Search

AbstractOutliers are outrageous values that occur in an experiment and can almost be inevitable. The presence of outliers in an experiment can affect the results of a response surface design due to disruption in the design’s structure. In this paper, a new class of orthogonal uniform composite designs (OUCD4) for fitting third-order response surface model are constructed using the minimax outlying effect criterion that minimizes the maximum outlying effect. These constructed designs referred to as orthogonal uniform composite minimax outlying (OUCO4) designs are robust to a single outlier. The OUCO4 designs are shown to be more efficient in terms of relative efficiency compared to the OUCD4. [ABSTRACT FROM AUTHOR]

The use of Almon technique is encouraged for estimation of the distributed lag model (DLM) to avoid some serious problems associated with the direct application of the ordinary least squares (OLS) method. In Almon technique, the OLS procedure is applied on the transformed regressors which may be correlated themselves. To tackle this issue, the use of ordinary ridge regression estimator (ORRE) combined with the Almon technique has been considered as an alternative approach in the literature. However, the ORRE may be sensitive to outliers in the y-direction and thus, its use combined with the Almon technique may raise doubts on the estimated lag coefficients. The present work addresses this issue and suggests an alternative estimation method for the DLM, which is robust in the presence of multicollinearity and outliers. The performance of the proposed estimator has been evaluated through an extensive Monte Carlo simulation study and empirical findings are presented using the mean squared error criterion. The results reveal an attractive performance of the proposed estimator in the presence of outliers. [ABSTRACT FROM AUTHOR]

AbstractRidge regression is a commonly used prediction method in cases of multicollinearity among regressors in multiple linear regression model. In this study, the performances of 366 different estimators proposed in the literature for ridge parameter estimation were evaluated. The criteria of estimators’ ratio of generating outliers and the proportion of normality besides the Mean Square Error (MSE) criterion were used for diagnosing ridge parameter estimators. Besides, the effect of outliers and deviations from normality generated by the ridge parameter estimators on the MSE was revealed by Spearman’s Rho correlation analysis. To do so, a Monte Carlo simulation was designed for 2420 different cases, considering the simulation parameters comprehensively in terms of the number of regressors, sample size, collinearity level and error variances. The results revealed that some ridge parameter estimators recommended according to MSE criterion, do not perform well in terms of outlier generation and normality criteria. Significant inter-linear correlations were also found among the ridge parameter estimators’ MSE performance criterion, ratios of outlier generation criterion and normality criterion. Thus, it is suggested that an effective ridge parameter estimator should perform well in terms of outlier generation and normality criteria, as well as having small MSE value. [ABSTRACT FROM AUTHOR]

Regression diagnostics help identify influential data points in a model. Detecting outliers in complex survey design data involving stratification, clustering, and unequal probability sampling is difficult due to the presence of masking, where one outlier makes it hard to detect others. The masking factor for survey–weighted linear regression is developed and applied to analyzing the Household Consumer Expenditure dataset of 68th round of the National Sample Survey Organization survey of India. Regression parameters are calculated before and after detection and removal of outliers. The standard error of regression parameters for survey-weighted least squares models is reduced by 2% for the intercept, 5% for variable “meat” (X5), 4% for “served processed food” (X9), and 4% for “packaged processed food” (X10). Inference alters the significance of regression coefficients of the variable “served processed food” (X9) leading to the emergence of significance. There is no change in inference for other variables. [ABSTRACT FROM AUTHOR]

An anonymous survey was given to n = 73 students in an asynchronous online statistical literacy course at a mid-sized Hispanic Serving Institution. Informed by teaching experience, literature on lexical ambiguity, and everyday usage of statistics words and phrases, the first author designed the survey to yield insight into how students view phrases such as "average person," "random person," and "outlier person," and to explore possible connections or patterns with such phrases. Findings suggest that students view phrases such as "random person" in a way much further from standard usage than they do phrases such as "anonymous person." Considerations such as diversity, agency, and variable identification are identified as possibly affecting usage and meriting further investigation. Recommendations for teaching and future research are provided. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Nonlinear models are commonly used for analyzing real-life data such as in medicine, engineering, and economics. To make efficient inferences about model parameter estimations and statistical results in nonlinear regression, assumptions related to error term are needed to be satisfied. Ordinary least squares and some modified least squares methods fail to give efficient parameter estimates when there are the problems of autocorrelation and outlier together in nonlinear regression. In this study, a novel hybrid robust tapering approach called as robust modified two-stage least squares is proposed to overcome the problems for obtaining more efficient parameter estimates in nonlinear regression. Two numerical examples and a comprehensive Monte–Carlo simulation study are given in order to examine the performance of robust modified two-stage least squares. [ABSTRACT FROM AUTHOR]

We investigate a shift parameter approach to logistic regression for robust classification. Shift parameter moves margin to the minimum of loss function. For robust estimation, margin-based logistic regression requires its own version of thresholding-type estimate which is different from residual-based regression. We discuss shift parameter estimation desirable to robust classification and propose some penalty functions producing such shift parameter estimates. Comparing to existing robust logistic regression methods requiring non-convex optimization or label transition modelling, our proposal is implemented in a simple alternating optimization: the classifier is obtained as a solution of conventional logistic regression with an offset and shift parameter is individually estimated in a closed form. We discuss some robust properties of the method and demonstrate its performance in linear and nonlinear classification with synthetic and real-world examples. [ABSTRACT FROM AUTHOR]

The ridge regression estimator (RRE) is a widely used estimation method for the multiple linear regression model when the explanatory variables are correlated. The situation becomes problematic for the RRE when the data set contains outliers in the y-direction. The use of the RRE in the presence of outliers may have some adverse effects on parameter estimates. To address this issue, the robust ridge estimators based on M-estimator are available in the literature which are less sensitive to the presence of outliers. It is a well-known fact that the selection of ridge parameter k is very crucial while using the RRE and the same phenomenon may happen in the case of robust ridge estimators. This study proposes some robust ridge estimators for the ridge parameter k. The performance of proposed estimators is evaluated with the help of the Monte Carlo simulations and a real application where the mean squared error (MSE) is considered as a performance evaluation criterion. Results show a better performance of the proposed robust ridge estimators as compared to the RRE, least square and M-estimation methods. While for modified ridge M-estimator, different ridge parameters found to be better for different conditions. [ABSTRACT FROM AUTHOR]

There is a wide range of outliers in spatial data, and these potential outliers will have a great impact on parameter estimation and corresponding statistical inference. Relying on the framework of maximum likelihood estimation (MLE), we investigate the asymptotic distribution of robust ML estimator under the mixed spatial autoregressive models with outliers and compare it with that of the ML estimator. Furthermore, based on the asymptotic theoretical result, we conduct the confidence interval of robust MLE and MLE. Similar to the results of MLE, we construct the second-order-corrected robust confidence interval using the parametric and semi-parametric bootstrap method. Simulation studies using Monte Carlo show that the robust estimator with the Huber loss function is more accurate and outperforms the MLE in most sample settings when data is contaminated by outliers. Then the use of the method is demonstrated in the analysis of the Neighborhood Crimes Data and the Boston Housing Price Data. The results further support the eligibility of the robust method in practical situations. [ABSTRACT FROM AUTHOR]

The assumption of normality has a crucial importance in many statistical procedures. Therefore, a number of normality tests are proposed. Also, many investigations are conducted on the performance of these normality tests under a set of alternative distribution. However, there are few studies to compare the performance of the commonly used normality tests in the presence of outliers, but they are not comprehensive. It is important, since the outliers may increase the variability in the data set, they cause the decrease in the statistical power. In this study we show the performance of the commonly used normality tests in the presence of outlier in the data set. An outlier generation method is implied to generate uniform tails and the effects of various magnitude of outliers on the normality tests are obtained in terms of penalized power and Type I error probability. As a result, the most powerful tests are suggested to the researchers for different magnitude of outliers, sample sizes and the contamination ratios. Two real data applications are given to illustrate the importance of choosing the appropriate test. [ABSTRACT FROM AUTHOR]

The Almon technique is a widely used estimation procedure for the distributed lag model (DLM) to encounter the problems associated with direct application of the ordinary least squares method to this model. The Almon estimator may be sensitive to outliers in the y-direction. This study is aimed to propose a robust estimator for parameter vector of the DLM when data set is contaminated with outliers. Moreover, this study proposes the robust t-tests and confidence intervals for the lag coefficients. Performance of our proposed estimator is evaluated through the Monte Carlo simulations by comparing the estimated mean squared error while the performance of t-tests and confidence intervals is evaluated using the null rejection rates and coverage, respectively. The simulation results reveal an attractive performance of the proposed methods in the presence of outliers in the y-direction. [ABSTRACT FROM AUTHOR]

The fraction nonconforming, which follows a binomial distribution, is one of the most critical quality characteristics of attribute processes. In addition, the multivariate binomial process plays an important role in industries due to the enormous diversity of quality characteristics. A multivariate binomial process is deemed out of control when it triggers a signal in a multivariate statistical process control chart. However, it is difficult to determine which quality characteristic triggers the nonconforming shift. In contrast to most current studies that identify the contributors of shifts in multivariate normal processes, this study discusses the contributors of fraction nonconforming shifts in multivariate binomial processes. First, a test that can be applied to detect outliers in a multivariate binomial distribution is proposed. In addition, a stepwise test method that can be used to determine the contributors of fraction nonconforming shifts in a multivariate binomial process is then developed. Numerical results indicate that the method proposed is effective in determining the contributors of fraction nonconforming shifts for a multivariate binomial process. [ABSTRACT FROM AUTHOR]

Presence of one or more outliers in the observations affect inference procedure in statistical analysis. Designs robust against presence of a single outlier can be found in the literature for both regression and block design set-ups. In this paper, an attempt has been made to find a robust design in a block design set-up for the estimation of a full set of orthonormal treatment contrasts when there are more than one outlier among the observations. It appears that symmetry and balance play an important role in this study; it is seen that as we deviate from them, designs deviate from robustness. [ABSTRACT FROM AUTHOR]

This work discourages using the logistic regression (LR) model for estimative purposes when the sample size is small. We propose a new model called the "Robust Bayesian Logistic (RBL) model" that minimizes bias in the estimated logistic regression coefficients when the sample size is small, and covariate corruption is suspected. For the prior specification in the proposed RBL model, all the logistic regression coefficients are assigned independent Student's t-distribution with the location parameter 0, scale parameter 1, and degree of freedom 7 for the constant term and degree of freedom of 1 for all other regression coefficients. In our experimental study, the proposed RBL model outperforms the Logistic Regression (LR) model by having a lower mean squared error (MSE) in the regression coefficients estimated for all the sample sizes considered. The proposed RBL model has a lower standard deviation than the LR model for all the estimated regression coefficients on the real-life dataset. We suggest that the proposed RBL model be considered for logistic modeling since it generates stable, consistent, and reliable estimates, especially when the sample size is small. The proposed RBL model is a fully Bayesian method implemented in the R environment using the RJAGS package. [ABSTRACT FROM AUTHOR]

The Exceptional Events Rule (EER) of the Clean Air Act was intended to address "exceptional" air quality events but, in practice, the way the rule is employed has significant impacts on regulatory data sets that are used to understand and manage air quality. Through this rule, the Environmental Protection Agency is entangled in the politics of classification, striving to separate the unnatural from the natural and the exceptional from the common with important consequences for air quality data and regulation. If deemed exceptional, the data can be removed from the regulatory record, not only altering our understanding of air quality—and, importantly, risk and exposure—but also the management of it. By analyzing regulatory data sets, texts, and appeals, this article explores the consequences of the rule's data exclusions. I argue that the act of producing "natural exceptions" has another unintended consequence: It inadvertently creates exceptional natures; that is, natures that despite their common occurrence are deemed rare. By repeatedly removing data, the EER changes understandings of normal or expected events and becomes a powerful tool for deregulation. Ironically, even as regulations produce exceptional natures, they are simultaneously undermined by them, leading to regular and repeated surprises, unnoticed hazards, undetected exposures, and deregulation. [ABSTRACT FROM AUTHOR]

Identification of influential observations is crucial in data analysis, particularly with high dimensional datasets, where the number of predictors is higher than the sample size. These rich datasets with extensive detail are increasingly exploited and analyzed in multiple fields of science, e.g., genomics, neuroscience, finance, etc. Unfortunately, classical diagnostic statistical tools are not tailored for identifying influential observations in high dimensional setup. In this paper, we use the concept of expectiles to develop an influence measure in high dimensional regression. The influence measure is based on the asymmetric marginal correlation, and its derived asymptotic distribution is used to define a threshold based on statistical principles. Our comprehensive simulation results display the favorable qualities of this influence measure under various scenarios. The usefulness of the proposed measure is illustrated through the analysis of a neuroimaging dataset. An R package implementing the procedure is publicly available on GitHub (). [ABSTRACT FROM AUTHOR]

This article concentrated on the diagnostics measures to identify outlier observations using the restricted Liu estimator (RLE) of the vector of parameters in linear measurement error models (LMEMs). To this end, the mean shift outlier model (MSOM) has been determined to detect outliers and the corrected score test statistic. Also, using the RLE, generalized leverage matrices were constructed to identify high-leverage observations. Furthermore, to identify the influential observations, different statistics that are single-case deletion methods are used based on RLE. Finally, a simulation study and a real example are provided to illustrate the performance of the influence measures. [ABSTRACT FROM AUTHOR]

Antalya 2 tide gauge (TG) station is located on the coast of Turkey within the Eastern Mediterranean Sea. Relative sea level trends 6.0 ± 1.5 and 6.44 ± 0.45 mm/year over 1985–2009 at Antalya 2 TG are different from the trend (1.6 ± 1.5 mm/year over 1935–1977) at Antalya TG within 10 km. In order to investigate this trend discrepancy, the monthly mean series at Antalya 2 TG is re-analyzed for offsets, outliers and trend estimation. The Zivot-Andrews method and the Q p outlier test result in one offset at 1994.0417 year with magnitude of 71.24 ± 13.48 mm and nine outliers. The series, corrected for the offset and outliers, de-seasonalized and filled for missed points, is identified as trend-stationary process and analyzed for trend estimation by various models. The optimal model providing the lowest Akaike Information Criteria is polynomial linear trend with multiplicative seasonal Autoregressive Moving Average (ARMA(2,0)x(1,0)12). The estimated relative sea level trend by the optimal model is 1.77 ± 0.65 mm/year. The large trend discrepancy at Antalya 2 TG is accounted for by one offset primarily (∼71%) and nine outliers (∼3%). [ABSTRACT FROM AUTHOR]

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model. [ABSTRACT FROM AUTHOR]

This cross-sectional descriptive study utilized spatial statistics to test for hot/cold spots of SNAP under-participation in Texas. First, we estimated the percentage of SNAP eligible but not enrolled (EBNE) households, by census tract. Next, we utilized the Anselin's Local Moran's I statistic to identify statistically significant hot/cold spots of SNAP EBNE tracts throughout Texas and in Harris County. We found that hot spot census tracts had significantly higher densities, income levels, and lower poverty rates than other census tracts. Using spatial statistics to identify hot/cold spots of SNAP under-participation offers a novel method for understanding area SNAP utilization. [ABSTRACT FROM AUTHOR]

Singular spectrum analysis (SSA) is a nonparametric method for separating time series data into a sum of small numbers of interpretable components (signal + noise). One of the steps of the SSA method, which is referenced to Embedding, is extremely sensitive to contamination of outliers which are often founded in time series analysis. To reduce the effect of outliers, SSA based on Singular Spectrum Decomposition (SSD) method is proposed. In this article, the ability of SSA based on SSD and basic SSA are compared in time series reconstruction in the presence of outliers. It is noteworthy that the matrix norm used in Basic SSA is the Frobenius norm or L2-norm. There is a newer version of SSA that is based on L1-norm and called L1-SSA. It was confirmed that L1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L1-norm which is called L1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L1-norm in reconstructing the time series where polluted by outliers. [ABSTRACT FROM AUTHOR]

Missing data and outliers usually arise in longitudinal studies. Ignoring the effects of missing data and outliers will make the classical generalized estimating equation approach invalid. The longitudinal cohort study of rheumatoid arthritis patients was designed to investigate whether the Health Assessment Questionnaire score was associated with baseline covariates and changed with time. There exist dropouts and outliers in the data. In order to analyze the data, we develop a robust estimating equation approach. To deal with the responses missing at random, we extend a doubly robust method. To achieve robustness against outliers, we utilize an outlier robust method, which corrects the bias induced by outliers through centralizing the covariate matrix in the estimating equation. The doubly robust method for dropouts is easy to combine with the outlier robust method. The proposed method has the property of robustness in the sense that the proposed estimator is not only doubly robust against model misspecification for dropouts when there is no outlier in the data, but also robust against outliers. Consistency and asymptotic normality of the proposed estimator are established under regularity conditions. A comprehensive simulation study and real data analysis demonstrate that the proposed estimator does have the property of robustness. [ABSTRACT FROM AUTHOR]

It is of vital importance to search for an objective quality metric which can provide insights into the geometric strength of the underlying adjustment model. The Minimal Detectable Bias (MDB) measure has been extensively used in geodesy and photogrammetry. However, MDB is a hypothetical quality measure. To this end, the Maximum Tolerable Bias (MTB) metric is introduced in this contribution. The definition of MTB measure is independent of the distribution of observables, the test statistics, the specified significance level and the given detection power for the one-sided hypothesis test. Consequently, MTB is an objective quality measure for least-squares adjustment models. Examination of the scaled version of MTB can reveal the hardly detectable data points. All the hardly detectable points should be removed before performing conventional outlier detection procedures. [ABSTRACT FROM AUTHOR]

In many applications, it is very important to detect outliers during the analysis of normal data. Many existing methods preprocess the data to remove the outliers and then analyse the data accordingly when the data are contaminated by different unexpected outliers; however, it is difficult to use this method for applications where the data must be analysed online. In this article, we present an online monitoring approach for statistical process control (SPC) that is robust with respect to the presence of outliers. The Monte Carlo simulation results show that the proposed control chart is quite robust under the standard normally distributed data and, moreover, the control limit is not be affected by the number and sizes of the outliers. Furthermore, a real data example from a foetal heart rate (FHR) process is used to illustrate an application of our proposed procedure. [ABSTRACT FROM AUTHOR]

Binomial integer-valued AR processes have been well studied in the literature, but there is little progress in modeling bounded integer-valued time series with outliers. In this paper, we first review some basic properties of the binomial integer-valued AR(1) process and then we introduce binomial integer-valued AR(1) processes with two classes of innovational outliers. We focus on the joint conditional least squares (CLS) and the joint conditional maximum likelihood (CML) estimates of models' parameters and the probability of occurrence of the outlier. Their large-sample properties are illustrated by simulation studies. Artificial and real data examples are used to demonstrate good performances of the proposed models. [ABSTRACT FROM AUTHOR]

This paper introduces a new non-deletion method which identifies discordant subjects in nonlinear mixed effects models under a self-modeling framework. The new method decomposes the population level residuals into two parts and suggests two-dimensional plots to identify discordant subjects. An observation-wise investigation for alleged discordant subjects is also presented. The performances of the new methods are illustrated with simulation data and two real data examples. The new methods successfully identify the intended or important discordant subjects and observations. In a comparison with the local influence method, the new method reaches a consistent conclusion in a simpler and more efficient manner. [ABSTRACT FROM AUTHOR]

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations. [ABSTRACT FROM AUTHOR]

Metric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the overall goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise goodness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasizing the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown. [ABSTRACT FROM AUTHOR]

An electric-resistance-welded (ERW) tube is one of the leading contributor products for automotive manufacturers. Such tubes tend to fail due to weak weld quality that may be the result of several parameters, such as inappropriate selection of weld power, positions of forming rolls and fin pass rolls, mill operating speed and many more. This paper presents an application of classifier algorithm to predict weak welded tube during real production process. Real-time data with 86 independent variables are trained using logistic regression as classifier. A logistic regression model is validated on real-time test data with capability of predicting failure 82.55% of the time (often termed as sensitivity). Operating ranges for mill parameters are estimated with the help of model results. Significant yield improvement has been observed after deployment of model recommended operating ranges as recipe in manufacturing unit. Working of newly developed human machine interface (HMI) has been explained. This exercise has been performed for three different product segments being manufactured in Tubes Division, Tata Steel Limited. This work demonstrates an application of artificial intelligence in manufacturing plant for quality improvement. [ABSTRACT FROM AUTHOR]

Spatial regression models, used to model spatial relationships, have received considerable attention in recent years since numerous data sets have been collected with geographical references in space. The spatial error model (SEM), among spatial regression models, has been widely applied for spatial data in the literature due to its simple structure. However, it is known that the classical estimation methods such as the maximum likelihood and generalized moment can be influenced by the presence of outliers in the data. In this article, a robust estimation approach based on the robustified likelihood equations for SEM is proposed. The results of the simulation study show that the proposed estimator for SEM has smaller bias and mean squared errors and exhibits more robust empirical influence function than the classical methods, when there are outliers in the dataset. The results of all analysis show that the proposed estimator is robust to outliers. [ABSTRACT FROM AUTHOR]

Over the 50 years of its existence, Baarda's concept of reliability has been used as a standard practice for the quality control in geodesy and surveying. In this study, we analysed the pioneering work of Baarda (Publ Geod New Ser 2(4) 1967; Publ Geod New Ser 2(5) 1968) and recent studies on the subject. We highlighted that the advent of personal computers with powerful processors has rendered Monte Carlo method as an attractive and cost-effective approach for quality control purposes. We also provided an overview of the latest advances in the reliability theory for geodesy, with particular emphasis on Monte Carlo method. [ABSTRACT FROM AUTHOR]

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. This standard "detect-and-forget" approach has been shown to be problematic, and in this article we highlight the fact that it can lead to invalid inference and show how recently developed tools in selective inference can be used to properly account for outlier detection and removal. Our inferential procedures apply to a general class of outlier removal procedures that includes several of the most commonly used approaches. We conduct simulations to corroborate the theoretical results, and we apply our method to three real datasets to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R. for this article are available online. [ABSTRACT FROM AUTHOR]

The sample skewness and kurtosis of macroeconomic and financial time series are routinely scrutinized in the early stages of model-building and are often the central topic of studies in economics and finance. Notwithstanding the availability of several robust estimators, most scholars in economics rely on method-of-moments estimation that is known to be very sensitive to outliers. We carry out an extensive Monte Carlo analysis to evaluate the bias and root mean squared error of 12 different estimators of skewness and kurtosis. We consider nine statistical distributions that approximate the range of data generating processes of many macroeconomic and financial time series. Both in independently and identically distributed samples and in data generating processes featuring serial correlation L-moments and trimmed L-moments estimators are particularly resistant to outliers and deliver improvements over standard as well as alternative robust estimators of skewness and kurtosis. The application to 128 macroeconomic and financial time series sourced from a large, monthly frequency, database (i.e. the FRED-MD of McCracken and Ng, 2016) confirms the findings of the simulation study. [ABSTRACT FROM AUTHOR]

Determining outliers is more complicated in multivariate data sets than it is in univariate cases. The aim of this study is to evaluate the blocked adaptive computationally efficient outlier nominators (BACON) algorithm, the fast minimum covariance determinant (FAST-MCD) method, and the robust Mahalanobis distance (RM) method in multivariate data sets. For this purpose, outlier detection methods were compared for multivariate normal, Laplace, and Cauchy distributions with different sample sizes and numbers of variables. False-negative and false-positive ratios were used to evaluate the methods' performance. The results of this work indicate that the performance of these methods varies according to the distribution type. [ABSTRACT FROM AUTHOR]

Outlier detection in financial time series is made difficult by serial dependence, volatility clustering and heavy tails. Projections achieving maximal kurtosis proved to be useful for outlier detection in multivariate datasets but their widespread application has been hampered by computational and inferential difficulties. This paper addresses both problems within the framework of univariate and multivariate financial time series. Computation of projections with maximal kurtoses in univariate financial time series is simplified to a eigenvalue problem. Projections with maximal kurtoses in multivariate financial time series best separate outliers from the bulk of the data, under a finite mixture model. The paper also addresses kurtosis optimization within the framework of portfolio selection. Practical relevance of these theoretical results is illustrated with univariate and multivariate time series from several financial markets. Empirical results also suggest that projections removing excess kurtosis could transform a univariate financial time series to a time series very similar to a Gaussian process, while the effect of outliers might be alleviated by projections achieving minimal kurtosis. [ABSTRACT FROM AUTHOR]

We give qualitative and quantitative improvements to theorems which enable significance testing in Markov chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political gerrymandering. Our results can be used to demonstrate at a desired significance level that a given Markov chain state (e.g., a districting) is extremely unusual (rather than just atypical) with respect to the fragility of its characteristics in the chain. We also provide theorems specialized to leverage quantitative improvements when there is a product structure in the underlying probability space, as can occur due to geographical constraints on districtings. [ABSTRACT FROM AUTHOR]

Many monitoring approaches have been proposed to control reliability-related quality characteristics in single-stage processes. However, in practice, processes are made up of several sub-processes, so the most important feature of multi-stage processes, called cascade property, should be considered by establishing the relationship between the quality characteristics of interest. Moreover, outliers are commonly present in historical data set. In this paper, modelling and monitoring reliability data in the presence of outliers have been addressed. To this end, the accelerated failure time models have been integrated with robust regression techniques to find the accurate relationship among variables. The robust regression method, called M-estimator, has been used in order to dampen the detrimental impact of destructive outliers. Subsequently, a novel cumulative sum (CUSUM) and two exponentially weighted moving average control charts have been constructed for the sake of optimal monitoring of Weibull-distributed quality variable with dependent influential covariate. The performance of the proposed control schemes has been evaluated via extensive simulation studies. The results reveal that the CUSUM control chart outperforms its counterparts. Finally, a real case study in bag weaving industry has been considered to show the application of the proposed CUSUM control chart. [ABSTRACT FROM AUTHOR]

The relatively new Big Data systems, which operate at different levels, such as modes of monitoring, bulk analysis or techniques for data mining, are increasingly used by corporations and agencies to make sense of massive collections of data, as they promise access to an increasingly traceable and more predictable population. Although these systems have been objects of interest in scientific, economic and socio-political research for some time, they also play a more and more noticeable role in recent aesthetic and cultural discussions. This article argues that, as decisive modes of representation of knowledge production, algorithmic sorting and categorisation are relatively underexplored but important territory for scholars in the diverse field of the philosophy of aesthetics. This article presents the concept of the digital object as a way to comprehend the different modes of functioning inherent in the logic of algorithmic sorting, as they are "translated" into visual manifestations in the artworks of Rossella Biscotti, as the point of departure for analysing the 19th century punched card technologies built into the operation of automated looms and later electromechanical tabulating machines. [ABSTRACT FROM AUTHOR]

Robust design uses the ordinary least squares method to obtain adequate response functions for the process mean and variance by assuming that experimental data are normally distributed and that there is no major contamination in the data set. Under these assumptions, the sample mean and variance are often used to estimate the process mean and variance. In practice, the above assumptions are not always satisfied. When these assumptions are violated, one can alternatively use the sample median and median absolute deviation to estimate the process mean and variance. However, the median and median absolute deviation both suffer from a lack of efficiency under the normal distribution, although they are fairly outlier-resistant. To remedy this problem, we propose new robust design methods based on a highly efficient and outlier-resistant estimator. Numerical studies substantiate the new methods developed and compare the performance of the proposed methods with the ordinary dual-response robust design. [ABSTRACT FROM AUTHOR]

Outlier detection in data mining aims at identifying anomalous observations known as outliers. The standard communication network incremental outlier feature clustering technique has a low clustering impact, requires several iterations, and takes a long clustering time. A novel incremental outlier based on big data analysis is proposed to overcome these problems for communicating networks in a Blockchain environment. Through big data analysis, the Point feature clustering algorithm uses the kernel density estimation technique with Gaussian kernel function to estimate the incremental outlier density of the communication network in the Blockchain framework. It mines the incremental outlier and applies the empirical mode based on the outlier mined for optimal outcome. The decomposition technique is used to extract outlier features, give weights to the features, and calculate the outlier degree and clusters. According to the results, the communication network, based on the Blockchain environment, may be clustered for incremental outlier features, and then outliers are ideally detected optimally. The simulation of the proposed technique is performed on three types of datasets. The simulation to form a cluster with the proposed method takes around 10 s of clustering time. The simulation results reveal that the proposed incremental outlier feature clustering (OFC) technique has a better outlier feature clustering impact on Blockchain-based networks, and requires a fewer iterations due to low computational and space complexity than other existing clustering techniques. [ABSTRACT FROM AUTHOR]

Cylindrical data are bivariate data from the combination of circular and linear variables. However, up to now no work has been done on the detection of outlier in cylindrical data. We introduce a definition of outlier for cylindrical data and present a new test of discordancy to detect outlier in this type of data, based on the k-nearest neighbor's distance. Cut-off points of the new test statistic based on the Johnson-Wehrly distribution are calculated and its performance is examined using simulation. A practical example is presented using wind speed and wind direction data obtained from the Malaysian Meteorological Department. [ABSTRACT FROM AUTHOR]

Here, we propose a clustering technique for general clustering problems including those that have nonconvex clusters. For a given desired number of clusters K, we use three stages to find clusters. The first stage uses a hybrid clustering technique to produce a series of clusterings of various sizes (randomly selected). The key step in this stage is to find a K-means clustering using clusters where and then join these small clusters by using single linkage clustering. The second stage stabilizes the result of stage one by reclustering via the "membership matrix" under Hamming distance to generate a dendrogram. The third stage is to cut the dendrogram to get clusters where and then prune back to K to give a final clustering. A variant on our technique also gives a reasonable estimate for KT, the true number of clusters. We provide arguments to justify the steps in the stages of our methods and we provide examples involving simulated and published data to compare our technique with other techniques. An R library, GHC, implementing our method is available from Github. [ABSTRACT FROM AUTHOR]

The problem of fitting circles and circular arcs to observed points arises in many areas of science. However, the fitting results by using most geometric and algebraic methods are not usually acceptable in the presence of outliers. An iterative procedure for robust circle fitting is proposed. During the iteration, Taubin's method is employed to obtain the center and radius. And then the geometric distances from the data points to the circle are computed, with which outliers are identified and removed. Numerical examples demonstrate that the proposed iterative procedure can alleviate the corrupted effect of outliers on the circle parameter estimates. [ABSTRACT FROM AUTHOR]

Selection of relevant predictor variables for building a model is an important problem in the multiple linear regression. Variable selection method based on ordinary least squares estimator fails to select the set of relevant variables for building a model in the presence of outliers and leverage points. In this article, we propose a new robust variable selection criterion for selection of relevant variables in the model and establish its consistency property. Performance of the proposed method is evaluated through simulation study and real data. [ABSTRACT FROM AUTHOR]

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

This paper assesses the performance of common estimators adjusting for differences in covariates, such as matching and regression, when faced with the so-called common support problems. It also shows how different procedures suggested in the literature affect the properties of such estimators. Based on an empirical Monte Carlo simulation design, a lack of common support is found to increase the root-mean-squared error of all investigated parametric and semiparametric estimators. Dropping observations that are off support usually improves their performance, although the magnitude of the improvement depends on the particular method used. [ABSTRACT FROM AUTHOR]

The key issue in robust M-estimation is to construct the equivalent weights using the residuals of observations for down-weighting the outlying observations. However, the residuals of good observations are also possibly impacted by neighbouring outliers, thus directly down-weighting an observation according to its residual is not theoretically rigorous. Therefore, this paper focuses on the construction of equivalent weights for down-weighting the outlying and doubtful observations by removing the influence of the outlier on the correlated residuals. A down-weighting strategy using the corrected residuals to form the down-weighting factors is proposed. A simulated experiment and a practical experiment are respectively conducted to demonstrate the performances of the proposed down-weighting strategy compared to the direct down-weighting strategy (DDS) and recursive down-weighting strategy (RDS). The results show that the estimated performance of the proposed down-weighting strategy is comparable to that of RDS and the computation efficiency is obviously higher than that of RDS. [ABSTRACT FROM AUTHOR]

The United States Environmental Protection Agency (USEPA) is responsible for overseeing the cleanup of sites that fall within the jurisdiction of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA; also known as "Superfund"). This process almost always involves a remedial investigation/feasibility (RI/FS) study, including deriving upper confidence, prediction, and/or tolerance limits based on concentrations from a designated "background" area which are subsequently used to determine whether a remediated site has achieved compliance. Past USEPA guidance states outlying observations in the background data should not be removed based solely on statistical tests, but rather on some scientific or quality assurance basis. However, recent USEPA guidance states "extreme" outliers, based on tests that assume a normal (Gaussian) distribution, should always be removed from background data, and because "extreme" is not defined, USEPA has interpreted this to mean all outliers identified by a test should be removed. This article discusses problems with current USEPA guidance and how it contradicts past guidance, and illustrates USEPA's current policy via a case study of the Portland, Oregon Harbor Superfund site. Additional materials, including R code, data, and documentation of correspondence are available in the online supplement. [ABSTRACT FROM AUTHOR]

The histopathological analysis of tissue specimens is essential for the diagnosis and grading of colon cancer. But the procedures are subjective and lead to noteworthy intra/inter observer difference in analysis as it mainly depends on the graphical assessment of histopathologists. So, a dependable computer-aided method, which can automatically classify malignant and normal colon samples, is required but automating this method is challenging due to the presence of outliers. In this paper, we presented a new efficient method for detecting colon cancer from biopsy samples in the presence of outliers and the method consists of four important steps. Initially, the colon biopsy images are segmented through pillar k-means algorithm to form a set of redundant candidate region in which the clusters are formed. Then in the second stage from the clustered region the parameter called Lumen Circularity (LUC) is calculated and based on that a tree structure is generated where the samples are classified as normal or malignant. After classifying the samples the outliers among them are removed by calculating the Mahalanobis distance between the samples. Finally, the score-based classification is performed to classify the differentiation of normal as well as malignant colon biopsy samples into poor, moderate or great. The proposed methodology is implemented in the MATLAB platform and the experimental results show that our proposed method achieves an accuracy of 98.75%. [ABSTRACT FROM AUTHOR]

This paper presents a type of heavy-tailed market microstructure models with the scale mixtures of normal distributions (MM-SMN), which include two specific sub-classes, viz. the slash and the Student-t distributions. Under a Bayesian perspective, the Markov Chain Monte Carlo (MCMC) method is constructed to estimate all the parameters and latent variables in the proposed MM-SMN models. Two evaluating indices, namely the deviance information criterion (DIC) and the test of white noise hypothesis on the standardised residual, are used to compare the MM-SMN models with the classic normal market microstructure (MM-N) model and the stochastic volatility models with the scale mixtures of normal distributions (SV-SMN). Empirical studies on daily stock return data show that the MM-SMN models can accommodate possible outliers in the observed returns by use of the mixing latent variable. These results also indicate that the heavy-tailed MM-SMN models have better model fitting than the MM-N model, and the market microstructure model with slash distribution (MM-s) has the best model fitting. Finally, the two evaluating indices indicate that the market microstructure models with three different distributions are superior to the corresponding stochastic volatility models. [ABSTRACT FROM AUTHOR]