Robust Cross-validation Research Articles

Two-Stage Machine Learning-Based Approach to Predict Points of Departure for Human Noncancer and Developmental/Reproductive Effects.

Chemical points of departure (PODs) for critical health effects are crucial for evaluating and managing human health risks and impacts from exposure. However, PODs are unavailable for most chemicals in commerce due to a lack of in vivo toxicity data. We therefore developed a two-stage machine learning (ML) framework to predict human-equivalent PODs for oral exposure to organic chemicals based on chemical structure. Utilizing ML-based predictions for structural/physical/chemical/toxicological properties from OPERA 2.9 as features (Stage 1), ML models using random forest regression were trained with human-equivalent PODs derived from in vivo data sets for general noncancer effects (n = 1,791) and reproductive/developmental effects (n = 2,228), with robust cross-validation for feature selection and estimating generalization errors (Stage 2). These two-stage models accurately predicted PODs for both effect categories with cross-validation-based root-mean-squared errors less than an order of magnitude. We then applied one or both models to 34,046 chemicals expected to be in the environment, revealing several thousand chemicals of moderate concern and several hundred chemicals of high concern for health effects at estimated median population exposure levels. Further application can expand by orders of magnitude the coverage of organic chemicals that can be evaluated for their human health risks and impacts.

Analysis of Gradient Boosting, XGBoost, and CatBoost on Mobile Phone Classification

In the ever-evolving landscape of mobile phone technology, accurately classifying device specifications is paramount for market analysis and consumer decision-making. This research conducts a comprehensive analysis of mobile phone specification classification using three prominent machine learning algorithms: Gradient Boosting, XGBoost, and CatBoost. Through meticulous dataset acquisition and preprocessing steps, including resolution normalization and price categorization, features essential for classification analysis were standardized. Robust cross-validation techniques were employed to assess model performance effectively. The study demonstrates the significant impact of normalization techniques on improving model performance across all algorithms and fold variations. CatBoost consistently emerges as the top-performing algorithm, followed closely by XGBoost, with Gradient Boosting displaying respectable performance. Notably, CatBoost consistently achieves the highest AUC values and accuracy scores, demonstrating superior performance in accurately classifying mobile phone specifications. These findings underscore the importance of preprocessing methods and algorithm selection in achieving optimal classification results. For mobile phone manufacturers, leveraging machine learning algorithms for effective classification can inform product development strategies, optimizing offerings based on consumer preferences. Similarly, for data analysts, employing appropriate preprocessing techniques and algorithmic approaches can lead to more accurate predictions and informed decision-making. Future research avenues include exploring advanced preprocessing methods, investigating alternative algorithms, and incorporating additional features or datasets to enrich the classification process. Overall, this research contributes to understanding mobile phone specification classification through machine learning methodologies, offering actionable insights for industry practitioners and researchers to address evolving market dynamics and consumer preferences.

Estimating Obesity Levels Using Decision Trees and K-Fold Cross-Validation: A Study on Eating Habits and Physical Conditions

This study harnesses the predictive capabilities of machine learning to explore the determinants of obesity within populations from Mexico, Peru, and Colombia, using a Decision Tree algorithm bolstered by 5-fold cross-validation. Our comprehensive analysis of 2111 individuals' lifestyle and physical condition data yielded accuracy, precision, recall, and F1-scores that notably peaked in the third and fifth folds. The findings affirmed the significance of dietary habits and physical activity as substantial predictors of obesity levels. The variability in model performance across the folds underscored the importance of robust cross-validation in enhancing the model's generalizability. This research contributes to the burgeoning field of data science in public health by providing a viable model for obesity prediction and laying the groundwork for targeted health interventions. Our study's insights are pivotal for public health officials and policymakers, serving as a stepping stone towards more sophisticated, data-driven approaches to combating obesity. The study, however, recognizes the inherent limitations of self-reported data and the need for broader datasets that encompass more diverse variables. Future research directions include the analysis of longitudinal data to establish causal relationships and the comparison of various machine learning models to optimize predictive performance

Machine learning to predict the antimicrobial activity of cold atmospheric plasma-activated liquids

Plasma is defined as the fourth state of matter, and non-thermal plasma can be produced at atmospheric pressure under a high electrical field. The strong and broad-spectrum antimicrobial effect of plasma-activated liquids (PALs) is now well known. The antimicrobial effects of PALs depend on many different variables, which complicates the comparison of different studies and determining the most dominant parameters for the antimicrobial effect. The proven applicability of machine learning (ML) in the medical field is encouraging for its application in the field of plasma medicine as well. Thus, ML applications on PALs could present a new perspective to better understand the influences of various parameters on their antimicrobial effects. In this paper, comparative supervised ML models are presented by using previously obtained data to predict the in vitro antimicrobial activity of PALs. A comprehensive literature search was performed, and 12 distinct features related to PAL-microorganism interactions were collected from 33 relevant articles to automatically predict the antimicrobial activity of PALs. After the required normalization, feature encoding, and resampling steps, two supervised ML methods, namely classification and regression, are applied to the data to obtain microbial inactivation (MI) predictions. For classification, MI is labeled in four categories, and for regression, MI is used as a continuous variable. Sixteen different classifiers and 14 regressors are implemented to predict the MI value. Two different robust cross-validation strategies are conducted for classification and regression models to evaluate the proposed method: repeated stratified k-fold cross-validation and k-fold cross-validation, respectively. We also investigate the effect of different features on models. The results demonstrated that the hyperparameter-optimized Random Forest Classifier (oRFC) and Random Forest Regressor (oRFR) provided superior performance compared to other models for classification and regression. Finally, the best test accuracy of 82.68% for oRFC and R 2 of 0.75 for the oRFR are obtained. Furthermore, the determined most important features of predictive models are in line with the outcomes of PALs reported in the literature. An ML framework can accurately predict the antimicrobial activity of PALs without the need for any experimental studies. To the best of our knowledge, this is the first study that investigates the antimicrobial efficacy of PALs with ML. Furthermore, ML techniques could contribute to a better understanding of plasma parameters that have a dominant role in the desired antimicrobial effect. Moreover, such findings may contribute to the definition of a plasma dose in the future.

Classification and prediction of cognitive performance differences in older age based on brain network patterns using a machine learning approach.

Age-related cognitive decline varies greatly in healthy older adults, which may partly be explained by differences in the functional architecture of brain networks. Resting-state functional connectivity (RSFC) derived network parameters as widely used markers describing this architecture have even been successfully used to support diagnosis of neurodegenerative diseases. The current study aimed at examining whether these parameters may also be useful in classifying and predicting cognitive performance differences in the normally aging brain by using machine learning (ML). Classifiability and predictability of global and domain-specific cognitive performance differences from nodal and network-level RSFC strength measures were examined in healthy older adults from the 1000BRAINS study (age range: 55-85 years). ML performance was systematically evaluated across different analytic choices in a robust cross-validation scheme. Across these analyses, classification performance did not exceed 60% accuracy for global and domain-specific cognition. Prediction performance was equally low with high mean absolute errors (MAEs ≥ 0.75) and low to none explained variance (R2 ≤ 0.07) for different cognitive targets, feature sets, and pipeline configurations. Current results highlight limited potential of functional network parameters to serve as sole biomarker for cognitive aging and emphasize that predicting cognition from functional network patterns may be challenging.

Hand gesture classification using time–frequency images and transfer learning based on CNN

Hand gesture-based systems are one of the most effective technological advances and continue to develop with improvements in the field of human–computer interaction. Surface electromyography (sEMG) is utilized as a popular input data for gesture classification with elevated accuracy and advanced control capability. This paper presents a comparative hand gesture classification approach using time–frequency (TF) images of the spontaneous sEMG signals and the transfer learning method. 4-channel sEMG signals are collected from 30 subjects performing 7 specific hand gestures. After the required pre-processing, segmentation, and windowing steps, three TF analysis methods, namely Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Hilbert-Huang Transform (HHT), are applied to EMG signals to obtain TF images. Spectrograms from STFT, scalograms from CWT, and Hilbert-Huang spectra (HHS) from HHT obtained from multi-channel sEMG data are separately fused. TF images are then utilized to extract distinct features using seven state-of-the-art, pre-trained Convolutional Neural Network (CNN) architectures and classify seven hand gestures. Two different robust cross-validation strategies are conducted to evaluate the proposed method; stratified k-fold cross-validation (SKCV) and leave-one-subject-out cross-validation (LOOCV). We also investigate the effect of window size and the combination of Intrinsic Mode Functions (IMFs) on classification performance. The results demonstrated that the HHT utilizing IMFs obtained by Empirical Mode Decomposition (EMD) provided improved TF resolution and better results than STFT and CWT in the classification of sEMG signals. Finally, the best average accuracies (93.75% for SKCV) and (94.41% for LOOCV) are obtained by the HHT method with the pre-trained ResNet-50 model.

A multi-group assessment of safety culture among engineering students in the United Arab Emirates

PurposeThe purpose of this paper is to identify the factor structure of safety culture construct among engineering students at university context and to examine the measurement invariance of this instrument across different socio-demographic groups in a sample of engineering students in the United Arab Emirates (UAE).Design/methodology/approachAn exploratory online questionnaire was completed by 770 undergraduate and postgraduate engineering students across the UAE. Data were analyzed using a diversified multi-group and a robust and sophisticated cross-validation testing strategy. Confirmatory factor analysis (CFA) was used to test factor structures identified in previous studies. Multi-group invariance testing was conducted to determine the extent to which factor structure is comparable across groups (i.e. gender, educational and experiential background).FindingsThree-factor model was preferred for its parsimony. The results showed that the level of safety awareness and attitude is relatively satisfactory, whereas safety behaviour is inadequate. No significant difference was showed in multi-group invariance between demographic groups.Research limitations/implicationsThis research is a cross-sectional study and limited to the views of engineering students (informal group). The study would benefit from both informal and formal groups in assessing safety culture at university for a robust empirical evidence. The research highlights relevant implications for policy and program development, by pointing to the need to promote safety culture and mitigate safety-related accidents among engineering students.Originality/valueThis paper offers insight into benefit of understanding the level of safety culture among engineering students and extend knowledge of informal group involvement in safety-related accidents at university level.

Robust linear classification from limited training data

We consider the problem of linear classification under general loss functions in the limited-data setting. Overfitting is a common problem here. The standard approaches to prevent overfitting are dimensionality reduction and regularization. But dimensionality reduction loses information, while regularization requires the user to choose a norm, or a prior, or a distance metric. We propose an algorithm called RoLin that needs no user choice and applies to a large class of loss functions. RoLin combines “reliable” information from the top principal components with a robust optimization to extract any useful information from “unreliable” subspaces. It also includes a new robust cross-validation that is better than existing cross-validation methods in the limited-data setting. Experiments on 25 real-world datasets and three standard loss functions show that RoLin broadly outperforms both dimensionality reduction and regularization. Dimensionality reduction has \(14\%-40\%\) worse test loss on average as compared to RoLin. Against \(L_1\) and \(L_2\) regularization, RoLin can be up to 3x better for logistic loss and 12x better for squared hinge loss. The differences are greatest for small sample sizes, where RoLin achieves the best loss on 2x to 3x more datasets than any competing method. For some datasets, RoLin with 15 training samples is better than the best norm-based regularization with 1500 samples.

Automated Machine Learning Pipeline for Traffic Count Prediction

Research indicates that the projection of traffic volumes is a valuable tool for traffic management. However, few studies have examined the application of a universal automated framework for car traffic volume prediction. Within this limited literature, studies using broad data sets and inclusive predictors have been inadequate; such works have not incorporated a comprehensive set of linear and nonlinear algorithms utilizing a robust cross-validation approach. The proposed model pipeline introduced in this study automatically identifies the most appropriate feature-selection method and modeling approach to reduce the mean absolute percentage error. We utilized hyperparameter optimization to generate a universal automated framework, distinct from model optimization techniques that rely on a single case study. The resulting model can be independently customized to any respective project. Automating much of this process minimizes the work and expertise required for traffic count forecasting. To test the applicability of our models, we used Florida historical traffic data from between 2001 and 2017. The results confirmed that nonlinear models outperformed linear models in predicting passenger vehicles’ monthly traffic volumes in this specific case study. By employing the framework developed in this study, transportation planners could identify the critical links on US roads that incur overcapacity issues.

Robust regression with compositional covariates

Many biological high-throughput datasets, such as targeted amplicon-based and metagenomic sequencing data, are compositional. A common exploratory data analysis task is to infer robust statistical associations between high-dimensional microbial compositions and habitat- or host-related covariates. To address this, a general robust statistical regression framework RobRegCC (Robust Regression with Compositional Covariates) is proposed, which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for parsimonious model estimation, a data-driven robust initialization procedure, and a novel robust cross-validation model selection scheme. The procedure is implemented in the R package robregcc. Extensive simulation studies show the RobRegCC's ability to perform simultaneous sparse log-contrast regression and outlier detection over a wide range of settings. To demonstrate the seamless applicability of the workflow to real data, the gut microbiome dataset from HIV patients are analyzed and robust associations between a sparse set of microbial species and host immune response from soluble CD14 measurements are inferred.

A Universal Automated Data-Driven Modeling Framework for Truck Traffic Volume Prediction

Knowledge of the truck traffic volumes on state and interstate highways is critical for highway authorities and federal organizations. Increased urbanization, population growth, and economic development have led to an increased demand for freight travel. Several planning applications demand reliable and accurate truck traffic prediction. A review of the available literature indicated that limited research had been performed on the development and utilization of a universal automatic framework for truck traffic volume prediction. As a result, there is a gap to incorporate inclusive predictors, a broad dataset, a comprehensive feature selection approach, and a robust cross-validation method that utilizes both linear and non-linear algorithms. The present study uses a hyperparameter optimization framework to select the appropriate feature selection method and modeling approach among a comprehensive list of available state of the art approaches. Distinct from models based on individual case studies, the proposed framework allows for greater customization and minimized MAPE error. The developed framework automates much of the traffic count forecasting process, and the resulting method is less labor-intensive and may be utilized without the need for experienced data analysts. Florida's interstate highways historical traffic data were used to test the feasibility of the proposed framework. The results of the Florida Case Study revealed the superiority of non-linear models in the generalization and prediction of traffic volumes over linear models. The random forest algorithm results on the test dataset in this study demonstrate this model's ability to predict truck traffic with 86% accuracy. Spatial variables were the most significant variable group, followed by road characteristics.

A multifunctional cross-validation high-throughput screening protocol enabling the discovery of new SHP2 inhibitors

The protein tyrosine phosphatase Src homology phosphotyrosyl phosphatase 2 (SHP2) is implicated in various cancers, and targeting SHP2 has become a promising therapeutic approach. We herein described a robust cross-validation high-throughput screening protocol that combined the fluorescence-based enzyme assay and the conformation-dependent thermal shift assay for the discovery of SHP2 inhibitors. The established method can effectively exclude the false positive SHP2 inhibitors with fluorescence interference and was also successfully employed to identify new protein tyrosine phosphatase domain of SHP2 (SHP2-PTP) and allosteric inhibitors. Of note, this protocol showed potential for identifying SHP2 inhibitors against cancer-associated SHP2 mutation SHP2-E76A. After initial screening of our in-house compound library (∼2300 compounds), we identified 4 new SHP2-PTP inhibitors (0.17% hit rate) and 28 novel allosteric SHP2 inhibitors (1.22% hit rate), of which SYK-85 and WS-635 effectively inhibited SHP2-PTP (SYK-85: IC50 = 0.32 μmol/L; WS-635: IC50 = 4.13 μmol/L) and thus represent novel scaffolds for designing new SHP2-PTP inhibitors. TK-147, an allosteric inhibitor, inhibited SHP2 potently (IC50 = 0.25 μmol/L). In structure, TK-147 could be regarded as a bioisostere of the well characterized SHP2 inhibitor SHP-099, highlighting the essential structural elements for allosteric inhibition of SHP2. The principle underlying the cross-validation protocol is potentially feasible to identify allosteric inhibitors or those inactivating mutants of other proteins.

Age differences in predicting working memory performance from network-based functional connectivity

Deterioration in working memory capacity (WMC) has been associated with normal aging, but it remains unknown how age affects the relationship between WMC and connectivity within functional brain networks. We therefore examined the predictability of WMC from fMRI-based resting-state functional connectivity (RSFC) within eight meta-analytically defined functional brain networks and the connectome in young and old adults using relevance vector machine in a robust cross-validation scheme. Particular brain networks have been associated with mental functions linked to WMC to a varying degree and are associated with age-related differences in performance. Comparing prediction performance between the young and old sample revealed age-specific effects: In young adults, we found a general unpredictability of WMC from RSFC in networks subserving WM, cognitive action control, vigilant attention, theory-of-mind cognition, and semantic memory, whereas in older adults each network significantly predicted WMC. Moreover, both WM-related and WM-unrelated networks were differently predictive in older adults with low versus high WMC. These results indicate that the within-network functional coupling during task-free states is specifically related to individual task performance in advanced age, suggesting neural-level reorganization. In particular, our findings support the notion of a decreased segregation of functional brain networks, deterioration of network integrity within different networks and/or compensation by reorganization as factors driving associations between individual WMC and within-network RSFC in older adults. Thus, using multivariate pattern regression provided novel insights into age-related brain reorganization by linking cognitive capacity to brain network integrity.

Modeling regional precipitation over the Indus River basin of Pakistan using statistical downscaling

Complex processes govern spatiotemporal distribution of precipitation within the high-mountainous headwater regions (commonly known as the upper Indus basin (UIB)), of the Indus River basin of Pakistan. Reliable precipitation simulations particularly over the UIB present a major scientific challenge due to regional complexity and inadequate observational coverage. Here, we present a statistical downscaling approach to model observed precipitation of the entire Indus basin, with a focus on UIB within available data constraints. Taking advantage of recent high altitude (HA) observatories, we perform precipitation regionalization using K-means cluster analysis to demonstrate effectiveness of low-altitude stations to provide useful precipitation inferences over more uncertain and hydrologically important HA of the UIB. We further employ generalized linear models (GLM) with gamma and Tweedie distributions to identify major dynamic and thermodynamic drivers from a reanalysis dataset within a robust cross-validation framework that explain observed spatiotemporal precipitation patterns across the Indus basin. Final statistical models demonstrate higher predictability to resolve precipitation variability over wetter southern Himalayans and different lower Indus regions, by mainly using different dynamic predictors. The modeling framework also shows an adequate performance over more complex and uncertain trans-Himalayans and the northwestern regions of the UIB, particularly during the seasons dominated by the westerly circulations. However, the cryosphere-dominated trans-Himalayan regions, which largely govern the basin hydrology, require relatively complex models that contain dynamic and thermodynamic circulations. We also analyzed relevant atmospheric circulations during precipitation anomalies over the UIB, to evaluate physical consistency of the statistical models, as an additional measure of reliability. Overall, our results suggest that such circulation-based statistical downscaling has the potential to improve our understanding towards distinct features of the regional-scale precipitation across the upper and lower Indus basin. Such understanding should help to assess the response of this complex, data-scarce, and climate-sensitive river basin amid future climatic changes, to serve communal and scientific interests.

Need for Cross-Validation of Single Particle Cryo-EM.

Cross-validation is used to determine the validity of a model on unseen data by assessing if the model is overfitted to noise. It is widely used in many fields, from artificial intelligence to structural biology in X-ray crystallography and nuclear magnetic resonance. Although there are concerns of map overfitting in cryo-electron microscopy (cryo-EM), cross-validation is rarely used. The problem is that establishing a performance metric of the maps over unseen data (given by 2D-projection images) is difficult due to the low signal-to-noise ratios in the individual particles. Here, I present recent advances for cryo-EM map reconstruction. I highlight that the gold-standard procedure can fail to detect map overfitting in certain cases, showing the necessity of assessing the map quality on unbiased data. Finally, I describe the challenges and advantages of developing a robust cross-validation methodology for cryo-EM.

Towards a new generation of parton densities with deep learning models

We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework based on graph generated models for PDF parametrization and gradient descent optimization. The best model configuration is derived from a robust cross-validation mechanism through a hyperparametrization tune procedure. We show that results provided by this new framework outperforms the current state-of-the-art PDF fitting methodology in terms of best model selection and computational resources usage.

QSAR modelling of a large imbalanced aryl hydrocarbon activation dataset by rational and random sampling and screening of 80,086 REACH pre-registered and/or registered substances.

The Aryl hydrocarbon receptor (AhR) plays important roles in many normal and pathological physiological processes, including endocrine homeostasis, foetal development, cell cycle regulation, cellular oxidation/antioxidation, immune regulation, metabolism of endogenous and exogenous substances, and carcinogenesis. An experimental data set for human in vitro AhR activation comprising 324,858 substances, of which 1,982 were confirmed actives, was used to test an in-house-developed approach to rationally select Quantitative Structure-Activity Relationship (QSAR) training set substances from an unbalanced data set. In the first iteration, active and inactive substances were selected by random to make QSAR models. Then, more inactive substances were added to the training set in two further iterations based on incorrect or out-of-domain predictions to produce larger models. The resulting ‘rational’ model, comprising 832 actives and four times as many inactives, i.e. 3,328, was compared to a model with a training set of same size and proportion of inactives chosen entirely by random. Both models underwent robust cross-validation and external validation showing good statistical performance, with the rational model having external validation sensitivity of 85.1% and specificity of 97.1%, compared to the random model with sensitivity 89.1% and specificity 91.3%. Furthermore, we integrated the training sets for both models with the 93 external validation test set actives and 372 randomly selected inactives to make two final models. They also underwent external validations for specificity and cross-validations, which confirmed that good predictivity was maintained. All developed models were applied to predict 80,086 EU REACH substances. The rational and random final models had 63.1% and 56.9% coverage of the REACH set, respectively, and predicted 1,256 and 3,214 substances as actives. The final models as well as predictions for AhR activation for 650,000 substances will be published in the Danish (Q)SAR Database and can, for example, be used for priority setting, in read-across predictions and in weight-of-evidence assessments of chemicals.

Forecasting Geoenvironmental Risks: Integrated Applications of Mineralogical and Chemical Data

Management of solid mine wastes requires detailed material characterisation at the start of a project to minimize opportunities for the generation of acid and metalliferous drainage (AMD). Mine planning must focus on obtaining a thorough understanding of the environmental properties of the future waste rock materials. Using drill core obtained from a porphyry Cu project in Northern Europe, this study demonstrates the integrated application of mineralogical and geochemical data to enable the construction of enviro-geometallurgical models. Geoenvironmental core logging, static chemical testing, bulk- and hyperspectral mineralogical techniques, and calculated mineralogy from assay techniques were used to critically evaluate the potential for AMD formation. These techniques provide value-adding opportunities to existing datasets and provide robust cross-validation methods for each technique. A new geoenvironmental logging code and a new geoenvironmental index using hyperspectral mineralogical data (Hy-GI) were developed and embedded into the geochemistry-mineralogy-texture-geometallurgy (GMTG) approach for waste characterisation. This approach is recommended for new mining projects (i.e., early life-of-mine stages) to ensure accurate geoenvironmental forecasting, therefore facilitating the development of an effective waste management plan that minimizes geoenvironmental risks posed by the mined materials.

Weighted cross validation in model selection

Outliers and gross errors in the data, as well as deviations from the normality assumption of the error distribution, impact adversely statistical analyses that are based on classical procedures such as least squares and maximum likelihood methods. We briefly review the cross‐validation (CV) method to model selection and discuss its robust extension based on weighted likelihood methodology. The main advantage of weighted CV is that it is computationally fast, much faster than many of the robust model selection procedures proposed in the literature. We present the weighted CV algorithm, its operating characteristics, and illustrate its performance under symmetric and asymmetric contamination. The procedure, in the absence of contamination and under mild conditions, is asymptotically equivalent to the CV method for model selection. Additionally, it is asymptotically loss efficient and differs from the robust CV procedure introduced in the literature in that it downweights only those observations that do not fit well the full model.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical Models > Linear Models Statistical Models > Model Selection

Robust Likelihood Cross-Validation for Kernel Density Estimation

Likelihood cross-validation for kernel density estimation is known to be sensitive to extreme observations and heavy-tailed distributions. We propose a robust likelihood-based cross-validation method to select bandwidths in multivariate density estimations. We derive this bandwidth selector within the framework of robust maximum likelihood estimation. This method establishes a smooth transition from likelihood cross-validation for nonextreme observations to least squares cross-validation for extreme observations, thereby combining the efficiency of likelihood cross-validation and the robustness of least-squares cross-validation. We also suggest a simple rule to select the transition threshold. We demonstrate the finite sample performance and practical usefulness of the proposed method via Monte Carlo simulations and a real data application on Chinese air pollution.