Kinds Of Outliers Research Articles

How to Classify, Detect, and Manage Univariate and Multivariate Outliers, With Emphasis on Pre-Registration

Researchers often lack knowledge about how to deal with outliers when analyzing their data. Even more frequently, researchers do not pre-specify how they plan to manage outliers. In this paper we aim to improve research practices by outlining what you need to know about outliers. We start by providing a functional definition of outliers. We then lay down an appropriate nomenclature/classification of outliers. This nomenclature is used to understand what kinds of outliers can be encountered and serves as a guideline to make appropriate decisions regarding the conservation, deletion, or recoding of outliers. These decisions might impact the validity of statistical inferences as well as the reproducibility of our experiments. To be able to make informed decisions about outliers you first need proper detection tools. We remind readers why the most common outlier detection methods are problematic and recommend the use of the median absolute deviation to detect univariate outliers, and of the Mahalanobis-MCD distance to detect multivariate outliers. An R package was created that can be used to easily perform these detection tests. Finally, we promote the use of pre-registration to avoid flexibility in data analysis when handling outliers.

Spurious PIV vector detection and correction using a penalized least-squares method with adaptive order differentials

Spurious vectors (also called “outliers”) in particle image velocimetry (PIV) experiments can be classified into two categories according to their space distribution characteristics: scattered and clustered outliers. Most of the currently used validation and correction methods treat these two kinds of outliers together without discrimination. In this paper, we propose a new technique based on a penalized least-squares (PLS) method, which allows automatic classification of flows with different types of outliers. PIV vector fields containing scattered outliers are detected and corrected using higher-order differentials, while lower-order differentials are used for the flows with clustered outliers. The order of differentials is determined adaptively by generalized cross-validation and outlier classification. A simple calculation method of eigenvalues of different orders is also developed to expedite computation speed. The performance of the proposed method is demonstrated with four different velocity fields, and the results show that it works better than conventional methods, especially when the number of outliers is large.

Robust and computationally feasible community detection in the presence of arbitrary outlier nodes

Community detection, which aims to cluster $N$ nodes in a given graph into $r$ distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM) is extended to the generalized stochastic block model (GSBM) that allows for adversarial outlier nodes, which are connected with the other nodes in the graph in an arbitrary way. Under this model, we introduce a procedure using convex optimization followed by $k$-means algorithm with $k=r$. Both theoretical and numerical properties of the method are analyzed. A theoretical guarantee is given for the procedure to accurately detect the communities with small misclassification rate under the setting where the number of clusters can grow with $N$. This theoretical result admits to the best-known result in the literature of computationally feasible community detection in SBM without outliers. Numerical results show that our method is both computationally fast and robust to different kinds of outliers, while some popular computationally fast community detection algorithms, such as spectral clustering applied to adjacency matrices or graph Laplacians, may fail to retrieve the major clusters due to a small portion of outliers. We apply a slight modification of our method to a political blogs data set, showing that our method is competent in practice and comparable to existing computationally feasible methods in the literature. To the best of the authors’ knowledge, our result is the first in the literature in terms of clustering communities with fast growing numbers under the GSBM where a portion of arbitrary outlier nodes exist.

Detection of Outliers in a Time Series of Available Parking Spaces

With the provision of any source of real-time information, the timeliness and accuracy of the data provided are paramount to the effectiveness and success of the system and its acceptance by the users. In order to improve the accuracy and reliability of parking guidance systems (PGSs), the technique of outlier mining has been introduced for detecting and analysing outliers in available parking space (APS) datasets. To distinguish outlier features from the APS’s overall periodic tendency, and to simultaneously identify the two types of outliers which naturally exist in APS datasets with intrinsically distinct statistical features, a two-phase detection method is proposed whereby an improved density-based detection algorithm named “local entropy based weighted outlier detection” (EWOD) is also incorporated. Real-world data from parking facilities in the City of Newcastle upon Tyne was used to test the hypothesis. Thereafter, experimental tests were carried out for a comparative study in which the outlier detection performances of the two-phase detection method, statistic-based method, and traditional density-based method were compared and contrasted. The results showed that the proposed method can identify two different kinds of outliers simultaneously and can give a high identifying accuracy of 100% and 92.7% for the first and second types of outliers, respectively.

Interventions in log-linear Poisson autoregression

We consider the problem of estimating and detecting outliers in count time series data following a log-linear observation driven model. Log-linear models for count time series arise naturally because they correspond to the canonical link function of the Poisson distribution. They yield both positive and negative dependence, and covariate information can be conveniently incorporated. Within this framework, we establish test procedures for detection of unusual events (‘interventions’) leading to different kinds of outliers, we implement joint maximum likelihood estimation of model parameters and outlier sizes and we derive formulae for correcting the data for detected interventions. The effectiveness of the proposed methodology is illustrated with two real data examples. The first example offers a fresh data analytic point of view towards the polio data. Our methodology identifies different forms of outliers in these data by an observation-driven model. The second example deals with some campylobacterosis data which we analyzed in a previous communication, by a different model. The results are reconfirmed by the new model that we put forward in this communication. The reliability of the procedure is verified using artificial data examples.

A continuous optimization framework for hybrid system identification

We propose a new framework for hybrid system identification, which relies on continuous optimization. This framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions. The former is inspired by traditional estimation methods, while the latter is inspired by recent algebraic and support vector regression approaches to hybrid system identification. In both cases, the identification problem is recast as a continuous optimization program involving only the real parameters of the model as variables, thus avoiding the use of discrete optimization. This program can be solved efficiently by using standard optimization methods even for very large data sets. In addition, the proposed framework easily incorporates robustness to different kinds of outliers through the choice of the loss function.

ARFIMA processes and outliers: a weighted likelihood approach

In this paper, we consider the problem of robust estimation of the fractional parameter, d, in long memory autoregressive fractionally integrated moving average processes, when two types of outliers, i.e. additive and innovation, are taken into account without knowing their number, position or intensity. The proposed method is a weighted likelihood estimation (WLE) approach for which needed definitions and algorithm are given. By an extensive Monte Carlo simulation study, we compare the performance of the WLE method with the performance of both the approximated maximum likelihood estimation (MLE) and the robust M-estimator proposed by Beran (Statistics for Long-Memory Processes, Chapman & Hall, London, 1994). We find that robustness against the two types of considered outliers can be achieved without loss of efficiency. Moreover, as a byproduct of the procedure, we can classify the suspicious observations in different kinds of outliers. Finally, we apply the proposed methodology to the Nile River annual minima time series.

Outlier detection in ARMA models

Abstract. We consider an autoregressive moving-average (ARMA) time series where the observations are perturbed by two kinds of outliers: an additive outlier (AO) or an innovation outlier (IO). Abraham and Yatawara [Journal of Time Series Analysis (1988) Vol. 9, pp. 109–19] investigate a sequential test which successively detects and identifies the outlier type. In this article, we propose an extension of this test, called ‘modified sequential test’, which performs the two procedures simultaneously and coherently. The asymptotic distribution of the test statistic is calculated under the null hypothesis that no outlier is present. Comparison of the two test procedures using simulation experiments shows that the proposed test gives a better power especially in the case of an IO.

Trimming Tools in Exploratory Data Analysis

Exploratory graphical tools based on trimming are proposed for detecting main clusters in a given dataset. The trimming is obtained by resorting to trimmed k-means methodology. The analysis always reduces to the examination of real valued curves, even in the multivariate case. As the technique is based on a robust clustering criterium, it is able to handle the presence of different kinds of outliers. An algorithm is proposed to carry out this (computer intensive) method. As with classical k-means, the method is specially oriented to mixtures of spherical distributions. A possible generalization is outlined to overcome this drawback.

On Robustness in the Logistic Regression Model

SUMMARY We investigate robustness in the logistic regression model. Copas has studied two forms of robust estimator: A robust-resistant estimate of Pregibon and an estimate based on a misclassification model. He concluded that robust-resistant estimates are much more biased in small samples than the usual logistic estimate is and recommends a bias-corrected version of the misclassification estimate. We show that there are other versions of robust-resistant estimates which have bias often approximately the same as and sometimes even less than the logistic estimate; these estimates belong to the Mallows class. In addition, the corrected misclassification estimate is inconsistent at the logistic model; we develop a simple consistent modification. The modified estimate is a member of the Mallows class but, unlike most robust estimates, it has an interpretable tuning constant. The results are illustrated on data sets featuring different kinds of outliers.