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Shewhart chart is typically formed under normality assumptions. In reality, much data is contaminated with occasional outliers, which may diminish the Shewhart chart's sensitivity. Hence, robust charts are introduced as outlier-resistant and robust against non-normality. This paper intends to study the robust monitoring of contaminated data using (i) median chart based on median absolute deviation (MAD), and (ii) trimmed mean chart based on winsorized standard deviation. These charts are compared with the conventional Shewhart mean ()X charts based on standard deviation and range. In general, through extensive simulations, the robust charts are quite comparable with the X charts for normal data of small sample size (n), but for large n, the median chart based on MAD is marginally preferred by all the benchmarks considered. However, when a process is contaminated, both robust charts outshine the X charts substantially in a series of investigations. [ABSTRACT FROM AUTHOR]

Abstract This paper extends the conventional semi-parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1—outliers occur in data set, 2—multicollinearity exists in predictors. For this purpose, the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function. Then, inspired by the conventional local linear smoothing method, a kernel-based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology. Some common goodness-of-fit criteria are also used to examine the performance of the proposed method. The effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study. The proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses. The numerical results clearly indicate that 1—the proposed method is not sensitive to the outliers, 2—the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3—comparing to existing fuzzy multiple regressions, the proposed model provides more efficient predictions. Highlights • A fuzzy semi-parametric regression model is proposed when multicollinearity and/or outliers occur. • The fuzzy model contains the fuzzy predictors-responses. • The ridge methodology and a novel robust method are applied to evaluate crisp coefficients. • The method is compared with several methods using various goodness-of-fit-measures. [ABSTRACT FROM AUTHOR]

A Gaussian measurement error assumption, that is, an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t distribution helps reduce the bias. However, it may be less efficient in estimating parameters if the heavy tailed assumption is uniformly applied to all of the data when most of them are normally observed. We propose a mixture error assumption that selectively converts Gaussian errors into Student's t errors according to latent outlier indicators, leveraging the best of the Gaussian and Student's t errors; a parameter estimation can be not only robust but also accurate. Using simulated hospital profiling data and astronomical time series of brightness data, we demonstrate the potential for the proposed mixture error assumption to estimate parameters accurately in the presence of outliers. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by simulations and real data examples presented in the paper. [ABSTRACT FROM AUTHOR]

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed algorithms have been proposed, which frame the signal/object labelling problem in terms of cluster analysis after extracting source-specific features, however, the number of clusters is assumed to be known. We propose a new method called gravitational clustering to adaptively estimate the time-varying number of clusters based on a set of feature vectors. The key idea is to exploit the physical principle of gravitational force between mass units: streaming-in feature vectors are considered as mass units of fixed position in the feature space, around which mobile mass units are injected at each time instant. The cluster enumeration takes advantage of the fact that the highest attraction on the mobile mass units is exerted by regions with a high density of feature vectors, i.e., gravitational clusters. By sharing estimates among neighboring nodes via a diffusion-adaptation scheme, cooperative and distributed cluster enumeration is achieved. Numerical experiments concerning robustness against outliers, convergence and computational complexity are conducted. The application to distributed cooperative multi-view camera networks illustrates the applicability to real-world problems. [ABSTRACT FROM AUTHOR]

To achieve the automotive quality for semiconductor devices represented by “zero-defect,” part average testing (PAT) is actively applied to outgoing test. PAT has been generally used on wafer level test. This time we expanded it to package level test and established the method of detecting the characteristic variations and screening out the outliers. Moreover, we suggest a way of thinking about the outliers and consideration on the basis of the actual data analysis. We were especially conscious of the statistical meaning of the outliers which were detected. It has been demonstrated that the expanded PAT to package level test can reject the outliers of characteristics variation even within spec. The outliers in distribution of characteristic variations were detected by maintaining chip traceability. The new method can screen out outliers outside the 6-sigma within spec, and there was a clear inflection point between the distribution of the abnormal data and that of the population. It was assumed that hidden failure devices which had not been rejected as early failure were screened out. Detecting the outlier with the new method can reduce the failure rate to the target. [ABSTRACT FROM AUTHOR]

In this paper, we extend the closed form moment estimator (ordinary MCFE) for the autoregressive conditional duration model given by Lu et al (2016) and propose some closed form robust moment-based estimators for the multiplicative error model to deal with the additive and innovational outliers. The robustification of the closed form estimator is done by replacing the sample mean and sample autocorrelation with some robust estimators. These estimators are more robust than the quasi-maximum likelihood estimator (QMLE) often used to estimate this model, and they are easy to implement and do not require the use of any numerical optimization procedure and the choice of initial value. The performance of our proposal in estimating the parameters and forecasting conditional mean μ t of the MEM(1,1) process is compared with the proposals existing in the literature via Monte Carlo experiments, and the results of these experiments show that our proposal outperforms the ordinary MCFE, QMLE, and least absolute deviation estimator in the presence of outliers in general. Finally, we fit the price durations of IBM stock with the robust closed form estimators and the benchmarks and analyze their performances in estimating model parameters and forecasting the irregularly spaced intraday Value at Risk. [ABSTRACT FROM AUTHOR]

To suppress the influence of outliers on function estimation, we propose a least absolute deviation (LAD)-based robust support vector regression (SVR). Furthermore, an efficient algorithm based on the split-Bregman iteration is introduced to solve the optimization problem of the proposed algorithm. Both artificial and benchmark datasets are employed to compare the performance of the proposed algorithm with those of least squares SVR (LS-SVR), and two weighted versions of LS-SVR with the weight functions of Hampel and Logistic, respectively. Experiments demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this letter, we propose a robust direction-of-arrival (DOA) estimation algorithm in the context of sparse reconstruction, where some array sensors are miscalibrated. In this case, conventional DOA estimation algorithms suffer from degraded performance or even failed operations. In the proposed approach, the miscalibrated sensor observations are treated as outliers, and a weighting factor is adaptively optimized and applied to each sensor in order to effectively mitigate the effect of the outliers. An algorithm based on the maximum correntropy criterion is then developed to yield robust DOA estimation. The simulation results are presented to verify the effectiveness and superiority of the proposed approach compared with conventional DOA estimation algorithms. [ABSTRACT FROM AUTHOR]

Matrix completion aims to find the missing entries from incomplete observations using the low-rank property. Conventional convex optimization based techniques for matrix completion minimize the nuclear norm subject to a constraint on the Frobenius norm of the residual. However, they are not robust to outliers and have a high computational complexity. Different from the existing schemes based on solving a minimization problem, we formulate matrix completion as a feasibility problem. An alternating projection algorithm (APA) is devised to find a feasible point in the intersection of the low-rank constraint set and fidelity constraint set. To achieve resistance to outliers, the fidelity constraint set is modeled as an $\ell _p$ -ball, where the ball center corresponds to the observed data. Furthermore, there is no stepsize within the framework of APA. Convergence of the APA is analyzed and the local linear convergence rate is established. Simulation results demonstrate the efficiency, accuracy, and outlier robustness of the APA. [ABSTRACT FROM PUBLISHER]

In order to maintain a relatively high accuracy of navigation performance during global positioning system (GPS) outages, a novel robust least squares support vector machine (LS-SVM)-aided fusion methodology is explored to provide the pseudo-GPS position information for the inertial navigation system (INS). The relationship between the yaw, specific force, velocity, and the position increment is modeled. Rather than share the same weight in the traditional LS-SVM, the proposed algorithm allocates various weights for different data, which makes the system immune to the outliers. Field test data was collected to evaluate the proposed algorithm. The comparison results indicate that the proposed algorithm can effectively provide position corrections for standalone INS during the 300 s GPS outage, which outperforms the traditional LS-SVM method. Historical information is also involved to better represent the vehicle dynamics. [ABSTRACT FROM AUTHOR]

Multivariate mixture regression models can be used to investigate the relationships between two or more response variables and a set of predictor variables by taking into consideration unobserved population heterogeneity. It is common to take multivariate normal distributions as mixing components, but this mixing model is sensitive to heavy-tailed errors and outliers. Although normal mixture models can approximate any distribution in principle, the number of components needed to account for heavy-tailed distributions can be very large. Mixture regression models based on the multivariatetdistributions can be considered as a robust alternative approach. Missing data are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this paper, we propose a multivariatetmixture regression model with missing information to model heterogeneity in regression function in the presence of outliers and missing values. Along with the robust parameter estimation, our proposed method can be used for (i) visualization of the partial correlation between response variables across latent classes and heterogeneous regressions, and (ii) outlier detection and robust clustering even under the presence of missing values. We also propose a multivariatetmixture regression model using MM-estimation with missing information that is robust to high-leverage outliers. The proposed methodologies are illustrated through simulation studies and real data analysis. [ABSTRACT FROM PUBLISHER]

Sandwave migration rate is of critical importance for the hydrodynamic research as well as the coastal engineering application. To acquire this information, the correlation matching algorithm is applied in this paper. By searching for similar seafloor areas between multi-temporal digital terrain models, the migration rate can be estimated. To account for the impact of the morphological distortion as well as outliers in the survey data, the correlation matching is adjusted based on the robust estimation theory. By executing the correlation matching based on the least median square criterion, a robust initial estimate is obtained. Afterwards, the potential outliers are detected based on the initial matching result, and the corresponding weights are adjusted to zero. Finally, correlation matching is executed with the updated weights. With the above procedure, the impact of outliers can be accounted for. The developed method is applied on the bathymetry time-series data collected in Monterey Canyon, California. Comparison shows that the presented algorithm significantly improves the credibility of the estimation. The generated migration vector field not only reveals the main tendency of the migration rate in the region, but also highlights the unique local migration patterns, which is helpful for understanding the mechanism of the sandwave migration. [ABSTRACT FROM AUTHOR]

In this paper, ridge and non-ridge type estimators and their robust forms are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Another common problem in applied statistics is the presence of outliers in the data besides multicollinearity. In this respect, we propose some robust estimators for shrinkage parameter based on least trimmed squares (LTS) method. Given a set of n observations and the integer trimming parameter h ≤ n , the LTS estimator involves computing the hyperplane that minimizes the sum of the smallest h squared residuals. The LTS estimator is closely related to the well-known least median squares (LMS) estimator in which the objective is to minimize the median squared residual. Although LTS estimator has the advantage of being statistically more efficient than LMS estimator, the computational complexity of LTS is less understood than LMS. Here, we extract the robust estimators for linear and nonlinear parts of the model based on robust shrinkage estimators. It is shown that these estimators perform better than ordinary ridge estimator. For our proposal, via a Monté-Carlo simulation and a real data example, performance of the ridge type of robust estimators are compared with the classical ones in restricted semiparametric regression models. [ABSTRACT FROM AUTHOR]

CoPlot analysis is one of the multivariate data-visualizing techniques. It consists of two graphs: the first one represents the distribution ofp-dimensional observations over two-dimensional space, whereas the second shows the relations of variables with the observations. At CoPlot analysis, multidimensional scaling (MDS) and Pearson’s correlation coefficient (PCC) are used to obtain a map that demonstrates observations and variables simultaneously. However, both MDS and PCC are sensitive to outliers. When multidimensional dataset contains outliers, interpretation of the map, which is obtained from classical CoPlot analysis, may result in wrong conclusions. At this study, a novel approach to classical CoPlot analysis is presented. By using robust MDS and median absolute deviation correlation coefficient (MADCC), robust CoPlot map is improved. Numerical examples are given to illustrate the merits of the proposed approach. Also, obtained results are compared with the classical CoPlot analysis to emphasize the superiority of introduced robust CoPlot approach. [ABSTRACT FROM PUBLISHER]

Control Chart is a widely used on-line process control techniques to control variability. This paper focuses on variability due to dispersion of a quality characteristic. Classical methods of estimating parameters of the distribution of quality characteristic may be affected by the presence of outliers. In order to overcome such situation, robust estimators, which are less affected by the extreme values or small departures from the model assumptions, are introduced in industrial application. This article introduced a modification to trimmed standard deviation to increase its efficiency, and is used in controlling process dispersion. Authors constructed a phase-I control chart derived from standard deviation of trimmed mean, which is robust. Simulation study is conducted to assess its performance at phase-II. This robust control chart is compared with s-chart in terms of its efficiency to detect outliers or assignable causes of variation as well as its Average Run Length. [ABSTRACT FROM AUTHOR]

An Interacting Multiple Model (IMM) filter suppresses outliers by integrating model-conditioned estimation and model mode recognition through adaptive mode switches based on a Bayesian probability update. However, it may face significant outlier-caused peak errors, which are undesirable or even impermissible in many applications, for example, target tracking. This paper considers that, from the view of the Dempster-Shafer Theory, the IMM filter actually fuses the Bayesian beliefs of the model mode with Dempster's Rule of Combination, which can deal with uncertainties instead of the evidence conflicts that may exist as outliers appear. Therefore, we propose the adaptive robust multiple model (RMM) filter through introducing practical expert knowledge in the belief function framework, which runs online to reduce outlier-caused peak errors. In RMM, the Likelihood Temporal Ratio (LTR) is incorporated to provide extra information on the tendency of mode switching. Moreover, expert rules are introduced to construct adaptive belief functions using discount techniques and to select the combination rule that better deals with evidence conflicts when outliers appear. The simulations in target tracking scenarios show that the proposed RMM filter significantly reduces outlier-caused peak errors and hence obtains a lower rate of track loss in the cluttered environment. [ABSTRACT FROM AUTHOR]

Feature matching, which refers to establishing reliable correspondence between two sets of features (particularly point features), is a critical prerequisite in feature-based registration. In this paper, we propose a flexible and general algorithm, which is called locally linear transforming (LLT), for both rigid and nonrigid feature matching of remote sensing images. We start by creating a set of putative correspondences based on the feature similarity and then focus on removing outliers from the putative set and estimating the transformation as well. We formulate this as a maximum-likelihood estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. To ensure the well-posedness of the problem, we develop a local geometrical constraint that can preserve local structures among neighboring feature points, and it is also robust to a large number of outliers. The problem is solved by using the expectation–maximization algorithm (EM), and the closed-form solutions of both rigid and nonrigid transformations are derived in the maximization step. In the nonrigid case, we model the transformation between images in a reproducing kernel Hilbert space (RKHS), and a sparse approximation is applied to the transformation that reduces the method computation complexity to linearithmic. Extensive experiments on real remote sensing images demonstrate accurate results of LLT, which outperforms current state-of-the-art methods, particularly in the case of severe outliers (even up to 80%). [ABSTRACT FROM PUBLISHER]

Similarity measure is an important part of image registration. The main challenge of similarity measure is lack of robustness to different distortions. A well-known distortion is spatially-varying intensity distortion. Its main characteristic is correlation among pixels. Most traditional intensity based similarity measures (e.g., SSD, MI) assume stationary image and pixel to pixel independence. Hence, these similarity measures are not robust against spatially-varying intensity distortion. Here, we suppose that non-stationary intensity distortion has a sparse representation in transform domain, i.e. its distribution has high peak at origin and a long tail. We use two viewpoints of Maximum Likelihood (ML) and Robust M-estimator. First, using the ML view, we propose robust Huber similarity measure (RHSM) in spatial transform domain as a new similarity measure in a mono-modal setting. In fact, RHSM is a combination of ℓ 2 and ℓ 1 norms. To demonstrate robustness of the proposed similarity measure, image registration is treated as a non-linear regression problem. In this view, covariance matrix of estimated parameters is obtained based on the one-step M-estimator. Then with minimizing Fisher information function, robust similarity measure of RHSM is introduced. This measure produces accurate registration results on both artificial as well as real-world problems that we have examined. [ABSTRACT FROM AUTHOR]

We introduce a new transformation estimation algorithm using the L2E estimator and apply it to non-rigid registration for building robust sparse and dense correspondences. In the sparse point case, our method iteratively recovers the point correspondence and estimates the transformation between two point sets. Feature descriptors such as shape context are used to establish rough correspondence. We then estimate the transformation using our robust algorithm. This enables us to deal with the noise and outliers which arise in the correspondence step. The transformation is specified in a functional space, more specifically a reproducing kernel Hilbert space. In the dense point case for nonrigid image registration, our approach consists of matching both sparsely and densely sampled SIFT features, and it has particular advantages in handling significant scale changes and rotations. The experimental results show that our approach greatly outperforms state-of-the-art methods, particularly when the data contains severe outliers. [ABSTRACT FROM PUBLISHER]

Mixtures of distributions have been used as probability models for clustering data. Classification maximum likelihood (CML) procedure is a popular mixture of maximum likelihood approach to clustering. Yang (1993) extended CML to fuzzy CML (FCML) for a normal mixture model, called FCML-N. However, normal distributions are not robust for outliers. In general, t-distributions should be more robust to outliers than normal distributions. In this paper we consider FCML with multivariate t-distributions and then create a robust clustering algorithm, called FCML-T. To compare with the expectation & maximization for multivariate t-distributions (EM-T), the proposed FCML-T uses a much simpler equation for solving the degrees of freedom. Some numerical and real experimental examples are used to compare the FCML-T with FCML-N, EM for normal mixtures (EM-N) and EM-T. The results demonstrate the superiority and usefulness of the proposed FCML-T algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes robust methods for local planar surface fitting in 3D laser scanning data. Searching through the literature revealed that many authors frequently used Least Squares (LS) and Principal Component Analysis (PCA) for point cloud processing without any treatment of outliers. It is known that LS and PCA are sensitive to outliers and can give inconsistent and misleading estimates. RANdom SAmple Consensus (RANSAC) is one of the most well-known robust methods used for model fitting when noise and/or outliers are present. We concentrate on the recently introduced Deterministic Minimum Covariance Determinant estimator and robust PCA, and propose two variants of statistically robust algorithms for fitting planar surfaces to 3D laser scanning point cloud data. The performance of the proposed robust methods is demonstrated by qualitative and quantitative analysis through several synthetic and mobile laser scanning 3D data sets for different applications. Using simulated data, and comparisons with LS, PCA, RANSAC, variants of RANSAC and other robust statistical methods, we demonstrate that the new algorithms are significantly more efficient, faster, and produce more accurate fits and robust local statistics (e.g. surface normals), necessary for many point cloud processing tasks. Consider one example data set used consisting of 100 points with 20% outliers representing a plane. The proposed methods called DetRD-PCA and DetRPCA, produce bias angles (angle between the fitted planes with and without outliers) of 0.20° and 0.24° respectively, whereas LS, PCA and RANSAC produce worse bias angles of 52.49°, 39.55° and 0.79° respectively. In terms of speed, DetRD-PCA takes 0.033 s on average for fitting a plane, which is approximately 6.5, 25.4 and 25.8 times faster than RANSAC, and two other robust statistical methods, respectively. The estimated robust surface normals and curvatures from the new methods have been used for plane fitting, sharp feature preservation and segmentation in 3D point clouds obtained from laser scanners. The results are significantly better and more efficiently computed than those obtained by existing methods. [ABSTRACT FROM AUTHOR]

The performance of a process or product is usually characterized by a univariate response variable or a vector of response variables. However, in some applications, the performance of a process or product can better be characterized by a relationship between a response variable and one or more explanatory variables. This relationship which is often referred to as profile should be monitored over time to ensure proper performance of the process or product. In phase I or retrospective phase, profile parameters are unknown and should be estimated from a set of historical observations. In phase II or prospective phase, the estimated parameters are used to construct the required monitoring schemes to monitor process or product performance in the future. This paper addresses the issue of outliers in phase I. It should be noted that if these outliers are neglected during parameter estimation procedure, then the designed control charts applied in phase II lack the sufficient effectiveness in detecting shifts. This article proposes two approaches based on M-estimator and Theil-Sen method to obtain robust parameter estimations when outliers are present. A simulation study on a numerical example is executed, and the results show that the performance of the control charts designed by the proposed methods is uniformly better than the case when outlier profiles are present and traditional estimation methods such as maximum likelihood estimation (MLE) are applied. Moreover, it is shown that control charts based on Theil-Sen estimates outperform the ones based on the M-estimator method in terms of average run length (ARL) criterion significantly. [ABSTRACT FROM AUTHOR]

In shaded areas, Global Positioning System (GPS) signals may suffer significant degradation, making the measurements to be contaminated by different kinds of errors. These errors such as outliers arising due to multipath and line-of-sight signals can degrade the accuracy of GPS positioning. Moreover, the poor geometric constellation of satellites that the receiver is tracking may cause inverse problems, resulting in unstable and unreliable GPS positioning solutions. To tackle these problems, an iterative robust regularization method (IRRM) for the GPS positioning is proposed in this article. The IRRM employs the Cholesky factorization method to preclude computing the inverse of matrices, making it numerically stable and be easily implemented in engineering. Also included in this work is the derivation of the sufficient condition for the IRRM. Performance comparisons of the proposed algorithm with the least squares, the Cholesky factorization method for iterative least squares (CM), and the robust estimation are demonstrated via two static positioning problems. The experimental results, presented herein, exhibit the improved performance of the IRRM over conventional algorithms. [ABSTRACT FROM AUTHOR]

Outliers in terrain data are an obstacle to achieving accurate and robust solutions of Underwater Terrain Relative Navigation (UTRN). If not handled properly, navigation may be degraded or even divergent. To address the problem, this paper proposes a terrain-matching algorithm based on the robust estimation theory. In contrast to the conventional approach, the proposed algorithm can significantly reduce the interference of the outliers. Experimental results confirm the good performance of the proposed method. [ABSTRACT FROM AUTHOR]

Multilayer perceptron has been widely used in time series forecasting for last two decades. However, it is a well-known fact that the forecasting performance of multilayer perceptron is negatively affected when data have outliers and this is an important problem. In recent years, some alternative neuron models such as generalized-mean neuron, geometric mean neuron, and single multiplicative neuron have been also proposed in the literature. However, it is expected that forecasting performance of artificial neural network approaches based on these neuron models can be also negatively affected by outliers since the aggregation function employed in these models is based on mean value. In this study, a new multilayer feed forward neural network, which is called median neuron model multilayer feed forward (MNM-MFF) model, is proposed in order to deal with this problem caused by outliers and to reach high accuracy level. In the proposed model, unlike other models suggested in the literature, MNM which has median-based aggregation function is employed. MNM is also firstly defined in this study. MNM-MFF is a robust neural network method since aggregation functions in MNM-MFF are based on median, which is not affected much by outliers. In addition, to train MNM-MFF model, particle swarm optimization method was utilized. MNM-MFF was applied to two well-known time series in order to evaluate the performance of the proposed approach. As a result of the implementation, it was observed that the proposed MNM-MFF model has high forecasting accuracy and it is not affected by outlier as much as multilayer perceptron model. Proposed method brings improvement in 7 % for data without outlier, in 90 % for data with outlier, in 95 % for data with bigger outlier. [ABSTRACT FROM AUTHOR]

A regression methodology is introduced that obtains competitive, robust, efficient, high-breakdown regression parameter estimates as well as providing an informative summary regarding possible multiple outlier structure. The proposed method blends a cluster analysis phase with a controlled bounded influence (BI) regression phase, thereby referred to as cluster-based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point-addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster 'half-set' of observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group-additive DFFITS argument used to carefully activate the minor clusters through a BI regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stability, scale estimation and standard errors. The dendrogram of the clustering process and the weight plot are graphical displays available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical view point towards data analysis and the marriage of estimation with diagnostic summary. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A key concept of the forward search algorithm in confirmatory factor analysis is ordering of the data on the basis of observational residuals. These residuals are computed under the proposed model and measure the discrepancy between the observed and predicted response for each unit of the sample. Regression-type factor scores are used to estimate model predictions. Informative forward plots are created for indexing influential observations and to show the dynamics of the estimates throughout the search. The detailed influence of each observation on the model parameters and fit indices is analyzed and a robust model inference is achieved. Real and simulated data sets with known contamination schemes are used to demonstrate the performance of the forward search algorithm. [ABSTRACT FROM AUTHOR]

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample. [ABSTRACT FROM AUTHOR]

A new class of probability distributions, the so-called connected double truncated gamma distribution, is introduced. We show that using this class as the error distribution of a linear model leads to a generalized quantile regression model that combines desirable properties of both least-squares and quantile regression methods: robustness to outliers and differentiable loss function. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the linear discriminant analysis (LDA) is generalized by using an -norm optimization technique. Although conventional LDA based on the -norm has been successful for many classification problems, performances can degrade with the presence of outliers. The effect of outliers which is exacerbated by the use of the -norm can cause this phenomenon. To cope with this problem, we propose an LDA based on the -norm optimization technique (LDA-), which is robust to outliers. Arbitrary values of p can be used in this scheme. The experimental results show that the proposed method achieves high recognition rate for many datasets. The reason for the performance improvements is also analyzed. [Copyright &y& Elsevier]

Abstract: The output weights computing of extreme learning machine (ELM) encounters two problems, the computational and outlier robustness problems. The computational problem occurs when the hidden layer output matrix is a not full column rank matrix or an ill-conditioned matrix because of randomly generated input weights and biases. An existing solution to this problem is Singular Value Decomposition (SVD) method. However, the training speed is still affected by the large complexity of SVD when computing the Moore–Penrose (MP) pseudo inverse. The outlier robustness problem may occur when the training data set contaminated with outliers then the accuracy rate of ELM is extremely affected. This paper proposes the Extended Complete Orthogonal Decomposition (ECOD) method to solve the computational problem in ELM weights computing via ECODLS algorithm. And the paper also proposes the other three algorithms, i.e. the iteratively reweighted least squares (IRWLS-ELM), ELM based on the multivariate least-trimmed squares (MLTS-ELM), and ELM based on the one-step reweighted MLTS (RMLTS-ELM) to solve the outlier robustness problem. However, they also encounter the computational problem. Therefore, the ECOD via ECODLS algorithm is also used successfully in the three proposed algorithms. The experiments of regression problems were conducted on both toy and real-world data sets. The outlier types are one-sided and two-sided outliers. Each experiment was randomly contaminated with outliers, of one type only, with 10%, 20%, 30%, 40%, and 50% of the total training data size. Meta-metrics evaluation was used to measure the outlier robustness of the proposed algorithms compared to the existing algorithms, i.e. the minimax probability machine regression (MPMR) and the ordinary ELM. The experimental results showed that ECOD can effectively replace SVD. The ECOD is robust to the not full column rank or the ill-conditional problem. The speed of the ELM training using ECOD is also faster than the ordinary training algorithm. Moreover, the meta-metrics measure showed that the proposed algorithms are less affected by the increasing number of outliers than the existing algorithms. [Copyright &y& Elsevier]

We propose a new robust regression estimator using data partition technique and M estimation (DPM). The data partition technique is designed to define a small fixed number of subsets of the partitioned data set and to produce corresponding ordinary least square (OLS) fits in each subset, contrary to the resampling technique of existing robust estimators such as the least trimmed squares estimator. The proposed estimator shares a common strategy with the median ball algorithm estimator that is obtained from the OLS trial fits only on a fixed number of subsets of the data. We examine performance of the DPM estimator in the eleven challenging data sets and simulation studies. We also compare the DPM with the five commonly used robust estimators using empirical convergence rates relative to the OLS for clean data, robustness through mean squared error and bias, masking and swamping probabilities, the ability of detecting the known outliers, and the regression and affine equivariances. [ABSTRACT FROM AUTHOR]

Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these techniques, supersaturating models by augmenting the "natural" covariates in the problem with an additional indicator for each case in the data set. We attach a penalty term for these case-specific indicators which is designed to produce a desired effect. For regression methods with squared error loss, an g 1 penalty produces a regression which is robust to outliers and high leverage cases; for quantile regression methods, an g2 penalty decreases the variance of the fit enough to overcome an increase in bias. The paradigm thus allows us to robustify procedures which lack robustness and to increase the efficiency of procedures which are robust. We provide a general framework for the inclusion of case-specific parameters in regularization problems, describing the impact on the effective loss for a variety of regression and classification problems. We outline a computational strategy by which existing software can be modified to solve the augmented regularization problem, providing conditions under which such modification will converge to the optimum solution. We illustrate the benefits of including case-specific parameters in the context of mean regression and quantile regression through analysis of NHANES and linguistic data sets. [ABSTRACT FROM AUTHOR]

Abstract: Block principal component analysis (BPCA) is an important subspace learning method in modern image analysis. The utilization of the L2-norm, however, makes it sensitive to outliers. In this paper, we propose an L1-norm-based BPCA (BPCA-L1) as a robust alternative to BPCA. We show the equivalence between the L1-norm-based two-dimensional principal component analysis (2DPCA-L1) and the L1-norm-based principal component analysis (PCA-L1), both of which can be formulated as special cases of BPCA-L1. Experiments of image reconstruction and classification on benchmark image sets show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Relationships between primary and secondary data are frequently quantified using the correlation coefficient; however, traditional means of calculating experimental correlation coefficients are known to be adversely affected by outlier data. A new method for calculating a robust correlation coefficient is proposed based on a weighted average correlation calculated from different combinations or subsets of the original data. The proposed robust correlation coefficient is shown to have a higher breakdown point than either Pearson''s or Spearman''s correlation coefficients as well as two out of three other robust correlation coefficients. The least median of squares (LMS) correlation coefficient has the highest possible breakdown point; however, it also tends to give unrealistically high or low correlation coefficients. A simulation study demonstrates the differences between the proposed robust correlation coefficient and other robust correlation coefficients. When the sample size is small, the uncertainty in the measured correlation can be very large, especially when the measured correlation is low. The uncertainty in the correlation coefficient is calculated based on the measured correlation and the number of data. This sampling distribution for the correlation coefficient requires a number of independent data; however, earth sciences data are often spatially dependent. Thus, a method for calculating an effective number of independent data using the variogram is proposed. An example is presented that applies the developed techniques to a petroleum geostatistics problem. The methodologies presented in this paper are implemented in FORTRAN code made available as part of this paper. [Copyright &y& Elsevier]

Abstract: Various sparse principal component analysis (PCA) methods have recently been proposed to enhance the interpretability of the classical PCA technique by extracting principal components (PCs) of the given data with sparse non-zero loadings. However, the performance of these methods is prone to be adversely affected by the presence of outliers and noises. To alleviate this problem, a new sparse PCA method is proposed in this paper. Instead of maximizing the L 2-norm variance of the input data as the conventional sparse PCA methods, the new method attempts to capture the maximal L 1-norm variance of the data, which is intrinsically less sensitive to noises and outliers. A simple algorithm for the method is specifically designed, which is easy to be implemented and converges to a local optimum of the problem. The efficiency and the robustness of the proposed method are theoretically analyzed and empirically verified by a series of experiments implemented on multiple synthetic and face reconstruction problems, as compared with the classical PCA method and other typical sparse PCA methods. [Copyright &y& Elsevier]