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This research delves into a comprehensive investigation of a specific group of alkanes, with the primary objective of establishing meaningful associations between their inherent physical attributes and a set of graphical parameters ranging from topological indices to their associated graphical entropies. Though there are countless techniques to relate molecular structure and physical properties of chemical compounds, the pursuit has often been pricey and arduous. With a view to curb the expense and intense labour, this work focuses on attaining some of these properties using graphical interpretations and statistical interventions. Driven by this objective, we compute Sombor index, a recently developed topological tool and some of its variants for all structural isomers of alkanes with carbon range four to nine. Furthermore, our study employs multiple regression analysis to explore their connections with some physical attributes of alkanes while concurrently addressing the challenge posed by multicollinearity. We have adopted the technique of robust regression to scale down the impact of outliers in the dataset, while generating regression models. Further, the established results are justified with a 10-fold cross validation process and a comparison with the results obtained from different topological indices. The results of this research contribute a valuable insight to the fields of chemical informatics and structural analysis, offering an enhanced comprehension of the interplay between molecular structure and physical attributes within alkanes. [ABSTRACT FROM AUTHOR]

In this paper, we study an online learning algorithm with a robust loss function L σ for regression over a reproducing kernel Hilbert space (RKHS). The loss function L σ involving a scaling parameter σ > 0 can cover a wide range of commonly used robust losses. The proposed algorithm is then a robust alternative for online least squares regression aiming to estimate the conditional mean function. For properly chosen σ and step size, we show that the last iterate of this online algorithm can achieve optimal capacity independent convergence in the mean square distance. Moreover, if additional information on the underlying function space is known, we also establish optimal capacity-dependent rates for strong convergence in RKHS. To the best of our knowledge, both of the two results are new to the existing literature of online learning. [ABSTRACT FROM AUTHOR]

AbstractIn contrast to using means, there are two distinct approaches to developing robust measures effect size when dealing with two dependent variables. One is based on difference scores and the other focuses on the marginal distributions. The former approach is trivial based on extant results. This paper focuses on new robust methods based on the marginal distributions that take into account the strength of the association between the two dependent variables. Simulations are used to assess the extent a reasonably accurate confidence interval can be computed. Included is a proposed method for situations where there is a covariate. [ABSTRACT FROM AUTHOR]

A machine learning technique merging Bayesian method called Bayesian Additive Regression Trees (BART) provides a nonparametric Bayesian approach that further needs improved forecasting accuracy in the presence of outliers, especially when dealing with potential nonlinear relationships and complex interactions among the response and explanatory variables, which poses a major challenge in forecasting. This study proposes an adaptive trimmed regression method using BART, dubbed BART(Atr) to improve forecasting accuracy by identifying suspected outliers effectively and removing these outliers in the analysis. Through extensive simulations across various scenarios, the effectiveness of BART(Atr) is evaluated against three alternative methods: default BART, robust linear modeling with Huber's loss function, and data-driven robust regression with Huber's loss function. The simulation results consistently show BART(Atr) outperforming the other three methods. To demonstrate its practical application, BART(Atr) is applied to the well-known Boston Housing Price dataset, a standard regression analysis example. Furthermore, random attack templates are introduced on the dataset to assess BART(Atr)'s performance under such conditions. [ABSTRACT FROM AUTHOR]

This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels. [ABSTRACT FROM AUTHOR]

Accurate short-term load forecasting (STLF) is crucial for the power system. Traditional methods generally used signal decomposition techniques for feature extraction. However, these methods are limited in extrapolation performance, and the parameter of decomposition modes needs to be preset. To end this, this paper develops a novel STLF algorithm based on multi-scale perspective decomposition. The proposed algorithm adopts the multi-scale deep neural network (MscaleDNN) to decompose load series into low- and high-frequency components. Considering outliers of load series, this paper introduces the adaptive rescaled lncosh (ARlncosh) loss to fit the distribution of load data and improve the robustness. Furthermore, the attention mechanism (ATTN) extracts the correlations between different moments. In two power load data sets from Portugal and Australia, the proposed model generates competitive forecasting results. [ABSTRACT FROM AUTHOR]

In this research, it was reducing or excluding the effect of not satisfying the assumption of normal distribution of the data, due to the presence of types of outlying values in it when we wish to choose the best regression equation by robust methods, and this was achieved by introducing weights from the robust methods in the estimate and testing their robustness and suitability for the model in advance, And then selecting the weights resulting from the highest efficient robust methods and introducing these weights in the stages of selecting best regression equation, which results in a model that achieves two characteristics at the same time, which are robustness and reducing dimensions in return for increasing efficiency.The simulation approach was used on models with different dimensions, different sample sizes, and different contamination rates in the dependent variable once, in the independent variables again, and in both together, with a focus on studying the possible impact of the presence of outliers on the variables that will remain in the model and the variables that will be deleted. .To achieve the idea of the paper, a number of robust estimation methods were studied, and the results were compared with the ordinary least squares method (OLS) and the robust adaptive LASSO method on experimental data using simulation, as well as on data for a sample of thalassemia patients in Nineveh province..

Abstract A machine learning technique merging Bayesian method called Bayesian Additive Regression Trees (BART) provides a nonparametric Bayesian approach that further needs improved forecasting accuracy in the presence of outliers, especially when dealing with potential nonlinear relationships and complex interactions among the response and explanatory variables, which poses a major challenge in forecasting. This study proposes an adaptive trimmed regression method using BART, dubbed BART(Atr) to improve forecasting accuracy by identifying suspected outliers effectively and removing these outliers in the analysis. Through extensive simulations across various scenarios, the effectiveness of BART(Atr) is evaluated against three alternative methods: default BART, robust linear modeling with Huber’s loss function, and data-driven robust regression with Huber’s loss function. The simulation results consistently show BART(Atr) outperforming the other three methods. To demonstrate its practical application, BART(Atr) is applied to the well-known Boston Housing Price dataset, a standard regression analysis example. Furthermore, random attack templates are introduced on the dataset to assess BART(Atr)’s performance under such conditions.

Classical estimators fail to be efficient in practical scenarios when data is riddled with extreme values known as outliers. Robust estimation strategies are insensitive to outliers and may be used in such cases. The current work is focused on developing a novel robust estimation strategy using Huber M-estimation. A new chain-product type estimator for population mean has been suggested utilizing data on two auxiliary variables. A numerical comparison has been carried out between the proposed robust estimator and the corresponding classical estimator using real and simulated data containing outliers. Recommendations have been made for its practical use based on the encouraging results. [ABSTRACT FROM AUTHOR]

Quantile regression is increasingly encountered in modern big data applications due to its robustness and flexibility. We consider the scenario of learning the conditional quantiles of a specific target population when the available data may go beyond the target and be supplemented from other sources that possibly share similarities with the target. A crucial question is how to properly distinguish and use useful information from other sources to improve the quantile estimation and inference at the target. We develop transfer learning methods for high-dimensional quantile regression by detecting informative sources whose models are similar to the target and using them to improve the target model. We show that under reasonable conditions, the detection of the informative sources based on sample splitting is consistent. Compared to the naive estimator with only the target data, the transfer learning estimator achieves a much lower error rate as a function of the sample sizes, the signal-to-noise ratios, and the similarity measures among the target and the source models. Extensive simulation studies demonstrate the superiority of our proposed approach. We apply our methods to tackle the problem of detecting hard-landing risk for flight safety and show the benefits and insights gained from transfer learning of three different types of airplanes: Boeing 737, Airbus A320, and Airbus A380. [ABSTRACT FROM AUTHOR]

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators. [ABSTRACT FROM AUTHOR]

Copyright of Düzce University Journal of Forestry / Düzce Üniversitesi Orman Fakültesi Ormancılık Dergisi is the property of Duzce University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A key challenge of Fit for 55 will be reducing household emissions. For this, it is necessary to understand the factors that influence emissions and the specific role of household income. This study tests the validity of the environmental Kuznets curve (EKC) for households and links carbon emissions with income, housing, energy sources, and hidden energy poverty. We use individual household data from the Polish energy consumption survey complemented with data from a budget survey both compiled by Statistics Poland. The EKC is estimated in two scenarios, i.e. current energy mix, and zero-carbon electricity. Our model is based on the least trimmed squares technique. The study confirms the existence of the inverted U-shaped EKC in households, which is especially relevant for owners of small houses. This finding might be explained by the energy under-consumption often experienced by the poorest households, whereas wealthier households usually live in energy-efficient buildings and use less carbon-intensive fuels. The turning point is reached at 373 euros of income and 3425 kg of carbon emissions in a usual energy mix scenario compared to 560 euros and 5104 kg in a clean electricity scenario. Apart from income, household carbon emissions are interrelated with house size and hidden energy poverty, which should be in policymakers focus. [ABSTRACT FROM AUTHOR]

This paper presents a methodology, called ROBOUT, to identify outliers conditional on a high-dimensional noisy information set. In particular, ROBOUT is able to identify observations with outlying conditional mean or variance when the dataset contains multivariate outliers in or besides the predictors, multi-collinearity, and a large variable dimension compared to the sample size. ROBOUT entails a pre-processing step, a preliminary robust imputation procedure that prevents anomalous instances from corrupting predictor recovery, a selection stage of the statistically relevant predictors (through cross-validated LASSO-penalized Huber loss regression), the estimation of a robust regression model based on the selected predictors (via MM regression), and a criterion to identify conditional outliers. We conduct a comprehensive simulation study in which the proposed algorithm is tested under a wide range of perturbation scenarios. The combination formed by LASSO-penalized Huber loss and MM regression turns out to be the best in terms of conditional outlier detection under the above described perturbed conditions, also compared to existing integrated methodologies like Sparse Least Trimmed Squares and Robust Least Angle Regression. Furthermore, the proposed methodology is applied to a granular supervisory banking dataset collected by the European Central Bank, in order to model the total assets of euro area banks. [ABSTRACT FROM AUTHOR]

Electricity theft detection is very important for the economic benefits of power companies and the effectiveness of safe operation of power systems. At present, the traditional power theft detection method can only identify whether the user has power theft, but cannot perform rapid and accurate inspections for various types of power theft users. Aiming at the characteristics of medium-voltage users with large power consumption and regular power consumption, this paper proposed a method for detecting the type of power theft in medium-voltage distribution lines based on robust regression and convolutional neural network. Firstly, considering the existence of abnormal data due to factors such as communication delay interruption, a robust regression algorithm is used to reduce its impact and improve the accuracy of regression analysis. Secondly, the correction coefficient and error term of each user obtained by regression are taken as the characteristics of user stealing electricity, and input into the convolutional neural network model for training to complete the identification of stealing electricity type. Finally, the method is verified by simulation and measured data. The results show that under different disturbance conditions, the proposed method can accurately identify different types of power stealing behaviors, which can better assist on-site investigation, narrow the investigation scope and improve the verification rate.

Abstract The OLS model is built on the assumption of normality in the distribution of error terms. However, this assumption can be easily violated, especially when there are outliers in the data. A single outlier can disrupt the normality assumption of error terms, making the OLS model less effective. In such situations, M-estimators (MEs) come into play to obtain reliable estimates. We introduce a redescending M-estimators (RME) for robust regression to handle datasets with outliers. The proposed RME produces more robust estimates by effectively managing the influence of outliers, even at lower values of the tuning constant. We compared the performance of this estimator with existing RMEs using real-life data examples and an extensive simulation study. The results show that our suggested RME is more efficient than the compared ME in various situations.

AbstractIn presence of extreme-values or outliers, the ratio-type mean estimators are prominently developed by using the robust coefficients of regression and covariance matrices. In this article, we consider quantile regression coefficients while estimating the finite population mean. Incorporating Sarndal concept, we offer quantile-regression-based mean estimators under a simple random sample design. We calculate the mean squared error (MSE) for the suggested estimators and discover that they perform better than the existing estimators. Moreover, numerical representations and a simulation study support our discoveries in theory. [ABSTRACT FROM AUTHOR]

The current article discusses ratio type exponential estimators for estimating the mean of a finite population in sample surveys. The estimators uses robust regression’s Huber M-estimation function, and their bias as well as mean squared error expressions are derived. It was campared with Kadilar, Candan, and Cingi (Hacet J Math Stat, 36, 181–188, 2007) estimators. The circumstances under which the suggested estimators perform better than competing estimators are discussed. Five different population datasets with a well recognized outlier have been widely used in numerical and simulation-based research. These thorough studies seek to provide strong proof to back up our claims by carefully assessing and validating the theoretical results reported in our study. The estimators that have been proposed are intended to significantly improve both the efficiency and accuracy of estimating the mean of a finite population. As a result, the results that are obtained from statistical analyses will be more reliable and precise. [ABSTRACT FROM AUTHOR]

In this paper, we propose a MIXED penalty for the LAD regression model, which can estimate parameters and select important variables efficiently and stably. The proposed method has a good performance in the case of dependent variable with heavy tail and outliers, so this estimator is robust and efficient for tackling the problem of heterogeniety. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we give several simulation studies to examine the asymptotic results, which shows that the method we proposed behaves better. [ABSTRACT FROM AUTHOR]

In the current study, it is aimed to determine the socio-economic determinants of violence and property crimes for the member states of the European Union. For this purpose, Robust methods were used in practice. In the study, Robust Imputation Method was used to impute missing observations of some countries with missing observations on violence and property crime types, Robust Sparse Principal Components Analysis was used to reduce the dimension of the data set. According to the results of the Robust Regression Analysis for the model in which violent crime was used as the dependent variable, France, Belgium and Sweden were identified as outliers. While the relationship between real gdp per capita, unemployment rate and Gini coefficient and the number of violent crimes per hundred thousand people is positive, the relationship between the higher education enrollment rate and the young population rate of 15-24 years old and the number of violent crimes per hundred thousand people is negative. It was determined as. For the model in which property crime was used as the dependent variable, only Ireland was identified as an outlier. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Economics & Administrative Sciences is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The OLS model is built on the assumption of normality in the distribution of error terms. However, this assumption can be easily violated, especially when there are outliers in the data. A single outlier can disrupt the normality assumption of error terms, making the OLS model less effective. In such situations, M-estimators (MEs) come into play to obtain reliable estimates. We introduce a redescending M-estimators (RME) for robust regression to handle datasets with outliers. The proposed RME produces more robust estimates by effectively managing the influence of outliers, even at lower values of the tuning constant. We compared the performance of this estimator with existing RMEs using real-life data examples and an extensive simulation study. The results show that our suggested RME is more efficient than the compared ME in various situations. [ABSTRACT FROM AUTHOR]

The utilization of waste biomass-derived producer gas in dual-fuel engines has attracted a lot of interest as a sustainable energy option that encourages waste reduction as well as cleaner energy production. This research proposed a glass-box modeling strategy that combined the robust Huber and Tweedie regression approaches with SHAP (SHapley Additive exPlanations) analysis to estimate the performance and emissions of the test engine. The research demonstrated robustness over heteroscedasticity by using Huber and Tweedie regression methods, which are critical factors in real-world engine functioning. The Huber method consistently outscored both the LR and Tweedie-based prediction models in a comparison of prediction techniques for various parameters. Huber obtained remarkably high R2 values as 0.941 to 0.984, in addition to quite low root mean squared error. SHAP analysis helped in revealing the degree and direction of individual features' effect on the model. The engine load was observed to be having the most profound effect on the final model output. This study contributed to the development of waste biomass utilization in dual-fuel engines by providing a reliable prognostic tool for developing and running such systems in sustainable practices. [Display omitted] • Using waste biomass-derived producer gas for diesel engines improves sustainability. • ML with SHapley Additive exPlanations (SHAP) enhances prediction interpretability. • LR and Tweedie-based models reach high R-squared values and low RMSE. • SHAP pinpoints engine load as the key factor influencing the output power. [ABSTRACT FROM AUTHOR]

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators that are both proven to be robust to Huber-type contamination. For one of them, we obtain a non-asymptotic error bound and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators, we derive new results on kernel conditional mean embedding of distributions that are of independent interest. [ABSTRACT FROM AUTHOR]

There is a vast body of literature dedicated to identifying the major drivers that explain human impacts on the environment. In this study, we utilize the STIRPAT framework to assess whether two controversial factors should be considered when examining how humans affect the environment. Specifically, we investigate whether the quality of the democratic regime and the size of the informal economy play significant roles in determining human impacts on the environment. To address this question, we employ the extreme bounds analysis (EBA) to characterize these drivers as either robust or fragile. Based on the findings of this paper, both variables are classified as fragile, suggesting that they may not fully explain human impacts on the environment. We have taken great care in interpreting the results. [ABSTRACT FROM AUTHOR]

Violence targeting women has endured since ancient times, encompassing a spectrum of offenses ranging from psychological anguish to physical and sexual assault. This study introduces a crime index rooted in diverse categories that directly or indirectly contribute to fostering criminal intentions. A composite weighted index, comprising four sub-indexes focusing on Health, Socioeconomic status, Education, and Judiciary, was created. The stability and homogeneity of the index were assessed using reliability testing. Validation of the proposed index was carried out through comparative analysis of baseline and ensembled models. The hybrid model was proposed by combining multiple linear regression and robust regression techniques with random forest and stochastic gradient descent as meta-regressors. The models were assessed by the evaluation metrics MAE, RMSE, and MAPE. The findings indicate that the Index demonstrates strong reliability, supported by a significantly high correlation. The ensemble hybrid model approach, effectively captures the variance of the model, with less error when compared with the baseline models but the homogeneous ensemble approach proved to be the best with minimum error. Women in less developed regions with extreme geographical conditions are at a higher risk of falling prey to victimization. The Index and its statistics conclude that social factors significantly contribute to the occurrence of violence against women. These findings hold the potential for informing enhanced strategies to curtail the menace.

Ordinary least squares (OLS) regression is widely employed for statistical prediction and theoretical explanation in psychology studies. However, OLS regression has a critical drawback: it becomes less accurate in the presence of outliers and non-random error distribution. Several robust regression methods have been proposed as alternatives. However, each robust regression has its own strengths and limitations. Consequently, researchers are often at a loss as to which robust regression method to use for their studies. This study uses a Monte Carlo experiment to compare different types of robust regression methods with OLS regression based on relative efficiency (RE), bias, root mean squared error (RMSE), Type 1 error, power, coverage probability of the 95% confidence intervals (CIs), and the width of the CIs. The results show that, with sufficient samples per predictor (n = 100), the robust regression methods are as efficient as OLS regression. When errors follow non-normal distributions, i.e., mixed-normal, symmetric and heavy-tailed (SH), asymmetric and relatively light-tailed (AL), asymmetric and heavy-tailed (AH), and heteroscedastic, the robust method (GM-estimation) seems to consistently outperform OLS regression.

AbstractFederated learning (FL) is an emerging topic due to its advantage in collaborative learning with distributed data. Due to the heterogeneity in the local data-generating mechanism, it is important to consider personalization when developing federated learning methods. In this work, we propose a personalized federated learning (PFL) method to address the robust regression problem. Specifically, we aim to learn the regression weight by solving a Huber loss with the sparse fused penalty. Additionally, we designed our personalized federated learning for robust and sparse regression (PerFL-RSR) algorithm to solve the estimation problem in the federated system efficiently. Theoretically, we show that the proposed PerFL-RSR reaches a convergence rate of O(1/T), and the proposed estimator is statistically consistent. Thorough experiments and real data analysis are conducted to corroborate the theoretical results of our proposed personalized federated learning method. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Linear regression is one of the most used statistical techniques in neuroscience, including the study of the neuropathology of Alzheimer's disease (AD) dementia. However, the practical utility of this approach is often limited because dependent variables are often highly skewed and fail to meet the assumption of normality. Applying linear regression analyses to highly skewed datasets can generate imprecise results, which lead to erroneous estimates derived from statistical models. Furthermore, the presence of outliers can introduce unwanted bias, which affect estimates derived from linear regression models. Although a variety of data transformations can be utilized to mitigate these problems, these approaches are also associated with various caveats. By contrast, a robust regression approach does not impose distributional assumptions on data allowing for results to be interpreted in a similar manner to that derived using a linear regression analysis. Here, we demonstrate the utility of applying robust regression to the analysis of data derived from studies of human brain neurodegeneration where the error distribution of a dependent variable does not meet the assumption of normality. We show that the application of a robust regression approach to two independent published human clinical neuropathologic data sets provides reliable estimates of associations. We also demonstrate that results from a linear regression analysis can be biased if the dependent variable is significantly skewed, further indicating robust regression as a suitable alternate approach. [ABSTRACT FROM AUTHOR]

In many industrial applications, obtaining labeled observations is not straightforward as it often requires the intervention of human experts or the use of expensive testing equipment. In these circumstances, active learning can be highly beneficial in suggesting the most informative data points to be used when fitting a model. Reducing the number of observations needed for model development alleviates both the computational burden required for training and the operational expenses related to labeling. Online active learning, in particular, is useful in high‐volume production processes where the decision about the acquisition of the label for a data point needs to be taken within an extremely short time frame. However, despite the recent efforts to develop online active learning strategies, the behavior of these methods in the presence of outliers has not been thoroughly examined. In this work, we investigate the performance of online active linear regression in contaminated data streams. Our study shows that the currently available query strategies are prone to sample outliers, whose inclusion in the training set eventually degrades the predictive performance of the models. To address this issue, we propose a solution that bounds the search area of a conditional D‐optimal algorithm and uses a robust estimator. Our approach strikes a balance between exploring unseen regions of the input space and protecting against outliers. Through numerical simulations, we show that the proposed method is effective in improving the performance of online active learning in the presence of outliers, thus expanding the potential applications of this powerful tool. [ABSTRACT FROM AUTHOR]

Salt-and-pepper noise consists of outlier pixel values which significantly impair image structure and quality. Multiparent fractal image coding (MFIC) methods substantially exploit image redundancy by utilizing multiple domain blocks to approximate the range block, partially compensating for the information loss caused by noise. Motivated by this, we propose two novel image restoration methods based on MFIC to remove salt-and-pepper noise. The first method integrates Huber M-estimation into MFIC, resulting in an improved anti-salt-and-pepper noise robust fractal coding approach. The second method incorporates MFIC into a total variation (TV) regularization model, including a data fidelity term, an MFIC term and a TV regularization term. An alternative iterative method based on proximity operator is developed to effectively solve the proposed model. Experimental results demonstrate that these two proposed approaches achieve significantly enhanced performance compared to traditional fractal coding methods. [ABSTRACT FROM AUTHOR]

One challenging task in analyzing environmental data is how to achieve better prediction in presence of outliers, which is inevitable, especially in environmental modeling. The purpose of prediction is to draw valid conclusions and provide useful advices in environmental management. Robust approach is often desirable when there exist outliers. Robust nonparametric regression methods have attracted much attention from a practical point of view. As a nonparametric Bayesian approach, Bayesian additive regression trees (BART) provides a flexible regression that captures potential nonlinear relationships and complex interactions via the framework including sum-of-trees model, regularization prior and Bayesian backfitting MCMC algorithm (hereafter backfitting MCMC). When outliers are present in the data, we find out that BART has the highest prediction performance in simulation studies which are carried out in a variety of cases, compared to the well-known machine learning methods: random forest, support vector machine, extreme gradient boosting. The findings of this study demonstrate that BART approach is seen to be remarkably robust to outliers. For illustration, we also analyze two datasets which exist many underlying outliers: one from a study of forest fires related factors and the other from a study of biomass fuels. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Remote Sensing is the property of Editorial Office of Journal of Remote Sensing & Science Publishing Co. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

AbstractThis article is interested in estimating parameters of the linear regression model in a high-dimensional setting, i.e. with a large number of regressors. The lasso estimator does not possess high robustness with respect to the presence of outliers in the data. Our approach extends the least weighted squares estimator, which has appealing robustness and efficiency properties in linear regression with a small number of regressors. The novel LWS-lasso estimator is proposed here as an L1-regularized version of the least weighted squares. The analysis of a world tourism dataset as well as simulations show that LWS-lasso may outperform available regression estimators, especially in scenarios with high-dimensional data with a higher contamination by outliers. [ABSTRACT FROM AUTHOR]

AbstractSemiparametric mixture of regression (SMR) models provide a popular and flexible framework for modeling heterogeneous data that violates some of the parametric assumptions assumed in traditional finite mixture of regressions models. The majority of applications of SMR models assume normality for their error terms. As is well known, Gaussian distribution is sensitive to outliers or heavy-tailed distribution. In this article, we propose a more robust approach of SMR by modeling the error distribution as t distributions. By combining the EM algorithm and kernel density estimator, two algorithms are proposed to fit the robust SMR models and are proven to monotonically increase the likelihood function. We further investigate a modified version based on trimming for high leverage outliers. In real applications, a data adaptive mechanism is discussed to choose the degrees of freedom. A simulation study and three real data analyses show the superiority of the new methodology. [ABSTRACT FROM AUTHOR]

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to a large number of model parameters. A promising approach to high-dimensional likelihood-free inference involves estimating low-dimensional marginal posteriors by conditioning only on summary statistics believed to be informative for the low-dimensional component, and then combining the low-dimensional approximations in some way. In this article, we demonstrate that such low-dimensional approximations can be surprisingly poor in practice for seemingly intuitive summary statistic choices. We describe an idealized low-dimensional summary statistic that is, in principle, suitable for marginal estimation. However, a direct approximation of the idealized choice is difficult in practice. We thus suggest an alternative approach to marginal estimation which is easier to implement and automate. Given an initial choice of low-dimensional summary statistic that might only be informative about a marginal posterior location, the new method improves performance by first crudely localizing the posterior approximation using all the summary statistics to ensure global identifiability, followed by a second step that hones in on an accurate low-dimensional approximation using the low-dimensional summary statistic. We show that the posterior this approach targets can be represented as a logarithmic pool of posterior distributions based on the low-dimensional and full summary statistics, respectively. The good performance of our method is illustrated in low to moderate dimensional examples. Computer code to implement the methods for the examples of this article is available at . [ABSTRACT FROM AUTHOR]

Spatial data are becoming increasingly accessible to urban scientists, but these data are often prone to measurement error. Motivated by the analysis of the Milan (Italy) apartment market heterogeneity, we propose a semiparametric approach to adjust for the presence of measurement error in the covariates when estimating M-quantile regression. The M-quantile approach helps explain the heterogeneity across individual units, preserving robustness and efficiency in the estimates. The model's parameters are estimated within a penalised likelihood framework and an analytical expression is proposed to estimate standard errors. Asymptotic properties of estimates are also provided. [ABSTRACT FROM AUTHOR]

Outliers can cause the results of the analysis to be biased. Two approaches to dealing with existing outliers are removing the outliers or modifying the method used. Commonly used methods like machine learning (ML) often require enhanced robustness in predicting outliers. One such method is decision tree regression (DTR). However, the DTR method has limitations as it does not consider outliers and makes predictions at leaf nodes based on central values of the data, which can introduce biases into the results. One of the algorithm that retains outliers is the M-estimator from robust regression. This study proposes a modification of the M-estimator for DTR by using Huber weights on leaf nodes for DTR predictions. We used five regression datasets sourced from UCI. The results are that the dataset with outliers provides better predictions on the concrete dataset, superconductivity dataset, Boston dataset, and Airfoil dataset having the best mean absolute error (MAE) of 3.963, 9.140, 2.021, and 1.644, with QSAR fish toxicity the only exception, where has the best MAE of 0.522 for the outlier remover dataset. [ABSTRACT FROM AUTHOR]

Magnesite is an ore used in the production of a wide variety of industrial minerals and compounds and magnesium metal, as well as its alloys. The main components of magnesite are MgO and CO2. However, magnesite, which is not generally observed in nature as pure, contains certain amounts of SiO2, CaO, and Fe2O3. The loss on ignition (LOI) value in magnesite minerals largely depends on the CO2 content. This study aims to develop a model that estimates the LOI values of magnesite minerals by using SiO2, MgO, CaO, and Fe2O3tot data obtained from the geochemical analysis. Measurement of the LOI can provide important information not only for calculating the amount of volatiles in magnesite, but also about the acquisition of the element magnesium. With the estimation of LOI values, samples will not need to be subjected to LOI analysis. The data used in this study were compiled from the literature and information about the study areas, deposit types, analysis methods and the laboratory/device names was presented as supplementary material. The multivariate linear regression model was applied to represent the relationship between the LOI and these major oxides. A global independent data set comprising 170 observations was used to validate the proposed model. The preliminary analysis of the data is discussed in detail to improve the quality of the analysis. In the first step, the OLS estimation method is implemented to estimate the unknown parameters. Then, model assumptions are tested. Due to the existence of outliers, violation of the assumptions can lead to the misuse of the OLS method. In such cases, obtaining reliable estimates depends on strong estimators such as robust estimators, which are resistant to the outliers. Robust M-estimation methods can be used as effective tools for this purpose. For this reason, in the final step, we consider a robust M-estimation method based on Huber, Tukey, and Hampel objective functions. The results of OLS and robust regression methods, including parameter estimates, standard errors, residual standard error, and weighted R2 are presented as a comparison. The validity of the models and the importance of each explanatory variable to the relationship are also investigated. According to the residual standard error (RSE) which is a way to measure the standard deviation of the residuals in a regression model, and R W 2 values, a robust M- estimation method based on all three considered objective functions produces more accurate results in comparison with the outcomes of the conventional OLS method. In particular, the robust estimation method based on the Tukey objective function has the smallest RSE and largest R W 2 among the others. It is observed that deleting a few outlying points has a big impact on the regression results. In this study, a multi-linear relationship between the main oxide values and LOI was determined. As a result, an estimation model with 91% accuracy and an RSE value of 0.283 was proposed. In addition, some relationships were established between the outliers and the determination of the ranges of major oxide values in the magnesite mineral. Our results suggest that robust M-estimation can provide efficient and stable estimates when analyzing geochemical data that may contain outliers. The application of the multivariate regression analysis has been confirmed to estimate LOI by using SiO2, MgO, CaO, and Fe2O3tot as a new approach. This additional field investigation has shown promising results. Also, we recommend that this study can be improved by using more data and considering different magnesite deposit types. [ABSTRACT FROM AUTHOR]

Ordinary least squares (OLS) regression is widely employed for statistical prediction and theoretical explanation in psychology studies. However, OLS regression has a critical drawback: it becomes less accurate in the presence of outliers and non-random error distribution. Several robust regression methods have been proposed as alternatives. However, each robust regression has its own strengths and limitations. Consequently, researchers are often at a loss as to which robust regression method to use for their studies. This study uses a Monte Carlo experiment to compare different types of robust regression methods with OLS regression based on relative efficiency (RE), bias, root mean squared error (RMSE), Type 1 error, power, coverage probability of the 95% confidence intervals (CIs), and the width of the CIs. The results show that, with sufficient samples per predictor (n = 100), the robust regression methods are as efficient as OLS regression. When errors follow non-normal distributions, i.e., mixed-normal, symmetric and heavy-tailed (SH), asymmetric and relatively light-tailed (AL), asymmetric and heavy-tailed (AH), and heteroscedastic, the robust method (GM-estimation) seems to consistently outperform OLS regression. [ABSTRACT FROM AUTHOR]

In this work, we intersect data on size‐selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M‐quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M‐quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B‐spline on the effect of the day of the year. Analytic and bootstrap‐based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional response distribution. [ABSTRACT FROM AUTHOR]

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This article explores the concept of model uncertainty in linear regression analysis and proposes a method to characterize mean and variance uncertainty in the response variable. The authors introduce a family of estimators for regression parameters and parameters related to model uncertainty, and establish their consistency. The approach is applied to three different applications, including a forecasting model for the S&P Index. The article provides a valuable contribution to the limited literature on regression analysis under model uncertainty. [Extracted from the article]

Missing data is unavoidable in longitudinal clinical trials, and outcomes are not always normally distributed. In the presence of outliers or heavy-tailed distributions, the conventional multiple imputation with the mixed model with repeated measures analysis of the average treatment effect (ATE) based on the multivariate normal assumption may produce bias and power loss. Control-based imputation (CBI) is an approach for evaluating the treatment effect under the assumption that participants in both the test and control groups with missing outcome data have a similar outcome profile as those with an identical history in the control group. We develop a robust framework to handle non-normal outcomes under CBI without imposing any parametric modeling assumptions. Under the proposed framework, sequential weighted robust regressions are applied to protect the constructed imputation model against non-normality in the covariates and the response variables. Accompanied by the subsequent mean imputation and robust model analysis, the resulting ATE estimator has good theoretical properties in terms of consistency and asymptotic normality. Moreover, our proposed method guarantees the analysis model robustness of the ATE estimation in the sense that its asymptotic results remain intact even when the analysis model is misspecified. The superiority of the proposed robust method is demonstrated by comprehensive simulation studies and an AIDS clinical trial data application.

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators.