• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.471-487
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• 1996

In this paper we propose an efficient scoring type one-step GM-estimator, which has a bounded influence function and a high break-down point. The main point of the estimator is in the weighting scheme of the GM-estimator. The weight function we used depends on both leverage points and residuals So we construct an estimator which does not downweight good leverage points Unider some regularity conditions, we compute the finite-sample breakdown point and prove asymptotic normality Some simulation results are also presented.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.369-383
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• 1998

This paper deals with a robust regression estimator. We propose an efficient one-step GM-estimator, which has a bounded influence function and a high breakdown point. The main idea of this paper is to use the Mallows-type weights which depend on both the predictor variables and the residuals from a high breakdown initial estimator. The proposed weighting scheme severely downweights the bad leverage points and slightly downweights the good leverage points. Under some regularity conditions, we compute the finite-sample breakdown point and prove the asymptotic normality. Some simulation results and a numerical example are also presented.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.507-520
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• 1997

In this paper we propose a robust Wald-type test which is based on an efficient Mallows-type one-step GM-estimator. The proposed estimator based on the weight function of Song, Park and Nam (1996) has a bounded influence function and a high breakdown point. Under some regularity conditions, we compute the finite-sample breakdown point, and drive asymptotic normality of the proposed estimator. The level and power breakdown points, influence function and asymptotic distribution of the proposed test statistic are main points of this paper. To compare the performance of the proposed test with other tests, we perform some Monte Carlo simulations.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011

Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.225-232
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• 2000

The linear and quadratic discrimination functions based on normal theory are widely used to classify an observation to one of predefined groups. But the discriminant functions are sensitive to outliers. A high breakdown procedure to estimate location and scatter of multivariate data is the minimum volume ellipsoid or MVE estimator To obtain high breakdown classifiers outliers in multivariate data are detected by using the robust Mahalanobis distance based on MVE estimators and the weighted estimators are inserted in the functions for classification. A samll-sample MOnte Carlo study shows that the high breakdown robust procedures perform better than the classical classifiers.

• Structural Monitoring and Maintenance
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• v.6 no.4
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• pp.317-346
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• 2019

Performance assessment of pavements proves useful, in terms of handling the ride quality, controlling the travel time of vehicles and adequate maintenance of pavements. Roughness profiles provide a good measure of the deteriorating condition of the pavement. For the accurate estimates of pavement roughness from dynamic vehicle responses, vehicle parameters should be known accurately. Information on vehicle parameters is uncertain, due to the wear and tear over time. Hence, condition monitoring of pavement requires the identification of pavement roughness along with vehicle parameters. The present study proposes a scheme which estimates the roughness profile of the pavement with the use of accurate estimates of vehicle parameters computed in parallel. Pavement model used in this study is a two-layer Euler-Bernoulli beam resting on a nonlinear Pasternak foundation. The asphalt topping of the pavement in the top layer is modeled as viscoelastic, and the base course bottom layer is modeled as elastic. The viscoelastic response of the top layer is modeled with the help of the Burgers model. The vehicle model considered in this study is a half car model, fitted with accelerometers at specified points. The identification of the coupled system of vehicle-pavement interaction employs a coupled scheme of an unbiased minimum variance estimator and an optimization scheme. The partitioning of observed noisy quantities to be used in the two schemes is investigated in detail before the analysis. The unbiased minimum variance estimator (MVE) make use of a linear state-space formulation including roughness, to overcome the linearization difficulties as in conventional nonlinear filters. MVE gives estimates for the unknown input and fed into the optimization scheme to yield estimates of vehicle parameters. The issue of ill-posedness of the problem is dealt with by introducing a regularization equivalent term in the objective function, specifically where a large number of parameters are to be estimated. Effect of different objective functions is also studied. The outcome of this research is an overall measure of pavement condition.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.541-550
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• 2010

The $L_1$-regression estimator is susceptible to the leverage points, even though it is highly robust to the vertical outliers. This article is concerned with the improvement of robustness of the $L_1$-estimator. To improve its robustness, in terms of the breakdown point, we attempt to dampen the influence of the leverage points by means of reducing the weights corresponding to the leverage points. In addition the algorithm employs the linear scaling transformation technique, for higher computational efficiency with the large data sets, to solve the linear programming problem of $L_1$-estimation. Monte Carlo simulation results indicate that the proposed algorithm yields $L_1$-estimates which are robust to the leverage points as well as the vertical outliers.