• Journal of the Korean Data and Information Science Society
• /
• 제13권2호
• /
• pp.271-284
• /
• 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
• /
• 제4권1호
• /
• pp.21-32
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• 제17권6호
• /
• pp.803-810
• /
• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• 응용통계연구
• /
• 제19권1호
• /
• pp.97-110
• /
• 2006

대부분의 자료는 여러가지 원인으로 인한 특이치로 오염되어 있으며, 이러한 상황에서 신뢰성 있는 추정량을 얻어내고 이에 대한 통계적 추론을 시행하는 것은 중요한 문제이다. 그러나 이제까지 제안된 로버스트 회귀추정량들은 계산상의 어려움과 정규오차모형에서 최소제곱추정량에 비하여 떨어지는 효율성때문에 통계적 추론의 정확성을 확신할 수 없었다. 최근 제안된 Lee(2004)의 가중자기조율회귀추정량(weighted self-tuning estimator, WSTE)은 다른 로버스트 회귀추정량에 비하여 정확한 계산과정과 그에 따른 추정량의 점근적 정규성 및 고붕괴점을 갖는다. 그러나 통계적 추론을 위하여 이제까지 널리 사용해왔던 로버스트 추정량에 기반한 가중최소제곱추정방법(weighted least squares estimator)은 WSTE에서조차 정규오차모형하에서 최소제곱추정량과 동일한 수준의 효율성을 제공해주지 는 못한다. 본 논문에서는 WSTE에 기반한 또다른 통계적 추론 방법을 제안하고, 이 방법을 사용함으로써 정규오차모형 및 대표본에서 보다 정확한 결과를 얻을 수 있음을 몬테칼로 모의실험을 통해 제시하였다.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2007년도 제38회 하계학술대회
• /
• pp.1640-1641
• /
• 2007

In this paper, an experiment of weighted robust least squares frequency estimation for the Gaussian envelope chirp signal which is used in the time-frequency domain reflectometry system was carried out. By incorporating the forgetting factor to the frequency estimator, the weighted robust least squares filter achieved good enough frequency estimation performance for the chirp signal and it can be adopted to implement not only low cost time-frequency domain reflectometry but also real-time time-frequency domain reflectometry implementation.

• Communications for Statistical Applications and Methods
• /
• 제18권6호
• /
• pp.733-739
• /
• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Journal of the Korean Statistical Society
• /
• 제10권
• /
• pp.105-121
• /
• 1981

The problem of selection of a subset containing the largest of several slope parameters of regression equations is considered. The proposed selection procedure is based on the weighted median estimators for regression parameters and the median of rescaled absolute residuals for scale parameters. Those estimators are compared with the classical least squares estimators by a simulation study. A Monte Carlo comparison is also made between the new procedure based on the weighted median estiamtors and the procedure based on the least squares estimators. The results show that the proposed procedure is quite robust with respect to the heaviness of distribution tails.

• Journal of the Korean Data and Information Science Society
• /
• 제27권4호
• /
• pp.1059-1066
• /
• 2016

In this paper we propose a robust version of varying coefficient models, which is based on the regularized regression with L1 regularization. We use the iteratively reweighted least squares procedure to solve L1 regularized objective function of varying coefficient model in locally weighted regression form. It provides the efficient computation of coefficient function estimates and the variable selection for given value of smoothing variable. We present the generalized cross validation function and Akaike information type criterion for the model selection. Applications of the proposed model are illustrated through the artificial examples and the real example of predicting the effect of the input variables and the smoothing variable on the output.

• Wind and Structures
• /
• 제26권6호
• /
• pp.383-395
• /
• 2018

An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.

• 전기학회논문지
• /
• 제56권10호
• /
• pp.1859-1864
• /
• 2007

Existing barcode signal restoration algorithms are not robust to unmodeled outliers that may exist in scanned barcode images due to scratches, dirts, etc. In this paper, we describe a robust barcode signal restoration algorithm that uses the hybrid $L_1-L_2$ norm as a similarity measure. To optimze the similarity measure, we propose a modified iterative reweighted least squares algorithm based on the one step minimization of a quadratic surrogate function. In the simulations and experiments with barcode images, the proposed method showed better robustness than the conventional MSE based method. In addition, the proposed method converged quickly during optimization process.