• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.305-315
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• 2014

In a simple linear regression, a linear relationship between an explanatory variable and a response variable can be easily recognized in the scatter plot of them. The lack of fit test for the replicated data is commonly used for testing the linearity but it is not easy to test the linearity when the explanatory variable is not replicated. In this paper, we propose three new test statistics for testing the linearity regardless of replication using the principle of average slope and validate them through several simulations and empirical studies.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.185-193
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• 2002

The purpose of this paper is to suggest a method for detecting the linear regression change-points or variance change-points in regression model by the combination of Schwarz information criteria. The advantage of the suggested method is to detect change-points more detailed when one compares the suggest method with Chen (1998)'s method.

• Journal of the Korea Society of Computer and Information
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• v.20 no.12
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• pp.29-36
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• 2015

In this paper, we propose the horizontal line detection using the Haar-like features and linear regression in infrared images. In the marine environment horizon image is very useful information on a variety of systems. In the proposed method Haar-like features it was noted that the standard deviation be calculated in real time on a static area. Based on the pixel position, calculating the standard deviation of the around area in real time and, if the reaction is to filter out the largest pixel can get the energy map of the area containing the straight horizontal line. In order to select a horizontal line of pixels from the energy map, we applied the linear regression, calculating a linear fit to the transverse horizontal line across the image to select the candidate optimal horizontal. The proposed method was carried out in a horizontal line detecting real infrared image experiment for day and night, it was confirmed the excellent detection results than the legacy methods.

• 한국데이터정보과학회:학술대회논문집
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• 2004.10a
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• pp.61-61
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• 2004

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.197-204
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• 2009

In the model selection problem, the main objective is to choose the true model from a manageable set of candidate models. An information criterion gauges the validity of a statistical model and judges the balance between goodness-of-fit and parsimony; "how well observed values ran approximate to the true values" and "how much information can be explained by the lower dimensional model" In this study, we introduce some information criteria modified from the Akaike Information Criterion (AIC) and the Bayesian Information Criterion(BIC). The information criteria considered in this study are compared via simulation studies and real application.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.203-210
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• 1996

A linear neural unit with a modified anti-Hebbian learning rule has been shown to be able to optimally fit curves, surfaces, and hypersurfaces by adaptively extracting the minor component of the input data set. In this paper, we study how to use the robust version of this neural fitting method for linear regression analysis. Furthermore, we compare this method with other methods when data set is contaminated by outliers.

• Communications for Statistical Applications and Methods
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• v.24 no.2
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• pp.155-162
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• 2017

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination $R^2$ and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in $R^2$ and F-statistic.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.293-301
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• 2012

Quantile regression proposed by Koenker and Bassett (1978) is a statistical technique that estimates conditional quantiles. The advantage of using quantile regression is the robustness in response to large outliers compared to ordinary least squares(OLS) regression. A regression tree approach has been applied to OLS problems to fit flexible models. Loh (2002) proposed the GUIDE algorithm that has a negligible selection bias and relatively low computational cost. Quantile regression can be regarded as an analogue of OLS, therefore it can also be applied to GUIDE regression tree method. Chaudhuri and Loh (2002) proposed a nonparametric quantile regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning. Lee and Lee (2006) investigated wage determinants in the Korean labor market using the Korean Labor and Income Panel Study(KLIPS). Following Lee and Lee, we fit three kinds of quantile regression tree models to KLIPS data with respect to the quantiles, 0.05, 0.2, 0.5, 0.8, and 0.95. Among the three models, multiple linear piecewise quantile regression model forms the shortest tree structure, while the piecewise constant quantile regression model has a deeper tree structure with more terminal nodes in general. Age, gender, marriage status, and education seem to be the determinants of the wage level throughout the quantiles; in addition, education experience appears as the important determinant of the wage level in the highly paid group.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.187-191
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• 2000

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. In this paper, we propose a simple graphical method to detect outliers and to investigate the goodness of model fit in repeated measures data. The graphical method is based on the quantile-quantile(Q-Q) plots of the $X^2$ distribution and the standard normal distribution. We also propose diagnostic measures to detect influential observations. The proposed method is illustrated using two examples.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.