• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.233-241
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• 2006

Classical principal component analysis (PCA) can be formulated as finding the linear subspace that best accommodates multidimensional data points in the sense that the sum of squared residual distances is minimized. As alternatives to such LS (least squares) fitting approach, we produce LMS (least median of squares) and LTS (least trimmed squares)-type PCA by minimizing the median of squared residual distances and the trimmed sum of squares, in a similar fashion to Rousseeuw (1984)'s alternative approaches to LS linear regression. Proposed methods adopt the data-driven optimization algorithm of Croux and Ruiz-Gazen (1996, 2005) that is conceptually simple and computationally practical. Numerical examples are given.

• Journal of Korea Water Resources Association
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• v.31 no.6
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• pp.675-684
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• 1998

This paper presents the empirical formulas for determining the design-width for medium rivers in the Han river basin. The design flood, the watershed ares, and the channel slope of 216 medium rivers in the Han river basin are collected. the design width formulas are then determined by 1) the least squares (LS) method, 2)the least median squares (LMS) method, and 3) the reweighted least squares method based on the LMS (RLS). The six types of formulas are considered to determine the acceptable type for medium streams in the Han river basin. The root mean squared errors (RMSE), the absolute mean (AME) errors, and the mean errors (ME) are computed to test the formulas derived by three regression methods. It si found that the equation related stream width to the watershed area and the channel slope is acceptable for determining the design width for medium streams in the Han river basin. It is expected that the equations proposed by this study be used an index for determining the design-width for medium streams in the Han river basin.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.81-88
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• 2021

k-least quantile of squares (k-LQS) estimates are a generalization of least median of squares (LMS) estimates. They have not been used as much as LMS because their breakdown points become small as k increases. But if the size of outliers is assumed to be fixed LQS estimates yield a good fit to the majority of data and residuals calculated from LQS estimates can be a reliable tool to detect outliers. We propose to use LQS estimates for separating a clean set from the data in the context of outlyingness of the cases. Three procedures are suggested for the identification of outliers using LQS estimates. Examples are provided to illustrate the methods. A Monte Carlo study show that proposed methods are effective.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.673-685
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• 2018

Procrustes analysis is a useful technique useful to measure, compare shape differences and estimate a mean shape for objects; however it is based on a least squares criterion and is affected by some outliers. Therefore, we propose two generalized Procrustes analysis methods based on M-estimation and least median of squares estimation that are resistant to object outliers. In addition, two algorithms are given for practical implementation. A simulation study and some examples are used to examine and compared the performances of the algorithms with the least square method. Moreover since these resistant GPA methods are available for higher dimensions, we need some methods to visualize the objects and mean shape effectively. Also since we have concentrated on resistant fitting methods without considering shape distributions, we wish to shape analysis not be sensitive to particular model.

• Journal of Korean Society of Water and Wastewater
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• v.12 no.3
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• pp.99-106
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• 1998

This paper presents a procedure for determining the design rainfall depth and the design rainfall intensity at Incheon city area in Korea. In this study the eight probability distributions are considered to estimate the probable rainfall depths for 11 different durations. The Kolmogorov - Smirnov test and the Chi-square test are adopted to test each distribution. The probable rainfall intensity formulas are then determined by i) the least squares (LS) method, ii) the least median squares (LMS) method, iii) the reweighted least squares method based on the LMS (RLS), and iv) the constrained regression (CR) model. The Talbot, the Sherman, the Japanese, and the Unified type are considered to determine the best type for the Incheon station. The root mean squared (RMS) errors are computed to test the formulas derived by four methods. It is found that the Unified type is the most reliable and that all methods presented herein are acceptable for determining the coefficients of rainfall intensity formulas from an engineering point of view.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.485-494
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• 2004

An algorithm is proposed to identify multiple outliers in linear regression. It is based on the clustering of residuals from the least median of squares estimation. A cut-height criterion for the hierarchical cluster tree is suggested, which yields the optimal clustering of the regression outliers. Comparisons of the effectiveness of the procedures are performed on the basis of the classic data and artificial data sets, and it is shown that the proposed algorithm is superior to the one that is based on the least squares estimation. In particular, the algorithm deals very well with the masking and swamping effects while the other does not.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.269-279
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• 2002

We considered the problem for confirmation of multiple outliers and leverage points. Identification of multiple outliers and leverage points is difficult because of the masking effect and swamping effect. Rousseeuw and van Zomeren(1990) identified multiple outliers and leverage points by using the Least Median of Squares and Minimum Value of Ellipsoids which are high-breakdown robust estimators. But their methods tend to declare too many observations as extremes. Atkinson(1987) suggested a method for confirming of outliers and Fung(1993) pointed out Atkinson method's limitation and proposed another method by using the add-back model. But we analyzed that Fung's method is affected by adjacent effect. In this thesis, we proposed one procedure for confirmation of outliers and leverage points and compared three example with Fung's method.

• Journal of the Korea Society of Computer and Information
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• v.10 no.2 s.34
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• pp.21-30
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• 2005

In general, the robust estimation method is well known for a good statistical estimator that is insensitive to small departures from the idealized assumptions for which the estimation is optimized. While there are many existing robust estimation techniques that have been proposed in the literature, two main techniques used in computer vision are M-estimators and least-median of squares (LMS). Among these. we utilized the M-estimators since they are known to provide an optimal estimation of affine motion parameters. The M-estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized. To resolve these problems, we proposed an adaptive M-estimators algorithm that effectively separates outliers from non-outliers and estimate affine model parameters, using a continuous sigmoid weight function. The experimental results show the superiority of our method.

• Journal of Energy Engineering
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• v.22 no.3
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• pp.245-249
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• 2013

This paper attempts to estimate the kerosene demand function in Korea over the period 1981-2012. As the kerosene demand function provides us information on the pattern of consumer's kerosene consumption, it can be usefully utilized in predicting the impact of policy variables such as kerosene price and forecasting the demand for kerosene. We apply least absolute deviations and least median squares estimation methods as a robust approach to estimating the parameters of the kerosene demand function. The results show that short-run price and income elasticities of the kerosene demand are estimated to be -0.468 and 0.409, respectively. They are statisitically significant at the 1% level. The short-run price and income elasticities portray that demand for kerosene is price- and income-inelastic. This implies that the kerosene is indispensable goods to human-being's life, thus the kerosene demand would not be promptly adjusted to responding to price and/or income change. However, long-run price and income elasticities reveal that the demand for kerosene is price- and income-elastic in the long-run.

• Ocean and Polar Research
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• v.35 no.1
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• pp.1-14
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• 2013

Shoreline data of the barrier islands in Nakdong River Estuary for the last three decades were assembled using six sets of aerial photographs and seven sets of satellite images. Canny Algorithm was applied to untreated data in order to obtain a wet-dry boundary as a proxy shoreline. Digital Shoreline Analysis System (DSAS 4.0) was used to estimate the rate of shoreline changes in terms of five statistical variables; SCE (Shoreline Change Envelope), NSM (Net Shoreline Movement), EPR(End Point Rate), LRR (Linear Regression Rate), and LMS (Least Median of Squares). The shoreline in Jinwoodo varied differently from one place to another during the last three decades; the west tail has advanced (i.e., seaward or southward), the west part has regressed, the south part has advanced, and the east part has regressed. After the 2000s, the rate of shoreline changes (-2.5~6.7 m/yr) increased and the east advanced. The shoreline in Shinjado shows a counterclockwise movement; the west part has advanced, but the east part has retreated. Since Shinjado was built in its present form, the west part became stable, but the east part has regressed faster. The rate of shoreline changes (-16.0~12.0 m/yr) in Shinjado is greater than that of Jinwoodo. The shoreline in Doyodeung has advanced at a rate of 31.5 m/yr. Since Doyodeung was built in its present form, the south part has regressed at the rate of -18.2 m/yr, but the east and west parts have advanced at the rate of 13.5~14.3 m/yr. Based on Digital Shoreline Analysis, shoreline changes in the barrier islands in the Nakdong River Estuary have varied both temporally and spatially, although the exact reason for the shoreline changes requires more investigation.