Multiple Outliers Research Articles

Robust PC with wild bootstrap estimation of linear model in the presence of outliers, multicollinearity and heteroscedasticity error variance

The regression model estimator is considered efficient if it is robust and resistant to the presence of heteroscedasticity variance, multicollinearity or unusual observations called outliers. However, in regard to these problems, the wild bootstrap and robust wild bootstrap are no longer efficient since they could not produce the smallest variance. Hence this research investigates the use of robust PC with wild bootstrap techniques on regression model as an estimator for real and simulation data in a situation where multicollinearity, heteroscedasticity and multiple outliers are present. This paper proposed a robust procedure based on the weighted residuals which combined the Tukey bisquare weighted function, principal component analysis (PCA) to remedy the multicollinearity problems, least trimmed squares (LTS) estimator, robust location and scale, and the wild bootstrap sampling procedure of Wu and Liu that remedy the heteroscedasticity error variance. RPCW Boot Wu and RPCW Boot Liu were obtained through a modified version of R Boot Wu and R Boot Liu. Finally, based on the real data and simulation study, the performance of the RPCW Boot Wu and RPCW Boot Liu is compared with the existing R Boot Wu, R Boot Liu and also with Boot Wu, Boot Liu using the biased, RMSE and standard error. The numerical example and simulation study shows that the RPCW Boot Wu and RPCW Boot Liu techniques have proven to be a good alternative estimator for regression model with lower standard error values.

Whole-genome sequencing illuminates multifaceted targets of selection to humic substances in Eurasian perch.

Extreme environments are inhospitable to the majority of species, but some organisms are able to survive in such hostile conditions due to evolutionary adaptations. For example, modern bony fishes have colonized various aquatic environments, including perpetually dark, hypoxic, hypersaline and toxic habitats. Eurasian perch (Perca fluviatilis) is among the few fish species of northern latitudes that is able to live in very acidic humic lakes. Such lakes represent almost “nocturnal” environments; they contain high levels of dissolved organic matter, which in addition to creating a challenging visual environment, also affects a large number of other habitat parameters and biotic interactions. To reveal the genomic targets of humic‐associated selection, we performed whole‐genome sequencing of perch originating from 16 humic and 16 clear‐water lakes in northern Europe. We identified over 800,000 single nucleotide polymorphisms, of which >10,000 were identified as potential candidates under selection (associated with >3000 genes) using multiple outlier approaches. Our findings suggest that adaptation to the humic environment may involve hundreds of regions scattered across the genome. Putative signals of adaptation were detected in genes and gene families with diverse functions, including organism development and ion transportation. The observed excess of variants under selection in regulatory regions highlights the importance of adaptive evolution via regulatory elements, rather than via protein sequence modification. Our study demonstrates the power of whole‐genome analysis to illuminate the multifaceted nature of humic adaptation and provides the foundation for further investigation of causal mutations underlying phenotypic traits of ecological and evolutionary importance.

Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels

Information criteria for model choice are extended to the detection of outliers in regression models. For deletion of observations (hard trimming) the family of models is generated by monitoring properties of the fitted models as the trimming level is varied. For soft trimming (downweighting of observations), some properties are monitored as the efficiency or breakdown point of the robust regression is varied. Least Trimmed Squares and the Forward Search are used to monitor hard trimming, with MM- and S-estimation the methods for soft trimming. Bayesian Information Criteria (BIC) for both scenarios are developed and results about their asymptotic properties provided. In agreement with the theory, simulations and data analyses show good performance for the hard trimming methods for outlier detection. Importantly, this is achieved very simply, without the need to specify either significance levels or decision rules for multiple outliers.

Pediatric Forensic Analysis

Although the presence of forensic evidence aids in successful prosecution of sexual abuse, controversy remains regarding the timing and indications for collection of forensic evidence in child sexual abuse/assault. The purpose of this study was to describe forensic evidence findings in acute child sexual abuse after implementing more inclusive indications for collection of evidence in a pediatric emergency department and to identify factors associated with yield of DNA. Of the 306 evidence kits collected and analyzed, 110 (35.9%) kits were positive for an interpretable DNA profile foreign to the patient, which may or may not have contributed to the investigation of the sexual abuse concern. Several factors were associated with increased forensic yield of identifiable foreign DNA: increased age of child victim, 48 hours or less between the latest incident of sexual abuse and the collection of forensic evidence, child disclosure of high-severity sexual abuse acts (anal-genital or genital-genital contact) in the pediatric emergency department forensic interview, and sexual abuse by a nonrelative perpetrator. Finally, although certain factors were associated with increased yield of identifiable foreign DNA within each factor, there were multiple outliers where failure to collect forensic evidence would have resulted in a loss of recoverable foreign DNA.

Enriching stochastic model updating metrics: An efficient Bayesian approach using Bray-Curtis distance and an adaptive binning algorithm

In practical engineering, experimental data is not fully in line with the true system response due to various uncertain factors, e.g., parameter imprecision, model uncertainty, and measurement errors. In the presence of mixed sources of aleatory and epistemic uncertainty, stochastic model updating is a powerful tool for model validation and parameter calibration. This paper investigates the use of Bray-Curtis (B-C) distance in stochastic model updating and proposes a Bayesian approach addressing a scenario where the dataset contains multiple outliers. In the proposed method, a B-C distance-based uncertainty quantification metric is employed, that rewards models for which the discrepancy between observations and simulated samples is small while penalizing those which exhibit large differences. To improve the computational efficiency, an adaptive binning algorithm is developed and embedded into the Bayesian approximate computation framework. The merit of this algorithm is that the number of bins is automatically selected according to the difference between the experimental data and the simulated data. The effectiveness and efficiency of the proposed method is verified via two numerical cases and an engineering case from the NASA 2020 UQ challenge. Both static and dynamic cases with explicit and implicit propagation models are considered.

A New Reconstruction Method for Measurement Data With Multiple Outliers

Measurement data sometimes contains a few outliers that have a large deviation from actual value. For such data, the reconstruction results will be greatly distorted around the outliers. To solve this problem, a robust surface approximation method based on moving total least squares (MTLS) is presented in this paper, in which an improved random sample consensus (RANSAC) and classification and regression tree (CART) are introduced into the support domain to detect outliers. Firstly, the residuals of points in the support domain are calculated by the improved RANSAC with an introduced parameter, and then the abnormal residuals are identified by CART algorithm. The points corresponding to abnormal residuals are considered as abnormal points. After the abnormal points are eliminated, the remaining data is processed by weighted total least squares (WTLS) to obtain local fitting parameters. This method can avoid the adverse impact of human intervention and over elimination. The reconstruction results of the numerical simulation and measurement experiment illustrate the effectiveness of our method.

Prediction from Transmuted Rayleigh Distribution in the Presence of Outliers

The quality of the procedures used in statistical analysis depends largely on the assumed probability distribution. However, there are still many problems with data that do not follow any of the classical distributions; therefore, researchers have developed many standardized probability distributions by generalizing or transforming them. Transmuted Rayleigh distribution extends the Rayleigh distribution in the analysis of data and provides larger flexibility in modeling real data. In this article, Bayesian predictive intervals for order statistics of future observations from this distribution are obtained in the presence of outliers when the scale parameter is unknown. The slippage outlier model is utilized in addition to the two‐sample prediction scheme. We shall consider two cases: (i) a single outlier in the informative sample and (ii) multiple outliers in the future sample. Numerical computations are obtained to illustrate the effect of outliers on the Bayesian predictive intervals.

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.

A robust TDOA based solution for source location using mixed Huber loss

This paper proposes a source localization solution robust to measurement outliers in time differences of arrivals (TDOA) measurements. The solution uses a piecewise loss function named as mixed Huber loss (MHL) proposed based on the classical Huber loss (HL) and its refined version. The MHL is able to effectively mitigate the impact of all levels of measurement outliers by setting two triggering thresholds. In practice, appropriate triggering threshold values can be obtained through simulation given the level of measurement noise and a rough range of potential measurement outliers. A clustering based approach is proposed to further improve the robustness of localization solution against reference sensor related outliers. Simulations are included to examine the solution's performance and compare it with several benchmarks. The proposed MHL based solution is shown to be superior to the classical solution and the benchmarks. The solution is shown to be even robust to multiple measurement outliers. Furthermore, the influence of range measurement outliers in the reference sensor can be effectively mitigated by the clustering based approach.

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.

Unsupervised time series outlier detection with diversity-driven convolutional ensembles

With the sweeping digitalization of societal, medical, industrial, and scientific processes, sensing technologies are being deployed that produce increasing volumes of time series data, thus fueling a plethora of new or improved applications. In this setting, outlier detection is frequently important, and while solutions based on neural networks exist, they leave room for improvement in terms of both accuracy and efficiency. With the objective of achieving such improvements, we propose a diversity-driven, convolutional ensemble. To improve accuracy, the ensemble employs multiple basic outlier detection models built on convolutional sequence-to-sequence autoencoders that can capture temporal dependencies in time series. Further, a novel diversity-driven training method maintains diversity among the basic models, with the aim of improving the ensemble's accuracy. To improve efficiency, the approach enables a high degree of parallelism during training. In addition, it is able to transfer some model parameters from one basic model to another, which reduces training time. We report on extensive experiments using real-world multivariate time series that offer insight into the design choices underlying the new approach and offer evidence that it is capable of improved accuracy and efficiency.

Genomic Signatures of Domestication Selection in the Australasian Snapper (Chrysophrys auratus).

Domestication of teleost fish is a recent development, and in most cases started less than 50 years ago. Shedding light on the genomic changes in key economic traits during the domestication process can provide crucial insights into the evolutionary processes involved and help inform selective breeding programmes. Here we report on the recent domestication of a native marine teleost species in New Zealand, the Australasian snapper (Chrysophrys auratus). Specifically, we use genome-wide data from a three-generation pedigree of this species to uncover genetic signatures of domestication selection for growth. Genotyping-By-Sequencing (GBS) was used to generate genome-wide SNP data from a three-generation pedigree to calculate generation-wide averages of FST between every generation pair. The level of differentiation between generations was further investigated using ADMIXTURE analysis and Principal Component Analysis (PCA). After that, genome scans using Bayescan, LFMM and XP-EHH were applied to identify SNP variants under putative selection following selection for growth. Finally, genes near candidate SNP variants were annotated to gain functional insights. Analysis showed that between generations FST values slightly increased as generational time increased. The extent of these changes was small, and both ADMIXTURE analysis and PCA were unable to form clear clusters. Genome scans revealed a number of SNP outliers, indicative of selection, of which a small number overlapped across analyses methods and populations. Genes of interest within proximity of putative selective SNPs were related to biological functions, and revealed an association with growth, immunity, neural development and behaviour, and tumour repression. Even though few genes overlapped between outlier SNP methods, gene functionalities showed greater overlap between methods. While the genetic changes observed were small in most cases, a number of outlier SNPs could be identified, of which some were found by more than one method. Multiple outlier SNPs appeared to be predominately linked to gene functionalities that modulate growth and survival. Ultimately, the results help to shed light on the genomic changes occurring during the early stages of domestication selection in teleost fish species such as snapper, and will provide useful candidates for the ongoing selective breeding in the future of this and related species.

Stochastic comparisons of series and parallel systems with dependent log-logistic components

This paper studies the usual stochastic, star, convex transform, and dispersive orders of both series and parallel systems comprised of dependent log-logistic components. We establish that, without any restriction on the parameters, the lifetime of a parallel or series system with dependent components is smaller than that with dependent homogeneous components in the sense of the dispersive orders. Sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of multiple outlier dependent log-logistic distributed components. Under certain conditions on the Archimedean copula and the parameter, we also discuss convex transform order of series and parallel systems.

Multiple Upper Outlier Detection Procedure in Generalized Exponential Sample

Hawkins [6] defined an outlier as an observation that is significantly different from the remaining observations in a dataset so as to arouse suspicion that it was generated by different mechanism. Barnett and Lewis [2] defined an outlier as an observation that deviates significantly in the sample in which it occurs. Spatial outliers are different from outliers and many authors like Singh and Lalitha [9]. Outlier detection procedures for two parameter gamma distribution have been discussed by many authors. But one major disadvantage of the gamma distribution is that the distribution (or survival) function cannot be expressed in a closed form if the shape parameter is not an integer. Since it is in terms of an incomplete gamma function, one needs to obtain the distribution/survival function or the failure rate by numerical integration. This is a limitation in the usage of gamma distribution. It is observed that the generalized exponential distribution can be used as an alternative to the gamma distribution in many situations. Different properties like monotonicity of the hazard functions and tail behaviours of the gamma distribution and that of the generalized exponential distribution are quite similar in nature. But the latter one has a nice compact distribution (or survival) function. It is observed that for a given gamma distribution there exists a generalized exponential distribution so that the two distribution functions are almost identical. Since the gamma distribution function does not have a compact form, efficiently generating gamma random numbers is known to be problematic. It was observed that for all practical purposes it is possible to generate approximate gamma random numbers using generalized exponential distribution and the random samples thus obtained cannot be differentiated using any statistical tests. Many authors proposed a location and scale invariant test based on the test statistic Zk for testing the upper outliers in two-parameter exponential sample. Kumar et. al. [7] and Singh and Lalitha [10] have proposed test statistics for testing multiple upper outlier detection in gamma sample. Various test statistics have been proposed to detect outliers in an exponential sample. Likes [8] also proposed a new test statistics to detect outlier in the exponential case. In this paper, the test statistic proposed by Likes has been used to detect outliers in a generalized exponential sample and the critical value of the test statistics has been obtained. A simulation study is carried out to compare the theoretical developments.

Joint estimation and regularized aggregation of brain network in FMRI data

BackgroundIn the Gaussian graphical model framework, precision matrices reveal conditional dependence structure among random variables. In functional magnetic resonance imaging (fMRI) data, estimating such precision matrices of multi-subjects and aggregating them to a group-level is an essential step for constructing a group brain network. New methodIn this article, we considered joint estimation of multiple precision matrices with regularized aggregation. Also, in the construction of a group precision matrix, we integrated robust aggregation to the estimation. In the estimation of individual precision matrices, we took a regularization approach to induce sparsity, which made brain network estimation more realistic. ResultsWe demonstrated the effectiveness of the proposed method through simulated examples, and analyses on real fMRI data acquired during eye movement tasks assessing cognitive control. For the fMRI data, the joint estimation of multiple precision matrices (JEMP) with regularized aggregation (RA) captured more robust associations between task-relevant neural regions of interest (ROIs), compared to the analyses using JEMP alone. The JEMP with RA also was sensitive to increased neural efficiency after task practice. Comparison with existing method(s)The simple average of individual precision matrices may be affected by outliers and provide inconsistent outcomes between subject-level and group-level networks. In contrast, the proposed method yielded a robust group graph that could identify and ease the effect of outliers. ConclusionsThe proposed method identified regions of practice-induced attenuation associated with reduced cognitive demand after repeat task exposure. Through simulated and real data, we demonstrated that this method does not require any distribution assumption, can identify outliers, and provides robust, representative group brain networks. This method can be applied to datasets that have extensive variability and/or multiple outliers, including applications to specific, and general, cognitive processes, as well as for studies that may require longitudinal data, such as pharmaceutical trials.

Simultaneous feature selection and outlier detection with optimality guarantees.

Biomedical research is increasingly data rich, with studies comprising ever growing numbers of features. The larger a study, the higher the likelihood that a substantial portion of the features may be redundant and/or contain contamination (outlying values). This poses serious challenges, which are exacerbated in cases where the sample sizes are relatively small. Effective and efficient approaches to perform sparse estimation in the presence of outliers are critical for these studies, and have received considerable attention in the last decade. We contribute to this area considering high-dimensional regressions contaminated by multiple mean-shift outliers affecting both the response and the design matrix. We develop a general framework and use mixed-integer programming to simultaneously perform feature selection and outlier detection with provably optimal guarantees. We prove theoretical properties for our approach, that is,a necessary and sufficient condition for the robustly strong oracle property, where the number of features can increase exponentially with the sample size; the optimal estimation of parameters; and the breakdown point of the resulting estimates. Moreover, we provide computationally efficient procedures to tune integer constraints and warm-start the algorithm. We show the superior performance of our proposal compared to existing heuristic methods through simulations and use it to study the relationships between childhood obesity and the humanmicrobiome.

A Bayesian approach for predicting food and beverage sales in staff canteens and restaurants

Accurate demand forecasting is one of the key aspects for successfully managing restaurants and staff canteens. In particular, properly predicting future sales of menu items allows for a precise ordering of food stock. From an environmental point of view, this ensures a low level of pre-consumer food waste, while from the managerial point of view, this is critical to the profitability of the restaurant. Hence, we are interested in predicting future values of the daily sold quantities of given menu items. The corresponding time series show multiple strong seasonalities, trend changes, data gaps, and outliers. We propose a forecasting approach that is solely based on the data retrieved from point-of-sale systems and allows for a straightforward human interpretation. Therefore, we propose two generalized additive models for predicting future sales. In an extensive evaluation, we consider two data sets consisting of multiple time series collected at a casual restaurant and a large staff canteen and covering a period of 20 months. We show that the proposed models fit the features of the considered restaurant data. Moreover, we compare the predictive performance of our method against the performance of other well-established forecasting approaches.

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.

Development of methodology and reference intervals for the analysis of the free-ranging Atlantic horseshoe crab Limulus polyphemus hemolymph.

The Atlantic horseshoe crab, Limulus polyphemus, is valuable to fishing and biomedical industries, for education in public aquaria, and of ecological importance because the eggs provide a critical food source for migratory shorebirds. While hematologic and biochemical analyses are fundamental tools for health assessment, reports are limited for the four extant species of horseshoe crabs; Lpolyphemus (East Coast North America), Carcinoscorpius rotundicauda (mangrove horseshoe crab Southeast Asia), Tachypleus gigas, and Tachypleus tridentatus (Southeast and East Asia). This prospective study measured hemolymph values to determine RIs from free-ranging horseshoe crabs during the annual breeding aggregation in Delaware Bay, USA. Near-shore animals were briefly manually restrained for hemolymph collection from the cardiac sinus. Hematologic samples (25 males, 25 females) were collected for hemocytometer counts using the Natt and Herrick method. A second set of 50 animals (25 males, 25 females) was sampled for biochemistry measurands, including copper concentration by spectrophotometer, osmolality by vapor pressure osmometer, and protein electrophoresis. Total hemocyte counts varied widely (RI 6600-44300/µL). Electrolytes were consistent with osmoconformers living in seawater. There was a marked difference in sexes, with females showing much lower protein, glucose, and copper levels. Eleven females had multiple outliers, and all data were excluded from RI calculations. Further studies of this species outside of spawning season are needed. Expanding our knowledge of horseshoe crab health is important to decreasing morbidity and mortality in research applications and maximizing longevity and overall health in display settings.

Location and estimation of multiple outliers in weighted total least squares

Although the weighted total least squares (WTLS) adjustment is a rigorous method for estimating parameters in errors-in-variables (EIV) models, its solution is unreliable if the design matrix and/or observations contain multiple outliers. Existing methods are not capable of fully eliminating the influence of multiple outliers on the parameters. First, we reformulate an EIV model as a correction model by taking the outliers of the design matrix and observations into account, and we introduce the concept of total outliers to simplify the problem of detecting multiple outliers in EIV models. Then, based on the effect of the outliers on the estimated posteriori variance, we develop a full search algorithm to form a location matrix that can describe the location of the total outliers. Next, we derive a set of formulae to numerically estimate the unknown model parameters and total outliers simultaneously. Finally, the results of three numerical experiments show that the proposed method can effectively eliminate the influence of the outliers and obtain reliable parameters.