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Metric-based summary statistics such as mean and covariance have been introduced in neural spike train space. They can properly describe template and variability in spike train data, but are often sensitive to outliers and expensive to compute. Recent studies also examine outlier detection and classification methods on point processes. These tools provide reasonable result, whereas the accuracy remains at a low level in certain cases. In this study, we propose to adopt a well-established notion of statistical depth to the spike train space. This framework can naturally define the median in a set of spike trains, which provides a robust description of the ‘template’ of the observations. It also provides a principled method to identify ‘outliers’ and classify data from different categories. We systematically compare the new median, outlier detection and classification tools with state-of-the-art competing methods. The result shows the median has superior description for template than the mean. Moreover, the proposed outlier detection and classification perform more accurately than previous methods. [ABSTRACT FROM AUTHOR]

Although under-five mortality (U5M) rates have declined worldwide, many countries in sub-Saharan Africa still have much higher rates. Detection of subnational areas with unusually higher U5M rates could support targeted high impact child health interventions. We propose a novel group outlier detection statistic for identifying areas with extreme U5M rates under a multivariate survival data model. The performance of the proposed statistic was evaluated through a simulation study. We applied the proposed method to an analysis of child survival data in Malawi to identify sub-districts with unusually higher or lower U5M rates. The simulation study showed that the proposed outlier statistic can detect unusual high or low mortality groups with a high accuracy of at least 90%, for datasets with at least 50 clusters of size 80 or more. In the application, at most 7 U5M outlier sub-districts were identified, based on the best fitting model as measured by the Akaike information criterion (AIC). [ABSTRACT FROM AUTHOR]

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets. [ABSTRACT FROM AUTHOR]

Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that lie an abnormal distance from the other observation. The main achievements of this study consist of a novel mathematics-supported approach beside statistical regression models to identify and treat the outlier observations without direct elimination for a great and emerging challenge in humankind, such as neurodegenerative diseases. By this approach, a new method named as CMTMSOM is proposed with the contributions of the powerful convex and continuous optimization techniques referred to as conic quadratic programing. This method, based on the mean-shift outlier regression model, is developed by combining robustness of M-estimation and stability of Tikhonov regularization. We apply our method and other parametric models on Parkinson telemonitoring dataset which is a real-world dataset in Neuroscience. Then, we compare these methods by using well-known method-free performance measures. The results indicate that the CMTMSOM method performs better than current parametric models. [ABSTRACT FROM AUTHOR]

Outlier detection can be seen as a pre-processing step for locating data points in a data sample, which do not conform to the majority of observations. Various techniques and methods for outlier detection can be found in the literature dealing with different types of data. However, many data sets are inflated by true zeros and, in addition, some components/variables might be of compositional nature. Important examples of such data sets are the Structural Earnings Survey, the Structural Business Statistics, the European Statistics on Income and Living Conditions, tax data or – as in this contribution – household expenditure data which are used, for example, to estimate the Purchase Power Parity of a country. In this work, robust univariate and multivariate outlier detection methods are compared by a complex simulation study that considers various challenges included in data sets, namely structural (true) zeros, missing values, and compositional variables. These circumstances make it difficult or impossible to flag true outliers and influential observations by well-known outlier detection methods. Our aim is to assess the performance of outlier detection methods in terms of their effectiveness to identify outliers when applied to challenging data sets such as the household expenditures data surveyed all over the world. Moreover, different methods are evaluated through a close-to-reality simulation study. Differences in performance of univariate and multivariate robust techniques for outlier detection and their shortcomings are reported. We found that robust multivariate methods outperform robust univariate methods. The best performing methods in finding the outliers and in providing a low false discovery rate were found to be the generalized S estimators (GSE), the BACON-EEM algorithm and a compositional method (CoDa-Cov). In addition, these methods performed also best when the outliers are imputed based on the corresponding outlier detection method and indicators are estimated from the data sets. [ABSTRACT FROM AUTHOR]

Despite the popularity of high dimension, low sample size data analysis, there has not been enough attention to the sample integrity issue, in particular, a possibility of outliers in the data. A new outlier detection procedure for data with much larger dimensionality than the sample size is presented. The proposed method is motivated by asymptotic properties of high-dimensional distance measures. Empirical studies suggest that high-dimensional outlier detection is more likely to suffer from a swamping effect rather than a masking effect, thus yields more false positives than false negatives. We compare the proposed approaches with existing methods using simulated data from various population settings. A real data example is presented with a consideration on the implication of found outliers. [ABSTRACT FROM AUTHOR]

Mahalanobis square distances (MSDs) based on robust estimators improves outlier detection performance in multivariate data. However, the unbiasedness of robust estimators are not guaranteed when the sample size is small and this reduces their performance in outlier detection. In this study, we propose a framework that uses MSDs with incorporatedsmall sample correction factor(c) and show its impact on performance when the sample size is small. This is achieved by using two prototypes, minimum covariance determinant estimator andS-estimators with bi-weight andt-biweight functions. The results from simulations show that distribution of MSDs for non-extreme observations are more likely to fit to chi-square withpdegrees of freedom and MSDs of the extreme observations fit toFdistribution, whencis incorporated into the model. However, withoutc, the distributions deviate significantly from chi-square andFobserved for the case with incorporatedc. These results are even more prominent forS-estimators. We present seven distinct comparison methods with robust estimators and various cut-off values and test their outlier detection performance with simulated data. We also present an application of some of these methods to the real data. [ABSTRACT FROM PUBLISHER]

Although under-five mortality (U5M) rates have declined worldwide, many countries in sub-Saharan Africa still have much higher rates. Detection of subnational areas with unusually higher U5M rates could support targeted high impact child health interventions. We propose a novel group outlier detection statistic for identifying areas with extreme U5M rates under a multivariate survival data model. The performance of the proposed statistic was evaluated through a simulation study. We applied the proposed method to an analysis of child survival data in Malawi to identify sub-districts with unusually higher or lower U5M rates. The simulation study showed that the proposed outlier statistic can detect unusual high or low mortality groups with a high accuracy of at least 90%, for datasets with at least 50 clusters of size 80 or more. In the application, at most 7 U5M outlier sub-districts were identified, based on the best fitting model as measured by the Akaike information criterion (AIC)., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)

Functional box plots satisfy two needs; visualization of functional data, and the calculation of important box plot statistics. Data visualization illuminates key characteristics of functional sets missed by statistical tests and summary statistics. The calculation of box plot statistics for functional sets permits a novel comparison more suited to functional data. The functional box plot uses a depth method to visualize and rank smooth functional curves in terms of a mean, box, whiskers, and outliers. The functional box plot improves upon other classic functional data analysis tools such as functional principal components and discriminant analysis for outlier detection. This research adds wavelet analysis as a generating mechanism along with depth for functional box plots to visualize functional data and calculate relevant statistics. The wavelet analysis of variance box plot tool gives competitive error rates in Gaussian test cases with magnitude outliers, and outperforms the functional box plot, for Gaussian test cases with shape outliers. Further, we show wavelet analysis is well suited at approximating irregular and noisy functional data and show the enhanced capability of WANOVA box plots to classify shape outliers which follow a different pattern than other functional data for both simulated and real data instances. [ABSTRACT FROM AUTHOR]

To estimate the approximate relationship between the dependent variable and its independent variables, it is necessary to diagnose outliers commonly present in numerous real applications before constructing the model. Nevertheless, the techniques of the standard support vector regression (-SVR) and modified support vector regression () achieved good performance for outliers' detection for nonlinear functions with high-dimensional inputs. However, they still suffer from the costs of time and the setting of parameters. In this study, we propose a practical method for detecting outliers, using non-sparse-SVR, which minimizes time cost and introduces fixed parameters. We apply this approach for real and simulation data sets to test its effectiveness. [ABSTRACT FROM AUTHOR]

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that lie an abnormal distance from the other observation. The main achievements of this study consist of a novel mathematics-supported approach beside statistical regression models to identify and treat the outlier observations without direct elimination for a great and emerging challenge in humankind, such as neurodegenerative diseases. By this approach, a new method named as CM T MSOM is proposed with the contributions of the powerful convex and continuous optimization techniques referred to as conic quadratic programing. This method, based on the mean-shift outlier regression model, is developed by combining robustness of M-estimation and stability of Tikhonov regularization. We apply our method and other parametric models on Parkinson telemonitoring dataset which is a real-world dataset in Neuroscience. Then, we compare these methods by using well-known method-free performance measures. The results indicate that the CM T MSOM method performs better than current parametric models., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

This work proposes a two-stage procedure for identifying outlying observations in a large-dimensional data set. In the first stage, an outlier identification measure is defined by using a max-normal statistic and a clean subset that contains non-outliers is obtained. The identification of outliers can be deemed as a multiple hypothesis testing problem, then, in the second stage, we explore the asymptotic distribution of the proposed measure, and obtain the threshold of the outlying observations. Furthermore, in order to improve the identification power and better control the misjudgment rate, a one-step refined algorithm is proposed. Simulation results and two real data analysis examples show that, compared with other methods, the proposed procedure has great advantages in identifying outliers in various data situations. [ABSTRACT FROM AUTHOR]

Zero adjusted regression models are used to fit variables that are discrete at zero and continuous at some interval of the positive real numbers. Diagnostic analysis in these models is usually performed using the randomized quantile residual, which is useful for checking the overall adequacy of a zero adjusted regression model. However, it may fail to identify some outliers. In this work, we introduce a class of residuals for outlier identification in zero adjusted regression models. Monte Carlo simulation studies and two applications suggest that one of the residuals of the class introduced here has good properties and detects outliers that are not identified by the randomized quantile residual. [ABSTRACT FROM AUTHOR]

Zero adjusted regression models are used to fit variables that are discrete at zero and continuous at some interval of the positive real numbers. Diagnostic analysis in these models is usually performed using the randomized quantile residual, which is useful for checking the overall adequacy of a zero adjusted regression model. However, it may fail to identify some outliers. In this work, we introduce a class of residuals for outlier identification in zero adjusted regression models. Monte Carlo simulation studies and two applications suggest that one of the residuals of the class introduced here has good properties and detects outliers that are not identified by the randomized quantile residual., Competing Interests: No potential conflict of interest was reported by the authors., (© 2019 Informa UK Limited, trading as Taylor & Francis Group.)

In this paper, we revisit the alternative outlier model of Thompson [A note on restricted maximum likelihood estimation with an alternative outlier model, J. Roy. Stat. Soc. Ser. B 47 (1985), pp. 53-55] for detecting outliers in the linear model. Gumedze et al. [A variance shift model for detection of outliers in the linear mixed model, Comput. Statist. Data Anal. 54 (2010), pp. 2128-2144] called this model the variance shift outlier model (VSOM). The basic idea behind the VSOM is to detect observations with inflated variance and isolate them for further investigation. The VSOM is appealing because it downweights an outlier in the analysis, with the weighting determined automatically as part of the estimation procedure. We set up the VSOM as a linear mixed model and then use the likelihood ratio test (LRT) statistic as an objective measure for determining whether the weighting is required, i.e. whether the observation is an outlier. We also derived one-step updates of the variance parameter estimates based on observed, expected and average information matrices to obtain one-step LRT statistics which usually require less computation. Both the fully iterated and one-step LRTs are functions of the squared standard residuals from the null model and therefore can be computed directly without the need to fit the VSOM. We investigated the properties of the likelihood ratio tests and compare them. An extension of the model to detect a group of outliers is also given. We illustrate the proposed methodology using simulated datasets and a real dataset. [ABSTRACT FROM AUTHOR]

Outlier detection can be seen as a pre-processing step for locating data points in a data sample, which do not conform to the majority of observations. Various techniques and methods for outlier detection can be found in the literature dealing with different types of data. However, many data sets are inflated by true zeros and, in addition, some components/variables might be of compositional nature. Important examples of such data sets are the Structural Earnings Survey, the Structural Business Statistics, the European Statistics on Income and Living Conditions, tax data or - as in this contribution - household expenditure data which are used, for example, to estimate the Purchase Power Parity of a country. In this work, robust univariate and multivariate outlier detection methods are compared by a complex simulation study that considers various challenges included in data sets, namely structural (true) zeros, missing values, and compositional variables. These circumstances make it difficult or impossible to flag true outliers and influential observations by well-known outlier detection methods. Our aim is to assess the performance of outlier detection methods in terms of their effectiveness to identify outliers when applied to challenging data sets such as the household expenditures data surveyed all over the world. Moreover, different methods are evaluated through a close-to-reality simulation study. Differences in performance of univariate and multivariate robust techniques for outlier detection and their shortcomings are reported. We found that robust multivariate methods outperform robust univariate methods. The best performing methods in finding the outliers and in providing a low false discovery rate were found to be the generalized S estimators (GSE), the BACON-EEM algorithm and a compositional method (CoDa-Cov). In addition, these methods performed also best when the outliers are imputed based on the corresponding outlier detection method and indicators are estimated from the data sets., Competing Interests: No potential conflict of interest was reported by the authors., (© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.)

Support Vector Regression (SVR) is gaining in popularity in the detection of outliers and classification problems in high-dimensional data (HDD) as this technique does not require the data to be of full rank. In real application, most of the data are of high dimensional. Classification of high-dimensional data is needed in applied sciences, in particular, as it is important to discriminate cancerous cells from non-cancerous cells. It is also imperative that outliers are identified before constructing a model on the relationship between the dependent and independent variables to avoid misleading interpretations about the fitting of a model. The standard SVR and the μ-ε-SVR are able to detect outliers; however, they are computationally expensive. The fixed parameters support vector regression (FP-ε-SVR) was put forward to remedy this issue. However, the FP-ε-SVR using ε-SVR is not very successful in identifying outliers. In this article, we propose an alternative method to detect outliers i.e. by employing nu-SVR. The merit of our proposed method is confirmed by three real examples and the Monte Carlo simulation. The results show that our proposed nu-SVR method is very successful in identifying outliers under a variety of situations, and with less computational running time. [ABSTRACT FROM AUTHOR]

The presence of contamination often called outlier is a very common attribute in data. Among other causes, outliers in a homoscedastic model make the model heteroscedastic. Moreover, outliers distort diagnostic tools for heteroscedasticity such that it may not be correctly identified. In this article, we show how outliers affect heteroscedasticity diagnostics. We then proposed a robust procedure for detecting heteroscedasticity in the presence of outliers by robustifying the non-robust component of the Goldfeld–Quandt (GQ) test. The performance of the proposed procedure is examined using simulation experiment and real data sets. The proposed procedure offers great improvement where the conventional GQ and other procedures fail. [ABSTRACT FROM AUTHOR]

We provide a method for simultaneous variable selection and outlier identification using the mean-shift outlier model. The procedure consists of two steps: the first step is to identify potential outliers, and the second step is to perform all possible subset regressions for the mean-shift outlier model containing the potential outliers identified in step 1. This procedure is helpful for model selection while simultaneously considering outlier identification, and can be used to identify multiple outliers. In addition, we can evaluate the impact on the regression model of simultaneous omission of variables and interesting observations. In an example, we provide detailed output from the R system, and compare the results with those using posterior model probabilities as proposed by Hoeting et al. [Comput. Stat. Data Anal. 22 (1996), pp. 252-270] for simultaneous variable selection and outlier identification. [ABSTRACT FROM AUTHOR]

As there is an extensive body of research on diagnostics in regression models, various outlier detection methods have been developed. These methods have been extended to mixed effects models and generalized linear models, but there exist intrinsic drawbacks and limitations. This paper presents two-dimensional plots to identify discordant subjects and observations in generalized linear mixed effects models, displaying discordance in two directions. The sTudentized Residual Sum of Squares is not an extension of any regression tools but a new approach designed to efficiently reflect the characteristics of repeated measures. And this noteworthy clustering of outliers is identified in the plot. Applications to real-life examples are presented to illustrate the favorable/beneficial performance of the new tool. [ABSTRACT FROM AUTHOR]

The Zero-inflated Poisson distribution has been used in the modeling of count data in different contexts. This model tends to be influenced by outliers because of the excessive occurrence of zeroes, thus outlier identification and robust parameter estimation are important for such distribution. Some outlier identification methods are studied in this paper, and their applications and results are also presented with an example. To eliminate the effect of outliers, two robust parameter estimates are proposed based on the trimmed mean and the Winsorized mean. Simulation results show the robustness of our proposed parameter estimates. [ABSTRACT FROM AUTHOR]

Robust estimation of parameters, and identification of specific data points that are discordant with an assumed model, are often treated as different statistical problems. The two aims are, however, closely inter-related and in many cases the two analyses are required simultaneously. We present a simple diagnostic plot that connects existing robust estimators with simultaneous outlier detection, and uses the concept of false discovery rates to allow for the multiple comparisons induced by considering each point as a potential outlier. It is straightforward to implement, and applicable in any situation for which robust estimation procedures exist. Several examples are given. [ABSTRACT FROM AUTHOR]

A cluster methodology, motivated by a robust similarity matrix is proposed for identifying likely multivariate outlier structure and to estimate weighted least-square (WLS) regression parameters in linear models. The proposed method is an agglomeration of procedures that begins from clustering then-observations through a test of ‘no-outlier hypothesis’ (TONH) to a weighted least-square regression estimation. The cluster phase partition then-observations intoh-set called main cluster and a minor cluster of sizen−h. A robust distance emerge from the main cluster upon which a test of no outlier hypothesis’ is conducted. An initialWLSregression estimation is computed from the robust distance obtained from the main cluster. Until convergence, a re-weighted least-squares (RLS) regression estimate is updated with weights based on the normalized residuals. The proposed procedure blends an agglomerative hierarchical cluster analysis of a complete linkage through theTONHto the Re-weighted regression estimation phase. Hence, we propose to call it cluster-based re-weighted regression (CBRR). TheCBRRis compared with three existing procedures using two data sets known to exhibit masking and swamping. The performance ofCBRRis further examined through simulation experiment. The results obtained from the data set illustration and the Monte Carlo study shows that theCBRRis effective in detecting multivariate outliers where other methods are susceptible to it. TheCBRRdoes not require enormous computation and is substantially not susceptible to masking and swamping. [ABSTRACT FROM AUTHOR]

The analysis of compositional data using the log-ratio approach is based on ratios between the compositional parts. Zeros in the parts thus cause serious difficulties for the analysis. This is a particular problem in case of structural zeros, which cannot be simply replaced by a non-zero value as it is done, e.g. for values below detection limit or missing values. Instead, zeros to be incorporated into further statistical processing. The focus is on exploratory tools for identifying outliers in compositional data sets with structural zeros. For this purpose, Mahalanobis distances are estimated, computed either directly for subcompositions determined by their zero patterns, or by using imputation to improve the efficiency of the estimates, and then proceed to the subcompositional and subgroup level. For this approach, new theory is formulated that allows to estimate covariances for imputed compositional data and to apply estimations on subgroups using parts of this covariance matrix. Moreover, the zero pattern structure is analyzed using principal component analysis for binary data to achieve a comprehensive view of the overall multivariate data structure. The proposed tools are applied to larger compositional data sets from official statistics, where the need for an appropriate treatment of zeros is obvious. [ABSTRACT FROM AUTHOR]

Independence of error terms in a linear regression model, often not established. So a linear regression model with correlated error terms appears in many applications. According to the earlier studies, this kind of error terms, basically can affect the robustness of the linear regression model analysis. It is also shown that the robustness of the parameters estimators of a linear regression model can stay using the M-estimator. But considering that, it acquires this feature as the result of establishment of its efficiency. Whereas, it has been shown that the minimum Matusita distance estimators, has both features robustness and efficiency at the same time. On the other hand, because the Cochrane and Orcutt adjusted least squares estimators are not affected by the dependence of the error terms, so they are efficient estimators. Here we are using of a non-parametric kernel density estimation method, to give a new method of obtaining the minimum Matusita distance estimators for the linear regression model with correlated error terms in the presence of outliers. Also, simulation and real data study both are done for the introduced estimation method. In each case, the proposed method represents lower biases and mean squared errors than the other two methods. [ABSTRACT FROM AUTHOR]