• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.271-284
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• 2002

In this paper we consider the robust inference for the parameter of linear regression model based on weighted least squares. First we consider the sequential test of multiple outliers. Next we suggest the way to assign a weight to each observation $(x_i,\;y_i)$ and recommend the robust inference for linear model. Finally, to check the performance of confidence interval for the slope using proposed method, we conducted a Monte Carlo simulation and presented some numerical results and examples.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.21-32
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• 1997

Robust regression based on M-estimator reduces and/or bounds the influence of outliers in the y-direction only. Therefore, when several influential observations exist, diagnostics in the robust regression is required in order to detect them. In this paper, we propose influence diagnostics in the robust regression based on M-estimator and its one-step version. Noting that M-estimator can be obtained through iterative weighted least squares regression by using internal weights, we apply the weighted least squares (WLS) regression diagnostics to robust regression.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.903-908
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• 2009

The shrink parameter in ridge regression may be contaminated by outlying points. We propose robust cross validation scores in ridge regression instead of classical cross validation. We use robust location estimators such as median, least trimmed squares, absolute mean for robust cross validation scores. The robust scores have global robustness. Simulations are performed to show the effectiveness of the proposed estimators.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1037-1046
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• 2003

We propose an equivariant and robust estimator in multivariate regression model based on the least trimmed squares (LTS) estimator in univariate regression. We call this estimator as multivariate least trimmed squares (MLTS) estimator. The MLTS estimator considers correlations among response variables and it can be shown that the proposed estimator has the appropriate equivariance properties defined in multivariate regression. The MLTS estimator has high breakdown point as does LTS estimator in univariate case. We develop an algorithm for MLTS estimate. Simulation are performed to compare the efficiencies of MLTS estimate with coordinatewise LTS estimate and a numerical example is given to illustrate the effectiveness of MLTS estimate in multivariate regression.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.201-215
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• 2000

The classical method for regression analysis is the least squares method. However, if the data contain significant outliers, the least squares estimator can be broken down by outliers. To remedy this problem, the robust methods are important complement to the least squares method. Robust methods down weighs or completely ignore the outliers. This is not always best because the outliers can contain some very important information about the population. If they can be detected, the outliers can be further inspected and appropriate action can be taken based on the results. In this paper, I propose a sequential outlier test to identify outliers. It is based on the nonrobust estimate and the robust estimate of scatter of a robust regression residuals and is applied in forward procedure, removing the most extreme data at each step, until the test fails to detect outliers. Unlike other forward procedures, the present one is unaffected by swamping or masking effects because the statistics is based on the robust regression residuals. I show the asymptotic distribution of the test statistics and apply the test to several real data and simulated data for the test to be shown to perform fairly well.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.307-316
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• 2004

Principal Component Regression(PCR) and Partial Least Squares Regression(PLSR) are the two most popular regression techniques in chemometrics. In the field of chemometrics usually the number of regressor variables greatly exceeds the number of observation. So we have to reduce the number of regressors to avoid the identifiability problem. In this paper we compare PCR and PLSR techniques combined with various robust regression methods including regression depth estimation. We compare the efficiency, goodness-of-fit and robustness of each estimators under several contamination schemes.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.4
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• pp.314-320
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• 2012

This paper proposes a new robust motion deblurring filter using the inertial sensor measurements for strapdown image IR applications. With taking the PSF measurement error into account, the motion blurred image is modeled by the linear uncertain state space equation with the noise corrupted measurement matrix and the stochastic parameter uncertainty. This motivates us to solve the motion deblurring problem based on the recently developed robust least squares estimation theory. In order to suppress the ringing effect on the deblurred image, the robust least squares estimator is slightly modified by adoping the ridge-regression concept. Through the computer simulations using the actual IR scenes, it is demonstrated that the proposed algorithm shows superior and reliable motion deblurring performance even in the presence of time-varying motion artifact.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.355-366
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• 2003

A unified procedure for principal component regression (PCR), partial least squares (PLS) and ordinary least squares (OLS) is proposed. The process gives solutions for PCR, PLS and OLS in a unified and non-iterative way. This enables us to see the interrelationships among the three regression coefficient vectors, and it is seen that the so-called E-matrix in the solution expression plays the key role in differentiating the methods. In addition to setting out the procedure, the paper also supplies a robust numerical algorithm for its implementation, which is used to show how the procedure performs on a real world data set.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.97-110
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• 2006

Since it is well-established that even high quality data tend to contain outliers, one would expect fat? greater reliance on robust regression techniques than is actually observed. But most of all robust regression estimators suffers from the computational difficulties and the lower efficiency than the least squares under the normal error model. The weighted self-tuning estimator (WSTE) recently suggested by Lee (2004) has no more computational difficulty and it has the asymptotic normality and the high break-down point simultaneously. Although it has better properties than the other robust estimators, WSTE does not have full efficiency under the normal error model through the weighted least squares which is widely used. This paper introduces a new approach as called the reweighted WSTE (RWSTE), whose scale estimator is adaptively estimated by the self-tuning constant. A Monte Carlo study shows that new approach has better behavior than the general weighted least squares method under the normal model and the large data.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.10
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• pp.543-553
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• 2020

This paper examines the effect of COVID-19 pandemic on the Philippine stock exchange, peso-dollar rate and retail price of diesel using robust least squares regression and vector autoregression (VAR). The robust least squares regression using MM-estimation method concluded that COVID-19 daily infection has negative and statistically significant effect on the Philippine stock exchange index, peso-dollar exchange rate and retail pump price of diesel. This is consistent with the results of correlation diagnostics. As for the VAR model, the lag values of the independent variable disclose significance in explaining the Philippine stock exchange index, peso-dollar exchange rate and retail pump price of diesel. Moreover, in the short run, the impulse response function confirmed relative effect of COVID-19 daily infections and the variance decomposition divulge that COVID-19 daily infections have accounted for only minor portion in explaining fluctuations of the Philippine stock exchange index, peso-dollar exchange and retail pump price of diesel. In the long term, the influence levels off. The Granger causality test suggests that COVID-19 daily infections cause changes in the Philippine stock exchange index and peso-dollar exchange rate in the short run. However, COVID-19 infection has no causal link with retail pump price of diesel.