Robust Regression Method Research Articles

A Novel Statistical Method of Defining Geochemical Baselines and Source Identification for Trace Metals in Soil in Zhangjiagang County, China

Establishing accurate geochemical baselines by normalization procedures (NP) is important for distinguishing contaminated soils from the uncontaminated ones. In the areas with intensive anthropogenic influences, geochemical baselines are easily affected by the contaminated soils. The commonly used least squares method is not robust enough because it is sensitive to outliers, resulting in distorted regression relationship. A novel robust regression method, which can diminish the influences of outliers proposed, is proposed for defining more accurate geochemical baselines and the source of trace metals. Zhangjiagang County, which is under with intensive anthropogenic influences and high pollution risks, was selected as the study area. Trace metal data obtained from subsoils were used as normalizers, and SMDM-estimators were used in the robust regression for defining the geochemical baselines and the sources of trace metals in this area. The robust statistical method can successfully be applied in normalization procedures for defining soil geochemical baselines. The SMDM robust regressions reduced the influence of outliers, building a more reasonable regression fitted to data points for the selected trace metals in topsoil and subsoil. Subsoil trace metals are less affected than topsoil, so they can be used as normalizers to replace general elemental normalizers. It is found that the geochemical baselines defined by the novel robust regression method proposed in this study can fully reflect the natural variability of soil trace metals. Moreover, this method can also apparently reduce the effects of outliers on statistical analysis, improving the accuracy of geochemical baselines in the areas with intensive anthropogenic influences and high pollution risks.

Genetic robust kernel sample selection for chemometric data analysis

AbstractIn this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi‐objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M‐regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

Dimensionality reduced robust ordinal regression applied to life cycle assessment

Life Cycle Assessment quantifies the multi-dimensional impact of goods and services and can be handled by Multi-Criteria Decision Analysis. In Multi-Criteria Decision Analysis, Robust Ordinal Regression manages all the compatible preference functions at once when assessing a set of alternatives and a group of preferences on reference alternatives. Robust Ordinal Regression is thus a versatile method of reducing the cognitive effort required by decision makers for eliciting their preference structures in Life Cycle Assessment, although it does not directly operate on noisy alternatives and requires Stochastic Multicriteria Acceptability Analysis to deal with such scenarios.We propose integrating a dimensionality reduction technique, Principal Component Analysis, and Robust Ordinal Regression methods, to reduce the problem dimensionality and ensure the actual problem features are considered.A generated dataset, a dataset from literature and a Life Cycle Assessment case study are used to test the effectiveness of the proposed methods.

Analyst Optimism in the Automotive Industry: A Post-Bailout Boost and Methodological Insights

This paper empirically investigates the impact of the government bailout on analysts’ forecast optimism regardingfirms in the automotive industry. We compare the results from M- and MM-robust methodologies to the results from OLS regression in an event study context and find that inferences change. When M- and MM-robust estimation methods are used to estimate the same model, the results for key control variables fall directly in line with those of similar previous studies. Furthermore, an analysis of residuals indicates that the application of M- and MM estimation methods pulls the main prediction equation towards the main sample data, suggesting a more rigorous fit. Based on robust methods, we observe changes in analyst optimism during the announcement period of the bailout, as evidenced by the significantly positive variable of interest. We support our empirical results with simulations and confirm significant improvements in estimation accuracy when robust regression methods are applied to the samples contaminated by outliers.

Predicting Bankruptcy with Robust Logistic Regression

Using financial ratio data from 2006 and 2007, this study uses a three-fold cross validation scheme to compare the classification and pre diction of bankrupt firms by robust logistic regression with the Bianco and Yohai (BY) estimator versus maximum likelihood (ML) logistic regression. With both the 2006 and 2007 data, BY robust logistic regression improves both the classification of bankrupt firms in the training set and the prediction of bankrupt firms in the testing set. In an out of sample test, the BY robust logistic regression correctly predicts bankruptcy for Lehman Brothers; however, the ML logistic regression never predicts bankruptcy for Lehman Brothers with either the 2006 or 2007 data. Our analysis indicates that if the BY robust logistic regression significantly changes the estimated regression coefficients from ML logistic regression, then the BY robust logistic regression method can significantly improve the classification and prediction of bankrupt firms. At worst, the BY robust logistic regression makes no changes in the estimated regression coefficients and has the same classification and prediction results as ML logistic regression. This is strong evidence that BY robust logistic regression should be used as a robustness check on ML logistic regression, and if a difference exists, then BY robust logistic regression should be used as the primary classifier.

CEO Bonuses as Studied by Robust Logistic Regression

This investigation utilized a robust logistic regression method (BYLOGREG) to investigate CEO bonuses prior to the 2007-2009 financial crisis. The robust logistic regression analysis determined that the year and CEO tenure affected the probability that a CEO received a bonus in the 2004-2006 study period. The analysis refuted that ”management entrenchment” widely influenced CEO bonus compensation because the probability of receiving a bonus was negatively related to CEO tenure. The probability of receiving of bonus declined during the 2004-2006 study period because the percentage of CEOs that received a bonus was lowest in 2006. The robust logistic regression analysis found that the current year stock return was positively and statistically significantly related to the probability that a CEO received a bonus. The analysis also showed that managerial (financial) performance in the areas of growth of sales, ROE, and growth in earnings per share increased the probability that a CEO received a bonus. In this investigation, the size of the firm and the growth rate of equity were not statistically significant. Overall, robust logistic regression correctly classified 77% of the observations on the basis of the model variables, which indicated that most CEO bonuses could be explained by firm, CEO, and financial variables.The BY robust logistic regression proved to be robust to outliers in the CEO bonus sample studied. Interestingly, the relationship between stock return and the probability of a bonus was completely missed by a maximum likelihood (ML) logistic regression with the full CEO bonus sample, which contained outliers. After trimming the CEO bonus data set to remove outliers, the ML logistic regression coefficients changed dramatically. However, the BY robust logistic regression coefficients changed very little. Use of the residuals from the BY robust logistic equation should facilitate further inquiry into CEOs that received a bonus but were predicted to have a low probability of a bonus.

Distribución Regional De Mortalidad COVID-19 En Perú

Objectives: Compare the death rate from COVID-19 at the national level by regions and departments from March to September 2020. Methods: Quantitative, observational, cross-sectional, ecological and retrospective study. The data was extracted from the National Death System (SINADEF) in Microsoft Excel 2016 and imported into Stata. The variables were described as frequencies and percentages. Mortality was obtained by dividing the total deaths over the total population according to the last census. An adjusted exploratory analysis was performed using robust regression methods to evaluate the association between mortality by department and regions adjusted for age and sex of the deceased. P <0.05 was considered significant. Results: 32535 deaths were reported, 69.84% were male and the median was 67. The mortality rate in the Costa region 145 deaths were calculated (n = 24,276), followed by Sierra with 51 (n = 4434) and Selva with 63 (n = 2545). There were significant differences in mortality according to the region, in the comparison of the coast with the Sierra region a beta coefficient of -96.28 was found (p <0.001 IC -123.76 -68.77), while in the comparison with the Selva it was determined a coefficient of -50.38 (p 0.01 95% CI -91.47 -9.29). No significant association was found between the mortality rate and the average age or sex of the deceased by department. Conclusion: The death rate from COVID-19 at the national level was 101 per 100 000 inhabitants. The mortality rate found was higher on the Costa region than in the Sierra and Selva, regardless of the proportion of men, women or age.

The Comparison of Classical and Robust Biased Regression Methods for Determining Unemployment Rate in Turkey: Period of 1985-2012

Unemployment is one of the most important issues in macro economics. Unemployment creates many economic and social problems in the economy. The condition and qualification of labor force in a country show economical developments. In the light of these facts, a developing country should overcome the problem of unemployment. In this study, the performance of robust biased Robust Ridge Regression (RRR), Robust Principal Component Regression (RPCR) and RSIMPLS methods are compared with each other and their classical versions known as Ridge Regression (RR), Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR) in terms of predictive ability by using trimmed Root Mean Squared Error (TRMSE) statistic in case of both of multicollinearity and outliers existence in an unemployment data set of Turkey. Analysis results show that RRR model is chosen as the best model for determining unemployment rate in Turkey for the period of 1985-2012. Robust biased RRR method showed that the most important independent variable effecting the unemployment rate is Purchasing Power Parities (PPP). The least important variables effecting the unemployment rate are Import Growth Rate (IMP) and Export Growth Rate (EXP). Hence, any increment in PPP cause an important increment in unemployment rate, however, any increment in IMP causes an unimportant increase in unemployment rate. Any increment in EXP causes an unimportant decrease in unemployment rate.

A signature of estimate-stromal-immune score-based genes associated with the prognosis of lung adenocarcinoma.

BackgroundImmune and stromal component evaluation is necessary to establish accurate prognostic markers for the prediction of clinical outcomes in lung adenocarcinoma (LUAD). We aimed to develop a gene signature based on the Estimation of STromal and Immune cells in MAlignant Tumor tissues using Expression data (ESTIMATE)-stromal-immune score in LUAD.MethodsThe transcriptomic profiles of patients with LUAD were obtained from The Cancer Genome Atlas (TCGA), and the immune and stromal scores were derived using the ESTIMATE algorithm. The prognostic signature genes were selected from the differentially expressed genes (DEGs) using the robust partial likelihood-based cox proportional hazards regression method. The negative log-likelihood and the Akaike Information Criterion (AIC) were used to identify the optimal gene signature. The validation was carried out in 2 independent datasets from the Gene Expression Omnibus (GSE68571 and GSE72094).ResultsPatients with high ESTIMATE, stromal, and immune scores had better overall survivals (P=0.0035, P=0.066, and P=0.0077). The expression of thirty-seven genes was related to ESTIMATE-stromal-immune score. A risk stratification model was developed based on a gene signature containing CD74, JCHAIN, and PTGDS. The ESTIMATE-stromal-immune risk score was revealed to be a prognostic factor (P=0.009) after multivariate analysis. Four groups were classified based on this risk stratification model, yielding increasing survival outcomes (log-rank test, P=0.0051). This risk stratification model and other clinicopathological factors were combined to generate a nomogram. The calibration curves showed perfect agreement between the nomogram-predicted outcomes and those actually observed. Similar observations were made in 2 independent cohorts.ConclusionsThe gene signature based on the ESTIMATE-stromal-immune score could predict the prognosis of patients with LUAD.

Robust regression with compositional covariates including cellwise outliers

We propose a robust procedure to estimate a linear regression model with compositional and real-valued explanatory variables. The proposed procedure is designed to be robust against individual outlying cells in the data matrix (cellwise outliers), as well as entire outlying observations (rowwise outliers). Cellwise outliers are first filtered and then imputed by robust estimates. Afterwards, rowwise robust compositional regression is performed to obtain model coefficient estimates. Simulations show that the procedure generally outperforms a traditional rowwise-only robust regression method (MM-estimator). Moreover, our procedure yields better or comparable results to recently proposed cellwise robust regression methods (shooting S-estimator, 3-step regression) while it is preferable for interpretation through the use of appropriate coordinate systems for compositional data. An application to bio-environmental data reveals that the proposed procedure—compared to other regression methods—leads to conclusions that are best aligned with established scientific knowledge.

Robust functional principal components for sparse longitudinal data

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This method is robust against the presence of atypical observations, and can also be used to derive a new non-robust FPCA approach for sparsely observed functional data. We use local regression to estimate the values of the covariance function, taking advantage of the fact that for elliptically distributed random vectors the conditional location parameter of some of its components given others is a linear function of the conditioning set. This observation allows us to obtain robust FPCA estimators by using robust local regression methods. The finite sample performance of our proposal is explored through a simulation study that shows that, as expected, the robust method outperforms existing alternatives when the data are contaminated. Furthermore, we also see that for samples that do not contain outliers the non-robust variant of our proposal compares favourably to the existing alternative in the literature. A real data example is also presented.

Modeling of Chronological Age Using Least Trimmed Squares Ridge Regression

The popular method to estimation the parameters of a linear regression model is the ordinary least square method which, despite the simplicity of calculating and providing the BLUE estimator of parameters, in some situations leads to misleading solutions. For example, we can mention the problems of multi-collinearity and outliers in the data set. The least trimmed squares method which is one of the most popular of robust regression methods decreases the influence of outliers as much as possible. The main goal of this paper is to provide a robust ridge estimation in order to model dental age data. Among the methods used to determine age, the most popular method throughout the world is the modern modified Demirjian method that is based on the calcification of the permanent tooth in panoramic radiography. It has been shown that using the robust ridge estimator is leading to reduce the mean squared error in comparison with the OLS method. Also, the proposed estimators were evaluated in simulated data sets.

Sparse regression for extreme values

We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, in linear modeling problems, the presence of abnormal extreme values or outliers is considered an anomaly which should either be removed from the data or remedied using robust regression methods. In many situations, however, the extreme values in regression modeling are not outliers but rather the signals of interest; consider traces from spiking neurons, volatility in finance, or extreme events in climate science, for example. In this paper, we propose a new method for sparse high-dimensional linear regression for extreme values which is motivated by the Subbotin, or generalized normal distribution, which we call the extreme value linear regression model. For our method, we utilize an ℓp norm loss where p is an even integer greater than two; we demonstrate that this loss increases the weight on extreme values. We prove consistency and variable selection consistency for the extreme value linear regression with a Lasso penalty, which we term the Extreme Lasso, and we also analyze the theoretical impact of extreme value observations on the model parameter estimates using the concept of influence functions. Through simulation studies and a real-world data example, we show that the Extreme Lasso outperforms other methods currently used in the literature for selecting features of interest associated with extreme values in high-dimensional regression.

Scale calibration for high-dimensional robust regression

We present a new method for robust high-dimensional linear regression when the scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber M-estimator, for which theoretical bounds on the estimation error have recently been proposed in high-dimensional statistics literature. However, the variance of the error term in the linear model is intricately connected to the optimal parameter used to define the shape of the Huber loss. Our main idea is to use an adaptive technique, based on Lepski’s method, to overcome the difficulties of solving a joint nonconvex optimization problem with respect to the location and scale parameters. Furthermore, by including a weight term in the definition of the M-estimator, our consistency results hold even when the covariates are heavy-tailed. We then derive asymptotic normality of a one-step estimator constructed from the penalized Huber estimator, which can be used to construct confidence regions for subsets of coordinates. The one-step estimator is shown to be semiparametrically efficient when the covariates are sub-exponential. Our results substantially generalize previous work on high-dimensional inference, derived under sub-Gaussian assumptions on both the covariate and error distributions.

The Impact of Covid-19 Pandemic on the Global Economy: Emphasis on Poverty Alleviation and Economic Growth

The COVID-19 pandemic has devastated the global economy, which has rendered many of the world's population impoverished. Moreover, the pandemic has generated some uncertainties regarding economic and social policies. This phenomenon is lately the brunt of every government across the globe. This present study seeks to evaluate the pandemic's impact on poverty alleviation and the global GDP by considering individual countries' heterogeneous effects in a panel study. The motivation is to unravel the social and economic effects on the global economy. However, 170 countries are utilized in this study, and econometric panel techniques such as OLS and robust least square regression methods are utilized. The data was collected from OurWorldindata.com, comprising total COVID-19 cases, total deaths, stringency index, human development index, and gross domestic product per capita. The study's findings stipulate that many people's stringency and the contraction of the disease have inversely affected poverty alleviation and economic growth. Nevertheless, for the deaths recorded so far positively affects both poverty alleviation and economic growth. This development signals the essence of controlling population growth as it impedes economic growth and poverty alleviation. The study recommends that governments invest in health and education improvement and stimulate their economies to create employment that could propagate growth to improve poverty alleviation and economic growth.

Efficient Bias Robust Cross Section Factor Models

This paper introduces a theory based robust regression estimator, called the mOpt estimator, that minimizes the maximum bias with respect to a Tukey-Huber mixture model that includes a standard linear regression model with normally distribution errors as a special case, but also allows for a small fraction of unrestricted fat-tailed and skewed non-normal distribution variations from the standard model. The estimator has a very intuitive weighted least squares interpretation based on a data-dependent weight function that is equal to zero for robustly scaled prediction residuals that are larger in magnitude than 3.0, and thereby rejects outliers. We apply the robust regression method to single factor and multiple factor cross-section models for Size, BM, Beta and EP factors, and find that the robust regression results reverse the Fama-French 1992 (FF92) conclusions concerning the significance of the Size, Beta and EP factors. The difference in our results and those of FF92 is that the robust regression rejects approximately 4% to 5% of outliers, most of which, but not all, occur for microcap stocks, with smallcap stocks also having some influential outliers, and even largecaps have a few. We strongly recommend standard use of the mOpt estimator as an important complement to least squares for empirical asset pricing research, as well as for quantitative finance applications in general.

Diseconomies of Scale in Active Management: Robust Evidence

We take a deeper look at the robustness of evidence presented by Pastor, Stambaugh, and Taylor (2015) and Zhu (2018), who find that an actively managed mutual fund's returns relate negatively to both fund size and the size of the active mutual fund industry. When we apply robust regression methods, we confirm both studies' inferences about scale diseconomies at the fund and industry levels. Moreover, data errors play no role, as both studies' results are insensitive to applying various error screens and using alternative return benchmarks. We reject constant returns to scale even after dropping 25% of the most extreme return observations. Finally, we caution that asymmetric removal of influential observations delivers biased conclusions about diseconomies of scale.

A robust multiple regression model based on fuzzy random variables

In the present paper, a novel robust multiple regression model with fuzzy intercepts and non-fuzzy regression coefficients was proposed. A two-stage robust procedure adopted with fuzzy random variables and α-values of LR-fuzzy was also introduced to estimate the components of the model. Some common goodness-of-fit criteria were also used to evaluate the performance of the proposed method. The effectiveness of the proposed method was compared to some common fuzzy robust regression models through three numerical examples including a simulation study. The numerical results indicated the lower sensitivity of the proposed model to outliers and its higher precision compared to the other existing robust regression methods.

New Robust Regularized Shrinkage Regression for High-Dimensional Image Recovery and Alignment via Affine Transformation and Tikhonov Regularization

In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.

A reassessment of the amphibole-plagioclase NaSi-CaAl exchange thermometer with applications to igneous and high-grade metamorphic rocks

Abstract The amphibole-plagioclase NaSi-CaAl exchange thermometer by Holland and Blundy (1994) (expression B) has been extensively applied to calcic amphibole-bearing assemblages from metamorphic and igneous rocks, whereas the more recent calibrations of the amphibole-only thermometer by Ridolfi and Renzulli (2012) (expression 2) and Putirka (2016) (expressions 5 and 6) are employed for determining amphibole-saturation temperatures in hydrous magmas. However, a test of these expressions performed on experimental data compiled from the literature reveals significant inaccuracies, tending expression B to underestimate temperatures in high-Mg amphibole, and the amphibole-only expressions to overestimate temperatures in amphibole with either low Mg or high AlVI occupancies. Amphibole NaM4 and Fe3+ occupancies can also affect significantly the accuracy of expression B. In this work, we present three new accurate calibrations (expressions A1, A2, and B2) of the amphibole-plagioclase NaSi-CaAl exchange thermometer calculated by robust regression methods based on multiple maximum-likelihood estimators (MM-estimators; Yohai 1987), considering various calibration and test data subsets to evaluate the robustness of the derived parameters in the thermodynamic models, and the accuracy and precision of the expressions. Non-ideality in plagioclase was corrected using the ternary feldspar solution model of Elkins and Grove (1990) in expressions A1 and A2, whereas the simplified version of the Darken’s Quadratic Formalism (DQF) approach of Holland and Powell (1992) was used in expression B2. The formulation of the multisite macroscopic solution model of Powell and Holland (1993) was used for deriving the mixing parameters of amphibole in the three calibrations. Expression B2 is strictly pressure-independent, while the two others show a negligible dependence on pressure for plagioclase with low orthoclase component (<11 mol%). The three calibrations yield an overall precision close to those reported for the tested amphibole-based thermometers but are significantly more accurate, a requisite for an unambiguous interpretation of precision. The new expressions can be used in a wide range of igneous and high-grade metamorphic rocks that bear subcalcic to calcic amphibole and oligoclase or more calcic plagioclase. However, they must be applied only to amphibole-plagioclase pairs whose compositions lie in the optimal region of use prescribed in the work.