Robust non‐linear regression analysis

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

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.

Processing experimental data with uncertainty is a huge challenge for robust regression modeling and high-accuracy data forecasting. The objective of the present study is the development of a robust support vector regression model for processing observed data of independent variables containing polyhedral perturbation and achievement of high forecasting precision. Firstly, the conception of the data collection of polyhedral perturbation is given and analyzed. Secondly, a novel robust support vector regression model is constructed by replacing the original independent variables in a linear support vector regression model with the independent variables containing polyhedral perturbation. Thirdly, the novel robust linear support vector regression method is also expanded to the non-linear regression model. Both the two models are validated by the linear and nonlinear numerical regression experiments. Comparison of the experimental results show that the proposed method provide more accurate predictions than the traditional regression method for processing data with polyhedral perturbation.

Ochroma pyramidale (Cav. ex. Lam.) Urb. (balsa-tree) is a commercially important tree species that ranges from Mexico to northern Brazil. Due to its low weight and mechanical endurance, the wood is particularly well-suited for wind turbine blades, sporting equipment, boats and aircrafts; as such, it is in high market demand and plays an important role in many regional economies. This tree species is also well-known to exhibit a high degree of variation in growth. Researchers interested in modeling the height–diameter relationship typically resort to using ordinary least squares (OLS) to fit linear models; however, this method is known to suffer from sensitivity to outliers. Given the latter, the application of these models may yield potentially biased tree height estimates. The use of robust regression with iteratively reweighted least squares (IRLS) has been proposed as an alternative to mitigate the influence of outliers. This study aims to improve the modeling of height–diameter relationships of tree species with high growth variation, by using robust regressions with IRLS for data-sets stratified by site-index and age-classes. We implement a split sample approach to assess the model performance using data from Ecuador’s continuous forest inventory (n = 32,279 trees). A sensitivity analysis of six outlier scenarios is also conducted using a subsample of the former (n = 26). Our results indicate that IRLS regression methods can give unbiased height predictions. At face value, the sensitivity analysis indicates that OLS performs better in terms of standard error of estimate. However, we found that OLS suffers from skewed residual distributions (i.e., unreliable estimations); conversely, IRLS seems to be less affected by this source of bias and the fitted parameters indicate lower standard errors. Overall, we recommend using robust regression methods with IRLS to produce consistent height predictions for O. pyramidale and other tree species showing high growth variation.

The use of laser technology to scan hardwood log surfaces for defects holds great promise for improving processing efficiency and the value and volume of lumber produced. External and internal defect detection to optimize hardwood log and lumber processing is one of the top four technological needs in the nation’s hardwood industry. The location, type, and severity of defects on hardwood logs are the key indicators of log quality and value. These visual cues provide information about internal log characteristics and products for which the log is suitable. We scanned 162 logs with a high-resolution industrial four-head laser surface scanner. The resulting data sets contain hundreds of thousands of three-dimensional coordinate points. The size of the data and noise presented special problems during processing. Robust regression models were used to fit geometric shapes to the data. The estimated orthogonal distances between the fitted model and the log surface are converted to a two-dimensional image to facilitate defect detection. Using robust regression methods and standard image processing tools we have demonstrated that severe surface defects on hardwood logs can be detected using height and contour analyses of three-dimensional laser scan data.

Ordinary Least Squares (OLS) is one method of parameter estimation in regression analysis. However, the presence of outliers can cause estimation of regression coefficients obtained are not exact. Act of throwing away an outlier is not a wise move, because sometimes outliers provide significant information. Therefore, robust regression methods are needed to data contain outliers. This paper will use robust regression estimation method by M-estimation. This estimation use Iteratively Reweighted Least Squares (IRLS) method with weighting function by Huber and Tukey Bisquare. IRLS is applied to the case of food security in Central Java in 2007 that is influenced by the stock of rice, harvested area, average production, price of rice and the amount of consumption. The purpose of this writing is to compare goodness of M-estimation IRLS using Huber and Tukey Bisquare function in estimating the model parameters of food security in Central Java in 2007. Based on the research results can be concluded that the M-estimation by the Tukey Bisquare is better recommended than Huber function. This can be seen by value results of Mean Square Error and determination coefficient

We propose a two stage robust regression procedure to be applied when outliers and leverage points are present. It takes advantage of a high breakdown point MCD estimator and an efficient redescending M-estimator. Its performance was assessed by processing examples from the statistical literature and by carrying out a Monte Carlo simulation experiment; this procedure performs better than other robust regression methods. By pinpointing, labeling and investigating the data generation process of outlying observations, the procedure promotes an interactive attitude in the user and stimulates a thorough scrutiny of data based on subject matter knowledge.

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have been proposed in the literature, most of them can be highly sensitive to the presence of a small proportion of atypical observations in the training set. A review of outlier robust estimation methods for nonparametric regression models is provided, paying particular attention to practical considerations. Since outliers can also influence negatively the regression estimator by affecting the selection of bandwidths or smoothing parameters, a discussion of robust alternatives for this task is also included. Using many of the “classical” nonparametric regression estimators (and their robust counterparts) can be very challenging in settings with a moderate or large number of explanatory variables, so recently proposed robust nonparametric regression methods that scale well with a growing number of covariates are also discussed.

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.

Published equations for approximations of soil compression index in terms of in situ void ratio are varied and confusing. Many published expressions yield a positive compression index even for soils with zero void ratios. Furthermore, published expressions are normally based on a high correlation coefficient and limited test data. Significant measures such as standard errors are often omitted. Some published equations are limited to fine-grained or organic soils. Most available data exhibit a behavior in which significant scatter is observed for small values of void ratio. High void ratio values associated with organic soils produce high compression indices. The use of compression index in settlement calculation of organic soils deposits and especially peat is not justified. Over the past five years, significant amount of data was collected from published articles in reputable journals and conferences. A total of 1722 data points relating the compression index to soil void ratio were analyzed. Using MATLAB, the authors developed new regression models that relate the compression index of normally consolidated soils to its void ratio and including careful examination of data outliers. Using the methods of Robust Regression, the proposed regression models minimized the effects of data outliers and produced higher correlation coefficients with reduced associated standard errors. Although several artificial neural networks (ANN) regression models are available, such models were based on limited data without dealing with data outliers. The combined data set used is then largest ever assembled and offers clear insights into the behavior of mineral and organic soils. The proposed regression models differ from published empirical approximations by considering the impact of data outliers.

LDV measurements of particle fluctuation velocities in dilute gravity-driven gas-particle flows

Alzheimer's disease (AD) is a neurodegenerative disorder with slow onset, which could result in the deterioration of the duration of persistent neurological dysfunction. How to identify the informative longitudinal phenotypic neuroimaging markers and predict cognitive measures are crucial to recognize AD at early stage. Many existing models related imaging measures to cognitive status using regression models, but they did not take full consideration of the interaction between cognitive scores. In this paper, we propose a robust low-rank structured sparse regression method (RLSR) to address this issue. The proposed model simultaneously selects effective features and learns the underlying structure between cognitive scores by utilizing novel mixed structured sparsity inducing norms and low-rank approximation. In addition, an efficient algorithm is derived to solve the proposed non-smooth objective function with proved convergence. Empirical studies on cognitive data of the ADNI cohort demonstrate the superior performance of the proposed method.

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.

The variation of background harmonics, system harmonic impedance and load characteristics will affect the harmonic voltage and current at the point of common coupling(PCC), which will lead to large estimation error of harmonic contribution if ignored. In this paper, a simple and effective method is proposed to identify the abrupt transition points in the harmonic parameter data, then the harmonic voltage and current data are divided into several stable data sections, in which the background harmonic and system harmonic impedance are basically unchanged, and the load characteristics are relatively stable. On this basis, the harmonic contribution of the harmonic source is discussed and evaluated by using the robust regression method in the data segment, and the dynamic variation of the harmonic contribution parameter in the time period is obtained. The simulation results show that the proposed method can accurately identify the variation of harmonic parameters and divide the harmonic information into several stable data segments. The robust regression method has higher accuracy than other linear regression methods. The accuracy and effectiveness of the proposed method are proved.

Robust Multivariate Statistical Methods