Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution

Thetdistribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lassotregression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat thetdistribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesiantregression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.

In this paper we study several competing models under general class of skew-t distributions. Namely. we consider joint location and scale model (JLSM) under Student’s t and under skew-t distributions, respectively. Similarly, we consider the extension of JLSM to joint location-scale and skewness model (JLSSM) under skew-t distribution in heteroscedastic regression models for subset selection of variables and to deal with heavy-tailedness, and skewness in a data set. To this end, for the first time, we introduce and develop the information-theoretic measure of complexity (ICOMP) criterion in such problems to select the best subset of predictor variables. We provide the computational forms of the celebrated Fisher information and the inverse Fisher information matrices for these models to be used in ICOMP. A large-scale Monte Carlo simulation study is carried out to study the performance of ICOMP in such complicated models. In addition, a real example is provided on a real benchmark data set to select the best subset of the predictors under these three competing models without knowing the true structure and the distributional form of the regression model. Our approach shows the flexibility and versatility of our approach for model selection in complex models.

The partially linear varying coefficient spatial autoregressive model is a recently proposed semi-parametric spatial autoregressive model, in which some of the explanatory variables have varying coefficients while the remained explanatory variables possess constant ones. Although some estimation methods have been proposed for the partially linear varying coefficient spatial autoregressive model, the problem of selecting important explanatory variables in the parametric component of such model has not been addressed to date. In this paper, we propose a penalized profile least squares method to address this problem. Different from the existing estimation methods, the proposed method can simultaneously select the significant explanatory variables in the parametric component and estimate the corresponding nonzero regression coefficients. Furthermore, we provide a computationally feasible algorithm to obtain the penalized profile least squares estimator. The finite sample performance of the proposed variable selection method is evaluated through some simulation studies and illustrated by a real data example.

In this paper we propose a longitudinal credit rating model which accounts for the serial correlation in the ratings. We achieve this by imposing an autoregressive structure of order one on the errors of a multivariate ordinal regression model. The longitudinal structure of the model improves significantly both the goodness-of-fit and predictive performance compared to static models. By modeling the joint distribution of the ratings over time, the framework allows us to obtain predictions conditional on the past rating history of a firm, which clearly out-perform the unconditional predictions both in- and out-of-sample. This shows the importance of incorporating past rating information in the prediction. Another upside lies in the framework’s ability to deal with missing rating observations. A real data example is provided by using a sample of US publicly traded corporates rated by S&P for the years 1985–2016. The determinants of corporate credit ratings are pre-selected using the ordinal version of the least absolute shrinkage and selection operator (LASSO). Additionally, as a model extension we allow the regression coefficients of the selected variables to vary over time in the longitudinal model. This allows us to gain a better understanding of the drivers and evolution of the rating behavior over the sample period. Finally, based on the longitudinal model with LASSO selected variables, we find evidence that S&P exhibits procyclical aspects in their rating behavior. • A credit rating model accounting for the serial correlation in the ratings. • A variable selection exercise is performed using ordinal LASSO. • Predictions conditional on the past rating history of a firm. • Longitudinal structure improves goodness-of-fit and predictive performance. • Real data example of US corporates rated by S&P for the years 1985–2016.

We discuss a new weighted likelihood method for robust parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is correctly specified. This is achieved by appropriately weighting the score function at each observation in the maximum likelihood score equation. The weight function determines the compatibility of each observation with the model in relation to the remaining observations and applies a downweighting only if it is necessary, rather than automatically downweighting a proportion of the observations all the time. This allows the estimators to retain full asymptotic efficiency at the model. We establish all the theoretical properties of the proposed estimators and substantiate the theory developed through simulation and real data examples. Our approach provides an alternative to the weighted likelihood method of Markatou et al. (J Stat Plan Inference 57(2):215–232, 1997; J Am Stat Assoc 93(442):740–750, 1998).

Agencies that regulate electricity providers often apply nonparametric data envelopment analysis (DEA) to assess the relative efficiency of each firm. The reliability and validity of DEA are contingent upon selecting relevant input variables. In the era of big (wide) data, the assumptions of traditional variable selection techniques are often violated due to challenges related to high-dimensional data and their standard empirical properties. Currently, regulators have access to a large number of potential input variables. Therefore, our aim is to introduce new machine learning methods for regulators of the energy market. We also propose a new two-step analytical approach where, in the first step, the machine learning-based adaptive least absolute shrinkage and selection operator (ALASSO) is used to select variables and, in the second step, selected variables are used in a DEA model. In contrast to previous research, we find, by using a more realistic data-generating process common for production functions (i.e., Cobb–Douglas and Translog), that the performance of different machine learning techniques differs substantially in different empirically relevant situations. Simulations also reveal that the ALASSO is superior to other machine learning and regression-based methods when the collinearity is low or moderate. However, in situations of multicollinearity, the LASSO approach exhibits the best performance. We also use real data from the Swedish electricity distribution market to illustrate the empirical relevance of selecting the most appropriate variable selection method.

With the increasing demand for the development of human pose estimation, such as human-computer interaction and human activity recognition, there have been numerous approaches to detect the 2D poses of people in images more efficiently. Despite many years of human pose estimation research, the estimation of human poses with images remains difficult to produce satisfactory results. In this study, we propose a robust 2D human body pose estimation method using an RGB camera sensor. Our pose estimation method is efficient and cost-effective since the use of RGB camera sensor is economically beneficial compared to more commonly used high-priced sensors. For the estimation of upper-body joint positions, semantic segmentation with a fully convolutional network was exploited. From acquired RGB images, joint heatmaps accurately estimate the coordinates of the location of each joint. The network architecture was designed to learn and detect the locations of joints via the sequential prediction processing method. Our proposed method was tested and validated for efficient estimation of the human upper-body pose. The obtained results reveal the potential of a simple RGB camera sensor for human pose estimation applications.

This paper presents a novel variable selection method in additive nonparametric regression model. This work is motivated by the need to select the number of nonparametric components and number of variables within each nonparametric component. The proposed method uses a combination of hard and soft shrinkages to separately control the number of additive components and the variables within each component. An efficient algorithm is developed to select the importance of variables and estimate the interaction network. Excellent performance is obtained in simulated and real data examples.

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.

Variable selection in joint location, scale and skewness models with a skew-t-normal distribution

Modern regularization and variable selection methods, such as least absolute shrinkage and selection operator (lasso) and Bayesian variable selection, are important tools for psychological researchers to reduce the risk of overfitting, improve prediction in future samples, and increase model interpretability. Although missing data are common in psychological data, it is not straightforward to combine principled methods for addressing missing data with these modern variable selection methods. This challenge is well illustrated in a recent article by Gunn et al. (2023) with a comparison of three approaches for combining lasso with multiple imputation to address missing data. Each of the surveyed approaches results in markedly different results in terms of predictors selected. Their findings underscore limitations of the lasso for the purpose of variable selection. In this article, we show how to implement a Bayesian variable selection method, stochastic search variable selection (SSVS), with multiply imputed data. SSVS is a principled and consistent method for variable selection, and we demonstrate advantages relative to lasso in an example data set and simulation study. It is straightforward to apply an ITS strategy for SSVS using existing software. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Multiple imputation (MI) is a commonly used technique for handling missing data in large-scale medical and public health studies. However, variable selection on multiply-imputed data remains an important and longstanding statistical problem. If a variable selection method is applied to each imputed dataset separately, it may select different variables for different imputed datasets, which makes it difficult to interpret the final model or draw scientific conclusions. In this paper, we propose a novel multiple imputation-least absolute shrinkage and selection operator (MI-LASSO) variable selection method as an extension of the least absolute shrinkage and selection operator (LASSO) method to multiply-imputed data. The MI-LASSO method treats the estimated regression coefficients of the same variable across all imputed datasets as a group and applies the group LASSO penalty to yield a consistent variable selection across multiple-imputed datasets. We use a simulation study to demonstrate the advantage of the MI-LASSO method compared with the alternatives. We also apply the MI-LASSO method to the University of Michigan Dioxin Exposure Study to identify important circumstances and exposure factors that are associated with human serum dioxin concentration in Midland, Michigan.

The Welch-Satterthwaite t-test is one of the most prominent and often used statistical inference method in applications. The method is, however, not flexible with respect to adjustments for baseline values or other covariates, which may impact the response variable. Existing analysis of covariance methods are typically based on the assumption of equal variances across the groups. This assumption is hard to justify in real data applications and the methods tend to not control the type-1 error rate satisfactorily under variance heteroscedasticity. In the present paper, we tackle this problem and develop unbiased variance estimators of group specific variances, and especially of the variance of the estimated adjusted treatment effect in a general analysis of covariance model. These results are used to generalize the Welch-Satterthwaite t-test to covariates adjustments. Extensive simulation studies show that the method accurately controls the nominal type-1 error rate, even for very small sample sizes, moderately skewed distributions and under variance heteroscedasticity. A real data set motivates and illustrates the application of the proposed methods.

Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression

ABSTRACTRegularization methods for simultaneous variable selection and coefficient estimation have been shown to be effective in quantile regression in improving the prediction accuracy. In this article, we propose the Bayesian bridge for variable selection and coefficient estimation in quantile regression. A simple and efficient Gibbs sampling algorithm was developed for posterior inference using a scale mixture of uniform representation of the Bayesian bridge prior. This is the first work to discuss regularized quantile regression with the bridge penalty. Both simulated and real data examples show that the proposed method often outperforms quantile regression without regularization, lasso quantile regression, and Bayesian lasso quantile regression.