Presence Of Multiple Outliers Research Articles

Detection of Outliers in Circular Regression Model Via DFBETAcIS Statistic

The outlier issues in circular regression models have recently received much attention. The presence of outliers may cause the sign and magnitude of regression coefficients to vary, resulting in inaccurate model development and incorrect prediction. Many methods for detecting outliers in a circular regression model have been proposed in previous studies such as COVRATIO, D, M, A, and Chord statistics, but it is suspected that they are not very successful in the presence of multiple outliers in a data set since the masking and swamping is not considered in their studies. This study aimed to develop an outlier detection procedure using DFBETAc statistic for circular cases, where this new statistic will investigate and identify multiple outliers in the Jammalamadaka and Sarma circular regression model (JSCRM) by considering masking and swamping effect. Monte Carlo simulations are used to determine the corresponding cut-off point and the power of performance is investigated. The performance of the proposed statistic is evaluated by the proportion of detected outliers and the rate of masking and swamping. The simulation procedure is applied at 10% and 20% contamination levels for varying sample sizes. The results show that the proposed DFBETAcIS statistic for JSCRM successfully detect the outliers. For illustration purposes, this process is applied to wind direction data.

OWA fuzzy regression

In this paper, the Ordered Weighted Averaging (OWA) operators will be considered to propose general fuzzy regression modeling technique for crisp/fuzzy-input fuzzy-output data. Here, by considering various kinds of a special form of OWA operators we will be able to1.investigate different approaches for aggregation of residuals/errors,2.construct a multi-objective optimization problem,3.provide high-breakdown estimators,4.identify poorly fitted data points, which might be considered as outliers while limiting their effects on the model,5.show how robust alternatives to other fuzzy regression models can be obtained as a result. Finally, a special case of the OWA-based fuzzy regression model known as OWA-Least Trimmed Absolutes Deviations (OWA-LTAD) fuzzy regression model is studied in details for crisp-input fuzzy-output data. An algorithm is investigated in the present study for estimation process in which1.the highest breakdown value will always be achieved (up to the maximum of 0.5) for problems with multiple outliers,2.the poorly fitted dataset can be labeled as outliers in an elemental set. In the presence of multiple outliers, the new method is particularly useful, and the performance of the proposed approach is illustrated for modeling several simulated datasets and a real valued dataset all contaminated with multiple outliers as well. We will look at an application of the proposed approach, in particular, to detect outliers in such models.

Robust moving total least squares: A technique for the reconstruction of measurement data in the presence of multiple outliers

This article is concerned with the reconstruction of contaminated measurement data based on the moving total least squares (MTLS) method, which is extensively applied to many engineering and scientific fields. Traditional MTLS method is lack of robustness and sensitive to the outliers in measurement data. Based on the framework of MTLS method, we proposed a robust MTLS method called RMTLS method by introducing a two-step pre-process to detect and remove the anomalous nodes in the support domain. The first step is an iterative regression procedure that combines with k-medoids clustering to automatically reduce the weight of anomalous node for a regression-based reference (curve or surface). Based on the distances between reference and discrete points, the second step adopts a density function defined by a sorted distance sequence to select the normal points without setting a threshold artificially. After the two-step pre-process, weighted total least square is performed on the selected point set to obtain the estimation value. By disposing of the anomalous nodes in each independent support domain, multiple outliers can be suppressed within the whole domain. Furthermore, the suppression of multiple continual outliers is possible by adopting asymmetric support domain and introducing previous estimation points. The proposed method shows great robustness and accuracy in reconstructing the simulation and experiment data.

Comparative Study of Clustering-Based Outliers Detection Methods in Circular-Circular Regression Model

This paper is a comparative study of several algorithms for detecting multiple outliers in circular-circular regression model based on the clustering algorithms. Three measures of similarity based on the circular distance were used to obtain a cluster tree using the agglomerative hierarchical methods. A stopping rule for the cluster tree based on the mean direction and circular standard deviation of the tree height was used as the cutoff point and classifier to the cluster group that exceeded the stopping rule as potential outliers. The performances of the algorithms have been demonstrated using the simulation studies that consider several outlier scenarios with a certain degree of contamination. Application to real data using wind data and a simulated data set are given for illustrative purposes. Thus, it has been found that Satari’s algorithm (S-SL algorithm) performs well for any values of sample size n and error concentration parameter. The algorithms are good in identifying outliers which are not limited to one or few outliers only, but the presence of multiple outliers at one time.

Android positioning: from stand-alone to cooperative approaches

The request for continuous and accurate localization in most diverse environments is growing: a possible solution is the use of location information retrieved by smartphones. For Android devices, Global Navigation Satellite System-based positioning is one of the main localization source, but in some environments GNSS signals can be blocked or affected by multipath. In these circumstances, the navigation solution may experience severe degradation. The presence of multiple outliers and their exclusion can cause a significant reduction of the satellite geometry. A possible solution is the identification of blunders and the replacement of such measurements with observables provided by a nearby device. The merging of measurements from different devices is an open challenge that is addressed in this work. This paper analyzes three smartphone GNSS-based cooperative positioning approaches: Direct Measurement Sharing, where the aiding device provides its raw observations to the aided smartphone; Augmented Measurement Sharing, where clock parameters and their accuracy are shared along with the raw observables; Corrected Measurement Sharing CMS, where corrected observables are adopted. Specifically, measurements of the aiding device are at first corrected for the clock bias. The methods have been validated using static and kinematic real data: tests were performed using devices from three manufacturers with different versions of the Operating System (OS). From the tests, the effectiveness of the proposed methods is demonstrated and the benefits of the combined solutions with respect to the single device solutions are shown.

Robust Circular Distance and its Application in the Identification of Outliers in the Simple Circular Regression Model

Abstract: Background and Objective: The existence of outliers in any type of data influences the efficiency of an estimator. Few methods for detecting outliers in a simple circular regression model have been proposed in the study but it suspected that they are not very successful in the presence of multiple outliers in a data set. This study aimed to investigate new statistic to identify multiple outliers in the response variable in a simple circular regression model. Materials and Methods: The proposed statistic is based on calculating robust circular distance between circular residuals and circular location parameter. The performance of the proposed statistic is evaluated by the proportion of detected outliers and the rate of masking and swamping. The simulation study is applied for different sample sizes at 10 and 20% ratios of contamination. Results: The results from simulated data showed that the proposed statistic has the highest proportion of outliers and the lowest rate of masking comparing with some existing methods. Conclusion: The proposed statistic is very successful in detecting outliers with negligible amount of masking and swamping rates.

Moments of Order Statistics from Weibull Distribution in the Presence of Multiple Outliers

In this article, we derive exact expressions for the single and product moments of order statistics from Weibull distribution under the contamination model. We assume that X1, X2, …, Xn − p are independent with density function f(x) while the remaining, p observations (outliers) Xn − p + 1, …, Xn are independent with density function arises from some modified version of f(x), which is called g(x), in which the location and/or scale parameters have been shifted in value. Next, we investigate the effect of the outliers on the BLUE of the scale parameter. Finally, we deduce some special cases.

Geometric median and its application in the identification of multiple outliers

Geometric mean (GM) is having growing and wider applications in statistical data analysis as a measure of central tendency. It is generally believed that GM is less sensitive to outliers than the arithmetic mean (AM) but we suspect likewise the AM the GM may also suffer a huge set back in the presence of outliers, especially when multiple outliers occur in a data. So far as we know, not much work has been done on the robustness issue of GM. In quest of a simple robust measure of central tendency, we propose the geometric median (GMed) in this paper. We show that the classical GM has only 0% breakdown point while it is 50% for the proposed GMed. Numerical examples also support our claim that the proposed GMed is unaffected in the presence of multiple outliers and can maintain the highest possible 50% breakdown. Later we develop a new method for the identification of multiple outliers based on this proposed GMed. A variety of numerical examples show that the proposed method can successfully identify all potential outliers while the traditional GM fails to do so.

Quality Control in Cocoa Powder Production Process: A Robust MSPC Approach

To monitor a multivariate process mean, Hotelling’s T2 control chart is often used. However, the presence of multiple outliers may go undetected due to the masking effect or swamping effect. In this study, we propose a robust Hotelling’s T2 control charts where the mean vector and the covariance matrix are estimated by using fast minimum covariance determinant (FMCD) which gives a high breakdown point estimates. This study found that the latter approach performs far better than the former in terms of the ability in detecting an out-of-control situation during the start-up stage. We present and discuss our experience in monitoring the process mean of cocoa powder production process in a Malaysian company located in Johor Bahru.

Robust Hotelling's T2 control charts under non-normality: the case of t-Student distribution

Traditional multivariate control charts are based upon the assumption that the observations follow a multivariate normal distribution. In many practical applications, however, this supposition may be difficult to verify. In this paper, we use control charts based on robust estimators of location and scale to improve the capability of detection observations out of control under non-normality in the presence of multiple outliers. Concretely, we use a simulation process to analyse the behaviour of the robust alternatives to Hotelling's T 2, which use minimum volume ellipsoidal (MVE) and minimum covariance determinant (MCD) in the presence of observations with a Student's t-distribution. The results show that these robust control charts are good alternatives for small deviations from normality due to the fact that the percentage of out-of-control observations detected for these charts in the Phase II are higher.

Fault Detection and Isolation in Multiple MEMS-IMUs Configurations

This research presents methods for detecting and isolating faults in multiple micro-electro-mechanical system inertial measurement unit (MEMS-IMU) configurations. First, geometric configurations with n sensor triads are investigated. It is proved that the relative orientation between sensor triads is irrelevant to system optimality in the absence of failures. Then, the impact of sensor failure or decreased performance is investigated. Three fault detection and isolation (FDI) approaches (i.e., the parity space method, Mahalanobis distance method and its direct robustification) are reviewed theoretically and in the context of experiments using reference signals. It is shown that in the presence of multiple outliers the best performing detection algorithm is the robust version of the Mahalanobis distance.

On the One-Outlier Displaying Component

A method of displaying an outlier in a multivariate data set is the Outlier Displaying Component. This method is based on the sample mean vector and the sum of squares and cross-product matrix. The main weakness of this method is that both of these measures involve the very outlier that is being detected. This paper presents an approach to eliminating this weakness. By eliminating the outlier from the sample mean vector and the sum of squares and cross-product matrix, the proposed method combines a number of advantages: It enhances the separation of the outlier from the rest of the data so that it appears more distinct. It also increases the general dispersion in the projected data so that the presence of multiple outliers could be revealed.

A robust alternative to Hotelling's T2 control chart using trimmed estimators

AbstractA control chart is one of the primary techniques used in statistical process control. In phase I, historical observations are analysed in order to construct a control chart with which to determine whether the process has been in control over the period of time in which the data were collected. The presence of multiple outliers may go undetected by the usual control charts, such as Hotelling's T2 due to the masking effect. In this paper we propose a robust alternative to Hotelling's T2 control chart with estimators defined using trimming. Simulation studies show that the proposed control chart is more effective than T2 in detecting outliers. Copyright © 2008 John Wiley & Sons, Ltd.

Identification of Multiple Outliers in Logistic Regression

The use of logistic regression modeling has seen a great deal of attention in the literature in recent years. This includes all aspects of the logistic regression model including the identification of outliers. A variety of methods for the identification of outliers, such as the standardized Pearson residuals, are now available in the literature. These methods, however, are successful only if the data contain a single outlier. In the presence of multiple outliers in the data, which is often the case in practice, these methods fail to detect the outliers. This is due to the well-known problems of masking (false negative) and swamping (false positive) effects. In this article, we propose a new method for the identification of multiple outliers in logistic regression. We develop a generalized version of standardized Pearson residuals based on group deletion and then propose a technique for identifying multiple outliers. The performance of the proposed method is then investigated through several examples.

CFAR Outlier Detection With Forward Methods

Separation or classification of signal-present samples from noise-only samples is studied. The false-alarm probability implies how many noise-only samples are wrongly classified as outliers, and typically it should be smaller than some upper limit. The noise distribution parameters are not known a priori and have to be estimated. Multiple outliers have a strong influence to that estimation and may lead to uncontrollable false-alarm probability. The false-alarm probability control can be improved by robust estimators and/or by forward-detection methods. In this article, the false-alarm probability of the forward methods is analyzed. The forward consecutive mean excision (FCME) algorithm is enhanced to allow better false-alarm control. It is proposed that the forward method using the cell-averaging (CA) constant false-alarm rate (CFAR) technique can be applied for locating the outliers. The results show that its false-alarm probability stays close to the required value even in the presence of multiple outliers.

Relations for order statistics from non-identical logistic random variables and assessment of the effect of multiple outliers on the bias of linear estimators

In this paper, we establish some relations for the single moments of order statistics arising from n independent and non-identically distributed logistic random variables. These relations are then used to deduce a set of recurrence relations for the moments of order statistics from the multiple-outlier logistic model (with a slippage of p observations). The moments of order statistics from the p-outlier model are expressed in terms of the corresponding quantities from ( p - 1 ) -outlier and ( p - 2 ) -outlier models. We then use these recurrence relations along with the corresponding i.i.d. results originally derived by Shah [1970. Note on moments of a logistic order statistics, Ann. Math. Statist. 41, 2151–2152.] and the results for the single outlier model discussed by Balakrishnan [1992a. Relationships between single moments of order statistics from non-identically distributed variables. In: Sen, P.K., Salama, I.A. (Eds.), Order Statistics and Nonparametrics: Theory and Applications. Elsevier, Amsterdam, pp. 65–78.] to compute the bias of various linear estimators of the location and scale parameters of the logistic distribution in the presence of multiple outliers.

A new approach to influence diagnostics in superpopulations

Influence analysis on a model is one of the most studied topics from a frequentist viewpoint. Basically, disturbances are introduced into the model in order to measure the influence that one or a set of observations has on statistical analysis. The most common disturbance pattern is that of the omission of the observations whose influence is to be studied. In our model, we assume that there are only one or a few outliers because they may often be detected by deletion methods associated with regression diagnostics. However, these methods may fail in the presence of multiple outliers. In this case, the forward search can be used to avoid the masking and swamping problems. This article presents a Bayes approach for the influence analysis on a model in finite populations. Particularly, we develop a new approach to the study of influence in prediction theory, based on the given data rather than on the sampling design for data collection. We propose that the influence analysis on the superpopulation normal regression model and a measure based on the conditional bias from a Bayesian viewpoint is analyzed. Forward deletion formulae based on our influence measure can be defined, but this topic is beyond the scope of this article. Finally, we apply our proposed influence measure in a classic example for water contents of soil specimens. Copyright © 2005 John Wiley & Sons, Ltd.

Robust Estimation in Multivariate Control Charts for Individual Observations

Multivariate control charts, such as Hotelling's T2 control chart, are used for monitoring several quality characteristics measured simultaneously on a product or process. In the retrospective stage (Phase I) analysis of a historical data set, the presence of multiple outliers may go undetected by the conventional T2 chart, due to masking. In this paper we propose T2 control charts based on robust estimators of location and dispersion. Simulation studies show that the T2 control chart using the minimum volume ellipsoid (MVE) estimators is effective in detecting any reasonable number of outliers.

Exploring process data with the use of robust outlier detection algorithms

Abstract To implement on-line process monitoring techniques such as principal component analysis (PCA) or partial least squares (PLS), it is necessary to extract data associated with the normal operating conditions from the plant historical database for calibrating the models. One way to do this is to use robust outlier detection algorithms such as resampling by half-means (RHM), smallest half volume (SHV), or ellipsoidal multivariate trimming (MVT) in the off-line model building phase. While RHM and SHV are conceptually clear and statistically sound, the computational requirements are heavy. Closest distance to center (CDC) is proposed in this paper as an alternative for outlier detection. The use of Mahalanobis distance in the initial step of MVT for detecting outliers is known to be ineffective. To improve MVT, CDC is incorporated with MVT. The performance was evaluated relative to the goal of finding the best half of a data set. Data sets were derived from the Tennessee Eastman process (TEP) simulator. Comparable results were obtained for RHM, SHV, and CDC. Better performance was obtained when CDC is incorporated with MVT, compared to using CDC and MVT alone. All robust outlier detection algorithms outperformed the standard PCA algorithm. The effect of auto scaling, robust scaling and a new scaling approach called modified scaling were investigated. With the presence of multiple outliers, auto scaling was found to degrade the performance of all the robust techniques. Reasonable results were obtained with the use of robust scaling and modified scaling.

Bivariate boxplots, multiple outliers, multivariate transformations and discriminant analysis: The 1997 Hunter Lecture

Outliers can have a large influence on the model fitted to data. The models we consider are the transformation of data to approximate normality and also discriminant analysis, perhaps on transformed observations. If there are only one or a few outliers, they may often be detected by the deletion methods associated with regression diagnostics. These can be thought of as 'backwards' methods, as they start from a model fitted to all the data. However such methods become cumbersome, and may fail, in the presence of multiple outliers. We instead consider a 'forward' procedure in which very robust methods, such as least median of squares, are used to select a small, outlier free, subset of the data. This subset is increased in size using a search which avoids the inclusion of outliers. During the forward search we monitor quantities of interest, such as score statistics for transformation or, in discriminant analysis, misclassification probabilities. Examples demonstrate how the method very clearly reveals structure in the data and finds influential observations, which appear towards the end of the search. In our examples these influential observations can readily be related to patterns in the original data, perhaps after transformation.