Robust Regression Approach Research Articles

Decision Tree Regression with Residual Outlier Detection

This paper introduces a framework for identifying outliers in predictions made by regression tree models. Existing robust regression approaches tend to focus on the construction stage, which builds regression models that are less sensitive to outliers. In contrast, our approach focuses on identifying outliers during the prediction stage. The process of our proposed approach begins with building a regression tree using a training dataset. Predictions significantly deviating from the mean within each terminal node are automatically labeled as outliers. We show how the labelled data can be explored to better understand the characteristics of the outliers. We also identify the situations under which the data exploration may not work well. Further, we make use of the outlier labels and training data to construct an anomaly detector. Our results show that the proposed method can effectively detect outliers that may exist within datasets. Such outliers, when removed, result in improved data quality. Insights into its effectiveness and potential caveats are also discussed.

The proposal and application of a 2-Dimensional Fuzzy Monte Carlo Frontier analysis for estimating Islamic bank efficiency

AbstractThe current study proposes a novel 2-Dimensional Fuzzy Monte-Carlo Frontier Analysis to estimate and compare the level of efficiency for a sample of 49 Islamic Banks across 25 countries worldwide over the period 2013–2021. Additionally, in the second stage, we propose a bootstrapped robust regression approach to comprehensively examine the determinants of efficiency. Our results show that there is heterogeneity in the level of efficiency within the Islamic banking sector. Furthermore, we find that the Islamic banks in the sample experienced an improvement in efficiency over the examined period. Finally, we find that bank size, bank liquidity (measured by the ratio between net loans and gross loans), and bank risk (proxied by the ratio between loan loss reserves and gross loans) have a significant and positive impact on Islamic bank efficiency. Policy implications based on our findings are provided.

Fifty shades of QE revisited

Fabo et al. (2021) use OLS regression to show that central bankers report quantitatively larger effects of QE on output and inflation than do academic researchers. We reject the null hypothesis of a Gaussian distribution of the residuals in many of these specifications, except for the language regressions. We then repeat the analysis with regression estimators that are robust to a non-Gaussian residual distribution where this is feasible. We use the median regression and the MS regression estimator. With these robust regression approaches, the null hypothesis that central bank and academic researchers report the same quantitative effect of QE on output and inflation cannot be rejected, with point estimates which are less than half as large. This statistical challenge suggests that more research is required to understand better whether central bank researchers report different QE multipliers or not.

Application of robust regression in translational neuroscience studies with non-Gaussian outcome data.

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.

A Decision Support System for the Selection of Insulating Material in Energy Retrofit of Industrial Buildings: A New Robust Ordinal Regression Approach

The criteria for selecting insulating materials in the energy retrofitting of industrial buildings can often be conflicting, leading to a multicriteria decision-making problem. This is the first study to take an indirect elicitation approach to solving this selection problem, which is particularly applicable in the preliminary phases of negotiation with all of the decision-makers involved. We introduce a nonlinear indirect elicitation approach for PROMETHEE II that uses Bézier curves as nonlinear preference curves to fit the decision-maker's preferences, i.e., indifference and/or strict preferences for insulating materials that are taken as references. In our approach, no parameters need to be initially set, and thus, it has the advantage of setting both the preference curves on the criteria and the criteria weights when the decision-maker is not confident. The set of Bézier curves and criteria weights that best fits the preferences given by the decision-maker may thus be achieved and visualized, which provides managerial insights as it makes explicit the preference structure of the decision-maker. We use a case study to validate our proposal in a real setting and confirm that linear preference curves would have achieved less clear relations between the insulating materials used as references respect to Bèzier curves.

Exploring the economic impact of institutional entrepreneurship, social Innovation, and poverty reduction on carbon footprint in BRICS countries: what is the role of social enterprise?

The world is facing challenges to reduce carbon emissions, the complex interplay between socioeconomic dynamics and environmental sustainability is of utmost importance. In the context of the BRICS nations-Brazil, Russia, India, China, and South Africa-this study explores the intricate interactions between institutional entrepreneurship, institutional innovation, poverty reduction, social globalization, urbanization, and social entrepreneurship as well as their combined effects on the carbon footprint over the period of 1990 to 2021. This work examines the multi-dimensional interactions inside this nexus using a thorough analytical strategy that includes the Generalized Method of Moments (GMM), Three-Stage Least Squares (3SLS), and Robust regression approaches. Institutional entrepreneurship and innovation are the main forces behind institutional change and may have an impact on how people behave in terms of the environment. Strategies for reducing poverty frequently involve greater resource usage, which has an impact on carbon footprint. Examining social globalization's impact on carbon footprints is necessary given how it affects consumer habits and economic activity. Rapid urbanization is a dual problem because it spurs both increased energy demand and novel sustainability measures. With its emphasis on community-driven solutions, social entrepreneurship can provide regional solutions to reduce poverty and carbon emissions. The study's findings provide policymakers, practitioners, and researchers with insights into the complex web of socio-economic factors that underlies carbon footprint fluctuations. This research paves the way for informed policy decisions, sustainable business practices, and the pursuit of harmonious development that addresses both economic aspirations and environmental imperatives within the BRICS countries by illuminating the connections between institutional entrepreneurship, innovation, poverty reduction, social globalization, urbanization, social entrepreneurship, and carbon emissions.

Cash Management and Financial Performance of Quoted Non- Financial Firms in Nigeria: A Dynamic Robust Least Squares Regression Approach

This study investigates the impact which cash management and the financial performance of selected firms in Nigeria. The period which the study covers is from 2005 to 2020 of 76 non- financial firms quoted on the floor of the Nigerian Exchange Group the information about them are extracted from their financial statements. The results of the dynamic robust least squares indicated that while cash and cash equivalence (CCE), average collection period (ACP), days sales outstanding (DSO), days inventory outstanding (DIO) and sales growth (GSALES) are positively significant with economic value added (EVA); cash conversion cycle (CCC), average payment period (APP), days payment outstanding (DPO), quick ratio (QR), short term debt (STD) and capital expenditures (CAPEX) are negatively significant with it. The study concludes with some recommendations.

RegCloser: a robust regression approach to closing genome gaps

BackgroundClosing gaps in draft genomes leads to more complete and continuous genome assemblies. The ubiquitous genomic repeats are challenges to the existing gap-closing methods, based on either the k-mer representation by the de Bruijn graph or the overlap-layout-consensus paradigm. Besides, chimeric reads will cause erroneous k-mers in the former and false overlaps of reads in the latter.ResultsWe propose a novel local assembly approach to gap closing, called RegCloser. It represents read coordinates and their overlaps respectively by parameters and observations in a linear regression model. The optimal overlap is searched only in the restricted range consistent with insert sizes. Under this linear regression framework, the local DNA assembly becomes a robust parameter estimation problem. We solved the problem by a customized robust regression procedure that resists the influence of false overlaps by optimizing a convex global Huber loss function. The global optimum is obtained by iteratively solving the sparse system of linear equations. On both simulated and real datasets, RegCloser outperformed other popular methods in accurately resolving the copy number of tandem repeats, and achieved superior completeness and contiguity. Applying RegCloser to a plateau zokor draft genome that had been improved by long reads further increased contig N50 to 3-fold long. We also tested the robust regression approach on layout generation of long reads.ConclusionsRegCloser is a competitive gap-closing tool. The software is available at https://github.com/csh3/RegCloser. The robust regression approach has a prospect to be incorporated into the layout module of long read assemblers.

Predicting stock realized variance based on an asymmetric robust regression approach

AbstractThis paper introduces an asymmetric robust weighted least squares (ARLS) approach to improve the forecasting performance of the heterogeneous autoregressive model for realized volatility. The ARLS approach down‐weights extreme observations to limit the bad influence of outliers on the estimated parameters. Compared with existing robust regression methods, our model further takes into account the asymmetry of outliers using a class of kernel functions. Out‐of‐sample results show the ARLS approach can generate more accurate forecasts of the S&P 500 index realized volatility in the statistical and economic senses. The model that considers the asymmetry of outliers gains superior performance among various robust regression competitors. The forecasting improvements also hold in other international stock markets. More importantly, the source of the predictive ability of the ARLS model comes from the less biased and more efficient parameter estimation.

Mitigating the impact of outliers in traffic crash analysis: A robust Bayesian regression approach with application to tunnel crash data

Traffic crash datasets are often marred by the presence of anomalous data points, commonly referred to as outliers. These outliers can have a profound impact on the results obtained through the application of traditional methods such as logit and probit models, commonly used in the domain of traffic safety analysis, resulting in biased and unreliable estimates. To mitigate this issue, this study introduces a robust Bayesian regression approach, the robit model, which utilizes a heavy-tailed Student's t distribution to replace the link function of these thin-tailed distributions, effectively reducing the influence of outliers on the analysis. Furthermore, a sandwich algorithm based on data augmentation is proposed to enhance the estimation efficiency of posteriors. The proposed model is rigorously tested using a dataset of tunnel crashes, and the results demonstrate its efficiency, robustness, and superior performance compared to traditional methods. The study also reveals that several factors such as night and speeding have a significant impact on the injury severity of tunnel crashes. This research provides a comprehensive understanding of the outliers treatment methods in traffic safety studies and offers valuable recommendations for the development of appropriate countermeasures to effectively prevent severe injuries in tunnel crashes.

Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice

In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.

Estimating hydrogen absorption energy on different metal hydrides using Gaussian process regression approach

Hydrogen is a promising alternative energy source due to its significantly high energy density. Also, hydrogen can be transformed into electricity in energy systems such as fuel cells. The transition toward hydrogen-consuming applications requires a hydrogen storage method that comes with pack hydrogen with high density. Among diverse methods, absorbing hydrogen on host metal is applicable at room temperature and pressure, which does not provide any safety concerns. In this regard, AB2 metal hydride with potentially high hydrogen density is selected as an appropriate host. Machine learning techniques have been applied to establish a relationship on the effect of the chemical composition of these hosts on hydrogen storage. For this purpose, a data bank of 314 data point pairs was used. In this assessment, the different A-site and B-site elements were used as the input variables, while the hydrogen absorption energy resulted in the output. A robust Gaussian process regression (GPR) approach with four kernel functions is proposed to predict the hydrogen absorption energy based on the inputs. All the GPR models' performance was quite excellent; notably, GPR with Exponential kernel function showed the highest preciseness with R2, MRE, MSE, RMSE, and STD of 0.969, 2.291%, 3.909, 2.501, and 1.878, respectively. Additionally, the sensitivity of analysis indicated that ZR, Ti, and Cr are the most demining elements in this system.

Impact of Temperature and Population Size on the Spread of COVID-19 in Nigeria: A Robust Regression Approach

Background: COVID-19, a global pandemic ravaging many countries, shares some semblances with influenza, whose transmission can be affected by many factors. Atmospheric temperature and population density have been identified as two key factors influencing the spread of viruses. Nigerian states with different weather patterns and varying populations across her states have recorded about 173,908 COVID-19 cumulative confirmed cases between March 2020 and July 2021. Methods: Data sets of confirmed Covid-19 cases, average monthly temperature and population of each State, and Nigeria’s Federal Capital Territory were obtained. A test of assumptions of linear regression was carried out and there is the presence of outliers in the dataset. M-estimator as an alternative to Ordinary Least Square (O.L.S.) estimator for regression analysis was used to investigate the impacts of each State’s population size and atmospheric temperature on the rate of COVID-19 cases confirmed. The spearman rank correlation coefficient was also used to investigate the strength of the relationship be-tween the confirmed cases, the population and temperature. Results: Results show no multicollinearity (VIF=1.041) between the independent variables, and there is no autocorrelation as the Durbin-Watson test value gives 2.113 (approximately 2). There is a weak positive correlation between cumulative confirmed cases and population (r = 0.281), but a weak negative correlation exists between COVID-19 cumulative confirmed cases and atmospheric temperature (r = -0.341). For OLS estimation method, only population is significant (β1= 0.002, p < 0.002) but the population (β1= 0.0006, p < 0.05) and the atmospheric temperature ( β2= -683, p < 0.05) are both significant when M-estimation method was applied. Conclusion: The findings in this study show that population size and temperature are important factors in the spread of Covid-19. The spread of the pandemic may be partially suppressed with higher temperatures but increases with an increased population.

LOCOM: A logistic regression model for testing differential abundance in compositional microbiome data with false discovery rate control

Compositional analysis is based on the premise that a relatively small proportion of taxa are differentially abundant, while the ratios of the relative abundances of the remaining taxa remain unchanged. Most existing methods use log-transformed data, but log-transformation of data with pervasive zero counts is problematic, and these methods cannot always control the false discovery rate (FDR). Further, high-throughput microbiome data such as 16S amplicon or metagenomic sequencing are subject to experimental biases that are introduced in every step of the experimental workflow. McLaren et al. [eLife 8, e46923 (2019)] have recently proposed a model for how these biases affect relative abundance data. Motivated by this model, we show that the odds ratios in a logistic regression comparing counts in two taxa are invariant to experimental biases. With this motivation, we propose logistic compositional analysis (LOCOM), a robust logistic regression approach to compositional analysis, that does not require pseudocounts. Inference is based on permutation to account for overdispersion and small sample sizes. Traits can be either binary or continuous, and adjustment for confounders is supported. Our simulations indicate that LOCOM always preserved FDR and had much improved sensitivity over existing methods. In contrast, analysis of composition of microbiomes (ANCOM) and ANCOM with bias correction (ANCOM-BC)/ANOVA-Like Differential Expression tool (ALDEx2) had inflated FDR when the effect sizes were small and large, respectively. Only LOCOM was robust to experimental biases in every situation. The flexibility of our method for a variety of microbiome studies is illustrated by the analysis of data from two microbiome studies. Our R package LOCOM is publicly available.

Prolonged NoGo P3 latency as a possible neurobehavioral correlate of aggressive and antisocial behaviors: A Go/NoGo ERP study

Aggressive and antisocial behaviors are detrimental to society and constitute major challenges in forensic mental health settings, yet the associated neural circuitry remains poorly understood. Here, we investigated differences in aggressive and antisocial behaviors between healthy controls (n = 20) and violent mentally disordered offenders (MDOs; n = 26), and examined associations between aggressive and antisocial behaviors, behavioral inhibitory control, and neurophysiological activity across the whole sample (n = 46). Event-related potentials were obtained using EEG while participants completed a Go/NoGo response inhibition task, and aggressive and antisocial behaviors were assessed with the Life History of Aggression (LHA) instrument. Using a robust Bayesian linear regression approach, we found that MDOs scored substantially higher than healthy controls on LHA Aggression and Antisocial subscales. Using the whole sample and after adjusting for age, we found that scores on the LHA Aggression and Antisocial subscales were robustly associated with longer NoGo P3 latency, and less robustly with longer NoGo N2 latency. Post-hoc analyzes suggested that healthy controls and MDOs exhibited similar associations. With several limitations in mind, we suggest that prolonged NoGo P3 latency, reflecting decreased neural efficiency during the later stages of conflict monitoring or outcome evaluation, is a potential neurobehavioral correlate of aggressive and antisocial behaviors.

Online and Distributed Robust Regressions with Extremely Noisy Labels

In today’s era of big data, robust least-squares regression becomes a more challenging problem when considering the extremely corrupted labels along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer from several challenges when applied in huge dataset including (1) computational infeasibility of handling an entire dataset at once, (2) existence of heterogeneously distributed corruption, and (3) difficulty in corruption estimation when data cannot be entirely loaded. This article proposes online and distributed robust regression approaches, both of which can concurrently address all the above challenges. Specifically, the distributed algorithm optimizes the regression coefficients of each data block via heuristic hard thresholding and combines all the estimates in a distributed robust consolidation. In addition, an online version of the distributed algorithm is proposed to incrementally update the existing estimates with new incoming data. Furthermore, a novel online robust regression method is proposed to estimate under a biased-batch corruption. We also prove that our algorithms benefit from strong robustness guarantees in terms of regression coefficient recovery with a constant upper bound on the error of state-of-the-art batch methods. Extensive experiments on synthetic and real datasets demonstrate that our approaches are superior to those of existing methods in effectiveness, with competitive efficiency.

Interval joint robust regression method

Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets.

Modelling the overall image of coastal tourism destinations through personal values of tourists: A robust regression approach

The overall image of a destination is one of the main factors considered by tourists when choosing a destination to visit. Coastal destinations traditionally offer sun and beaches as tourist attractions, providing unique experiences and meaningful exchanges for tourists. Personal values are one of the most used and tested transcultural theories in different contexts and cultures. This study attempts to investigate the overall image of coastal tourism destinations through the personal values of tourists, in the context of international tourism. A random survey was conducted through Amazon Mechanical Turk (MTurk) with 1106 respondents. A set of the robust regression models was conducted to test the formulated hypotheses. Results support the hypothesis that the overall image of the destination is influenced by the respondents’ personal values. The findings also indicate that personal values and their respective effects change, according to the overall image of coastal tourism destinations. The data analysis revealed that there are significant direct positive and negative effects of personal values on the overall image. This study contributes to the theory and can be of interest to both academics and practitioners. In the face of these advances to understanding the attitudes of consumer behaviour, tourism marketers should focus on developing an overall image of coastal tourism destinations that emphasize independent action, feeling, and readiness for a new experience of this market segment.

Soil parameters affecting the levels of potentially harmful metals in Thessaly area, Greece: a robust quadratic regression approach of soil pollution prediction.

The behavior and possible contamination risk due to the presence of potentially harmful metals (PHM) were studied based on 2250 soil samples that were collected in a 5-year period (2013-2017) from the plain of Thessaly (prefectures of Karditsa, Trikala, and Larissa). The vertical distribution of metals was also investigated from sample profiles at three depths 0-30, 30-60, and 60-90cm. The soils of the sampling belong to four taxonomy soil orders that are dominant in the studied area (Alfisols, Inceptisols, Endisols, and Vertisols). In a novel approach, robust quadratic regression analysis on multiple variables was used to define prediction models of the concentrations of two metals: Fe which is an essential metal and the toxic Cd. Linear and quadratic regression formulae were estimated based on the iteratively reweighted least squares robust regression approach in an effort to eliminate the impact of the outliers. These formulae define how several soil properties affect the distribution of the considered metals in each soil order. The evaluation of the estimated regression equations based on the R2 metric indicates that they constitute a useful, reliable, and valuable tool for managing, describing, and predicting the pollution in the studied area.

Novel robust time series analysis for long-term and short-term prediction

Nonlinear phenomena are universal in ecology. However, their inference and prediction are generally difficult because of autocorrelation and outliers. A traditional least squares method for parameter estimation is capable of improving short-term prediction by estimating autocorrelation, whereas it has weakness to outliers and consequently worse long-term prediction. In contrast, a traditional robust regression approach, such as the least absolute deviations method, alleviates the influence of outliers and has potentially better long-term prediction, whereas it makes accurately estimating autocorrelation difficult and possibly leads to worse short-term prediction. We propose a new robust regression approach that estimates autocorrelation accurately and reduces the influence of outliers. We then compare the new method with the conventional least squares and least absolute deviations methods by using simulated data and real ecological data. Simulations and analysis of real data demonstrate that the new method generally has better long-term and short-term prediction ability for nonlinear estimation problems using spawner–recruitment data. The new method provides nearly unbiased autocorrelation even for highly contaminated simulated data with extreme outliers, whereas other methods fail to estimate autocorrelation accurately.