• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011

Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.531-539
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• 2009

Logistic regression is widely used as a datamining technique for the customer relationship management. The maximum likelihood estimator has highly inflated variance when multicollinearity exists among the regressors, and it is not robust against outliers. Thus we propose the robust principal components logistic regression to deal with both multicollinearity and outlier problem. A procedure is suggested for the selection of principal components, which is based on the condition index. When a condition index is larger than the cutoff value obtained from the model constructed on the basis of the conjoint analysis, the corresponding principal component is removed from the logistic model. In addition, we employ an algorithm for the robust estimation, which strives to dampen the effect of outliers by applying the appropriate weights and factors to the leverage points and vertical outliers identified by the V-mask type criterion. The Monte Carlo simulation results indicate that the proposed procedure yields higher rate of correct classification than the existing method.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.163-171
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• 1997

Function approximation from a set of input-output pairs has numerous applications in scientific and engineering areas. Multilayer feedforward neural networks have been proposed as a good approximator of nonlinear function. The back propagation(BP) algorithm allows multilayer feedforward neural networks to learn input-output mappings from training samples. It iteratively adjusts the network parameters(weights) to minimize the sum of squared approximation errors using a gradient descent technique. However, the mapping acquired through the BP algorithm may be corrupt when errorneous training data we employed. When errorneous traning data are employed, the learned mapping can oscillate badly between data points. In this paper we propose a robust BP learning algorithm that is resistant to the errorneous data and is capable of rejecting gross errors during the approximation process, that is stable under small noise perturbation and robust against gross errors.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.381-393
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• 2005

As a promising technique for dimension reduction in regression analysis, Sliced Inverse Regression (SIR) and an associated chi-square test for dimensionality were introduced by Li (1991). However, Li's test needs assumption of Normality for predictors and found to be heavily dependent on the number of slices. We will provide a unified asymptotic test for determining the dimensionality of the SIR model which is based on the probabilistic principal component analysis and free of normality assumption on predictors. Illustrative results with simulated and real examples will also be provided.