• 응용통계연구
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• 제2권1호
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• pp.54-64
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• 1989

Kurkjian 과 Zelen(1963)에 의해 조화행렬에서 행결합 행렬의 특성에 관계된 성질(Property) A가 제안되었다. 한편으로 Paik(1985)은 조화행렬이 블럭행렬로 분할되고, 분할된 블럭행렬간, 블럭행렬내에서 각각 순환하는 다중순환형식행렬을 갖는 경우를 정의하고, Paik(1985)은 이러한 특성을 갖는 계획을 성질 C라 하였다. 본 논문에서는 다중순환형식행렬을 갖는 조화행렬의 구조에 의하여 불완비블럭계획을 분류하였으며 분류의 목적은 축소된정규방정식의 해와 배치계획을 쉽게 하는데 있다.

• 대한원격탐사학회지
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• 제32권4호
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• pp.383-401
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• 2016

In this paper, we described the statistical modeling of crop yields using satellite images, climatic datasets, soil property maps, and fertilizer data for the Midwestern United States during 2001-2012. Satellite images were obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS), and climatic datasets were provided by the Parameter-elevation Regressions on Independent Slopes Model (PRISM) Climate Group. Soil property maps were derived from the Harmonized World Soil Database (HWSD). Our multivariate regression models produced quite good prediction accuracies, with differences of approximately 8-15% from the governmental statistics of corn and soybean yields. The unfavorable conditions of climate and vegetation in 2012 could have resulted in a decrease in yields according to the regression models, but the actual yields were greater than predicted. It can be interpreted that factors other than climate, vegetation, soil, and fertilizer may be involved in the negative biases. Also, we found that soybean yield was more affected by minimum temperature conditions while corn yield was more associated with photosynthetic activities. These two crops can have different potential impacts regarding climate change, and it is important to quantify the degree of the crop sensitivities to climatic variations to help adaptation by humans. Considering the yield decreases during the drought event, we can assume that climatic effect may be stronger than human adaptive capacity. Thus, further studies are demanded particularly by enhancing the data regarding human activities such as tillage, fertilization, irrigation, and comprehensive agricultural technologies.