• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.288-295
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• 1995

In this paper a hypotheses test procedure based on the least absolute deviation estimators for the unknown parameters in nonlinear regression models is investigated. The asymptotic distribution of the proposed likelihood ratio test statistic are established voth under the null hypotheses and a sequence of local alternative hypotheses. The asymptotic relative efficiency of the proposed test with classical test based on the least squares estimator is also discussed.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.609-617
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• 2006

A new fuzzy c-regression algorithm for switching regression analysis is presented, which combines fuzzy c-means clustering and least squares support vector machine. This algorithm can detect outliers in switching regression models while yielding the simultaneous estimates of the associated parameters together with a fuzzy c-partitions of data. It can be employed for the model-free nonlinear regression which does not assume the underlying form of the regression function. We illustrate the new approach with some numerical examples that show how it can be used to fit switching regression models to almost all types of mixed data.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.149-158
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• 2024

A least squares problem without correspondences is expressed as the following optimization: Π∈P^min_{m, x∈ℝn} ║Ax-Πy║, where A ∈ ℝ^m×n and y ∈ ℝ^m are given. In general, solving such an optimization problem is highly challenging. In this paper we use the rearrangement inequalities to find the closed form of solutions for certain cases. Moreover, despite the stringent constraints, we successfully tackle the nonlinear least squares problem without correspondences by leveraging rearrangement inequalities.

• Journal of the Korean Data and Information Science Society
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• v.24 no.2
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• pp.391-399
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• 2013

Partially linear regression is capable of providing more complete description of the linear and nonlinear relationships among random variables. In support vector regression (SVR) the hyper-parameters are known to affect the performance of regression. In this paper we propose an iterative reweighted least squares (IRWLS) procedure to solve the quadratic problem of partially linear support vector regression with a modified loss function, which enables us to use the generalized approximate cross validation function to select the hyper-parameters. Experimental results are then presented which illustrate the performance of the partially linear SVR using IRWLS procedure.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.879-886
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• 2009

The purpose of this article is to present the application of Least Squares Support Vector Machine in analyzing the existing structure of brand. We estimate the parameters of the Market Share Attraction Model using a non-parametric technique for function estimation called Least Squares Support Vector Machine, which allows us to perform even nonlinear regression by constructing a linear regression function in a high dimensional feature space. Estimation by Least Squares Support Vector Machine technique makes it a good candidate for solving the Market Share Attraction Model. To illustrate the performance of the proposed method, we use the car sales data in South Korea's car market.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.831-839
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• 2010

Least squares support vector machine (LS-SVM) is a kernel trick gaining a lot of popularities in the regression and classification problems. We use LS-SVM to propose a iterative algorithm for a nonlinear generalized autoregressive conditional heteroscedasticity model in the mean (GARCH-M) model to estimate the mean and the conditional volatility of stock market returns. The proposed method combines a weighted LS-SVM for the mean and unweighted LS-SVM for the conditional volatility. In this paper, we show that nonlinear GARCH-M models have a higher performance than the linear GARCH model and the linear GARCH-M model via real data estimations.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.957-963
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• 2007

In this paper, Nonlinear Autoregressive (NAR) method based on Least Square-Support Vector Regression (LS-SVR) is introduced and tested for nonlinear sustained vowel modeling. In the database of total 43 sustained vowel of Benign Vocal Fold Lesions having aperiodic waveform, this nonlinear synthesizer near perfectly reproduced chaotic sustained vowels, and also conserved the naturalness of sound such as jitter, compared to Linear Predictive Coding does not keep these naturalness. However, the results of some phonation are quite different from the original sounds. These results are assumed that single-band model can not afford to control and decompose the high frequency components. Therefore multi-band model with wavelet filterbank is adopted for substituting single band model. As a results, multi-band model results in improved stability. Finally, nonlinear sustained vowel modeling using NAR based on LS-SVR can successfully reconstruct synthesized sounds nearly similar to original voiced sounds.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.735-744
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• 2007

Support vector machine(SVM) is capable of providing a more complete description of the linear and nonlinear relationships among random variables. In this paper we propose a sparse kernel regression(SKR) to overcome a weak point of SVM, which is, the steep growth of the number of support vectors with increasing the number of training data. The iterative reweighted least squares(IRWLS) procedure is used to solve the optimal problem of SKR with a Laplacian prior. Furthermore, the generalized cross validation(GCV) function is introduced to select the hyper-parameters which affect the performance of SKR. Experimental results are then presented which illustrate the performance of the proposed procedure.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.183-191
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• 2010

Support vector quantile regression(SVQR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. In this paper we propose an iterative reweighted least squares(IRWLS) procedure to solve the problem of SVQR with a weighted quadratic loss function. Furthermore, we introduce the generalized approximate cross validation function to select the hyperparameters which affect the performance of SVQR. Experimental results are then presented which illustrate the performance of the IRWLS procedure for SVQR.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.627-641
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• 2021

An asymmetric least squares estimation method has been employed to estimate linear models for percentile regression. An asymmetric maximum likelihood estimation (AMLE) has been developed for the estimation of Poisson percentile linear models. In this study, we propose generalized nonlinear percentile regression using the AMLE, and the use of the parametric bootstrap method to obtain confidence intervals for the estimates of parameters of interest and smoothing functions of estimates. We consider three conditional distributions of response variables given covariates such as normal, exponential, and Poisson for three mean functions with one linear and two nonlinear models in the simulation studies. The proposed method provides reasonable estimates and confidence interval estimates of parameters, and comparable Monte Carlo asymptotic performance along with the sample size and quantiles. We illustrate applications of the proposed method using real-life data from chemical and radiation epidemiological studies.