Composite Quantile Regression Research Articles

Leveraging Transformer-Based Non-Parametric Probabilistic Prediction Model for Distributed Energy Storage System Dispatch

In low-voltage distribution networks, distributed energy storage systems (DESSs) are widely used to manage load uncertainty and voltage stability. Accurate modeling and estimation of voltage fluctuations are crucial to informed DESS dispatch decisions. However, existing parametric probabilistic approaches have limitations in handling complex uncertainties, since they always rely on predefined distributions and complex inference processes. To address this, we integrate the patch time series Transformer model with the non-parametric Huberized composite quantile regression method to reliably predict voltage fluctuation without distribution assumptions. Comparative simulations on the IEEE 33-bus distribution network show that the proposed model reduces the DESS dispatch cost by 6.23% compared to state-of-the-art parametric models.

Bayesian relative composite quantile regression approach of ordinal latent regression model with L1/2 regularization

AbstractOrdinal data frequently occur in various fields such as knowledge level assessment, credit rating, clinical disease diagnosis, and psychological evaluation. The classic models including cumulative logistic regression or probit regression are often used to model such ordinal data. But these modeling approaches conditionally depict the mean characteristic of response variable on a cluster of predictive variables, which often results in non‐robust estimation results. As a considerable alternative, composite quantile regression (CQR) approach is usually employed to gain more robust and relatively efficient results. In this paper, we propose a Bayesian CQR modeling approach for ordinal latent regression model. In order to overcome the recognizability problem of the considered model and obtain more robust estimation results, we advocate to using the Bayesian relative CQR approach to estimate regression parameters. Additionally, in regression modeling, it is a highly desirable task to obtain a parsimonious model that retains only important covariates. We incorporate the Bayesian penalty into the ordinal latent CQR regression model to simultaneously conduct parameter estimation and variable selection. Finally, the proposed Bayesian relative CQR approach is illustrated by Monte Carlo simulations and a real data application. Simulation results and real data examples show that the suggested Bayesian relative CQR approach has good performance for the ordinal regression models.

Bayesian relative composite quantile regression with ordinal longitudinal data and some case studies

ABSTRACT In real applied fields such as clinical medicine, environmental sciences, psychology as well as economics, we often encounter the task of conducting statistical inference for longitudinal data with ordinal responses. The traditional methods of longitudinal data analysis are often inclined to model continuous responses, which are no longer suitable for such ordinal data. Logistic regression and probit regression are two considerable methods which are frequently used to model ordinal longitudinal responses. However, such modelling methods just depict the mean feature of latent outcome variable and may produce non-robust results when encountering nor-normal errors or outliers. As a proper alternative of mean regression models, composite quantile regression (CQR) method is usually employed to derive robust estimation. The target of this paper is to investigate the CQR estimation approach for ordinal latent longitudinal model. The joint Bayesian hierarchical model is established and a relative CQR estimation approach is suggested to conduct posterior inference for the considered model. Further, in longitudinal data modelling, excessive predictors may be brought into in the models which result in the decrease of the model prediction precision. Bayesian L 1 / 2 regularized prior is incorporated into ordinal longitudinal CQR model to conduct variable selection simultaneously. Finally, simulation studies and two ordinal longitudinal data analysis are hired to illustrate the considered method.

Transfer learning with high dimensional composite quantile regression

Transfer learning has gained wide popularity due to its ability to enhance the performance of target tasks by utilizing external information sources. Despite this, current transfer learning methods often struggle to consistently and effectively handle heterogeneous and/or heavy tail data. To address this issue, we propose a robust transfer learning method based on the composite quantile regression model that can adapt to a variety of data types and integrate multiple quantile information. Additionally, this method can handle situations where the error term variance is infinite. A challenging scenario in transfer learning is that the transferable data set is unknown, so we design two detection algorithms to correctly identify valid transferable data sets. Through numerical simulations and empirical analysis, we verify the good performance of the above algorithms based on the high-dimensional composite quantile regression model.

Bayesian composite $$L^p$$-quantile regression

Abstract$$L^p$$ L p -quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, $$p=1$$ p = 1 , and expectiles, $$p=2$$ p = 2 , as special cases. This paper studies composite $$L^p$$ L p -quantile regression, simultaneously extending single $$L^p$$ L p -quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.

Truncated composite quantile regression with covariates measurement errors

Truncated data and measurement error data are often encountered in practice. In this paper, we study two classes of truncated composite quantile regression with covariates measured with errors. We propose weighted composite quantile regression estimators of the slope parameters based on weights which are random quantities and determined by the product-limit estimates of the distribution function of truncated variable. However, the estimators are often biased when one treats mismeasured covariates as error-free. To eliminate the bias and obtain consistent estimators, a debiasing technique is proposed. The resulting estimates are proved to be asymptotically normal and root n consistent under some mild conditions. Simulation studies and a real data example show that the proposed methods work promisingly.

Forecasting cryptocurrencies returns: Do macroeconomic and financial variables improve tail expectation predictions?

This study aims to jointly predict conditional quantiles and tail expectations for the returns of the most popular cryptocurrencies (Bitcoin, Ethereum, Ripple, Dogecoin and Litecoin) using financial and macroeconomic indicators as explanatory variables. We adopt a Monotone Composite Quantile Regression Neural Network (MCQRNN) model to make one- and five-steps-ahead predictions of Value-at-Risk (VaR) and Expected Shortfall (ES) based on a rolling window and compare the performance of our model against the Historical simulation and the standard ARMA(1,1)-GARCH(1,1) model used as benchmarks. The superior set of models is then chosen by backtesting VaR and ES using a Model Confidence Set procedure. Our results show that the MCQRNN performs better than both benchmark models for jointly predicting VaR and ES when considering daily data. Models with the implied volatility index, treasury yield spread and inflation expectations sharpen the extreme return predictions. The results are consistent for the two risk measures at the 1% and 5% level both, in the case of a long and short position and for all cryptocurrencies.

Sparse and debiased lasso estimation and inference for high-dimensional composite quantile regression with distributed data

Sparse and debiased lasso estimation and inference for high-dimensional composite quantile regression with distributed data

Quantile autoregressive conditional heteroscedasticity

Abstract This article proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(∞) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations, we can extrapolate the high quantile levels by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.

Optimal subsampling algorithms for composite quantile regression in massive data

Massive datasets have gained increasing prominence across various fields, but their analysis is often impeded by computational limitations. In response, Wang and Ma (Optimal subsampling for quantile regression in big data. Biometrika. 2021;108:99–112) have proposed an optimal subsampling method for quantile regression in massive datasets. Composite quantile regression, as a robust and efficient alternative to ordinary least squares regression and quantile regression in linear models, presents further complexities due to its distinct loss function. This paper extends the optimal subsampling method to accommodate composite quantile regression problems. We begin by deriving two new optimal subsampling probabilities for composite quantile regression, considering both the L- and A-optimality criteria Subsequently, we develop an adaptive two-step method based on these probabilities. The resulting estimators exhibit desirable asymptotic properties. In addition, to estimate the variance-covariance matrix without explicitly estimating the densities of the responses, we propose a combining subsamples method. Numerical studies on simulated and real data are conducted to assess and showcase the practical performance of our proposed methods.

An adapted loss function for composite quantile regression with censored data

An adapted loss function for composite quantile regression with censored data

Bayesian composite quantile regression for the single-index model.

By using a Gaussian process prior and a location-scale mixture representation of the asymmetric Laplace distribution, we develop a Bayesian analysis for the composite quantile single-index regression model. The posterior distributions for the unknown parameters are derived, and the Markov chain Monte Carlo sampling algorithms are also given. The proposed method is illustrated by three simulation examples and a real dataset.

DAmcqrnn: An approach to censored monotone composite quantile regression neural network estimation

Quantile regression neural network (QRNN) model has recently become popular in solving complex nonlinear problems, but the quantile curves achieved by QRNN model may cross each other, leading to unreliable results. To remedy this defect, monotone composite quantile regression neural network (MCQRNN) model is more attractive with non-crossing quantile predictions. However, few works have been involved in the literature to apply MCQRNN model for censoring issues. Based on the data augmentation algorithm, this study presents an iterative estimation method, which is a three-step alternating process, for censored MCQRNN model. Step 1 imputes the censored data through a data augmentation procedure. Step 2 updates the MCQRNN model with the imputed data. Step 3 makes predictions by the updated MCQRNN model. Simulation studies and real data application demonstrate that our proposed method is not only superior to the available censored methods with respect to quantile loss and C-index, but also yields very close prediction results to those obtained by full uncensored data. Avoiding the quantile crossing problem, the proposed method is more flexible to cope with different types of censoring, overcoming the limitation that the existing censored methods only work for single censoring type with unbelievable predictions caused by the crossing phenomenon.

Bayesian group bridge composite quantile regression

Bayesian regularized composite quantile regression (CQR) method with group bridge penalty is adopted to conduct covariate selection and estimation in CQR. MCMC algorithm was improved for posterior inference employing a scale mixture of normal of the asymmetric Laplace distribution (ALD). The suggested algorithm uses priors for the coefficients of regression, which are scale mixtures of multivariate uniform distributions with a particular Gamma distribution as a mixing distribution. Simulation results and analyses of real data show that the suggested MCMC sampler has excellent mixing feature and outperforms the current approaches in terms of prediction accuracy and model selection.

Composite quantile regression analysis of survival data with missing cause-of-failure information and its application to breast cancer clinical trial

The analysis of survival data can be challenging due to the presence of missing data. This paper proposes weighted composite quantile regression (CQR) for estimating a lot of quantile regression (QR) of survival data based on single-index coefficient model (SICM), which is a very general and flexible tool for exploring the relationship between response variable and a set of predictors. The statistical inference for SICM is considered when cause-of-failure information (censored or non-censored) is always observed. However, the cause-of-failure information may be missing at random (MAR) for various reasons. Regression calibration, imputation and inverse probability weighted approaches are applied to deal with the MAR assumption. The asymptotic normalities of the proposed estimators are established. Meanwhile, the oracle property of the variable selection based on adaptive LASSO penalty procedure is conducted. To assess the finite sample performance of the proposed estimators, simulation study with normal error and heavy-tail error are considered. As expected, the CQR estimators perform as good as the least-square estimators for normal error, and are more robust to heavy-tailed error. Finally, a breast cancer real data analysis is carried out to illustrate the proposed methodologies.

Prediction of water quality extremes with composite quantile regression neural network.

Water quality extremes, which water quality models often struggle to predict, are a grave concern to water supply facilities. Most existing water quality models use mean error functions to maximize the predictability of water quality mean value. This paper describes a composite quantile regression neural network (CQRNN) model, which simultaneously estimates non-crossing regression quantiles by minimizing the composite quantile regression error function. This method can improve the prediction of extremes. This paper evaluates the performance of CQRNN for predicting extreme values of turbidity and total organic carbon (TOC) and compares with quantile regression (QR), linear regression (LR), and k-nearest neighbors (KNN) in an application to the Hetch Hetchy Regional Water System, which is the primary water supply for San Francisco, CA. CQRNN is superior to QR, LR, and KNN for predicting the mean trend and extremes of turbidity and TOC, especially for the non-Gaussian turbidity data. The performance of CQRNN is the most stable relative to other methods over different training sample sizes.

Second Order Model with Composite Quantile Regression

In many fields, comprehensive evaluation is a very important topic. Both second order model and its modified one with quantile regression have been widely used in evaluation. Although quantile-type second order model has abilities in capturing a complete picture of different variables’ relations at different quantile levels. Sometimes we find it complex to summarize the conclusions of all quantile levels. Therefore, we propose a new second order model with composite quantile regression, which has the advantage of obtaining a whole evaluation result based on all quantile levels. More specifically, one of our paper’s main contributions is to develop a comprehensive evaluation model based on the classical second order model, quantile regression and composite quantile regression. What’s more, we introduce a modified partial least square estimation algorithm under the well-known partial least squares framework. The new algorithm has the ability in estimating both path and loading coefficients reflecting the relationships among manifest variables and latent variables at all quantile levels.

Composite smoothed quantile regression

Composite quantile regression (CQR) is an efficient method to estimate parameters of the linear model with non‐Gaussian random noise. The non‐smoothness of CQR loss prevents many efficient algorithms from being used. In this paper, we propose the composite smoothed quantile regression (CSQR) model and investigate the inference problem for a large‐scale dataset, in which the dimensionality is allowed to increase with the sample size while . After applying the convolution smoothing technique to the composite quantile loss, we obtain the convex and twice differentiable CSQR loss function, which can be optimized via the gradient descent algorithm. Theoretically, we establish the non‐asymptotic error bound for the CSQR estimators and further provide the Bahadur representation and the Berry–Esseen bound, from which the asymptotic normality of CSQR estimator can be immediately derived. To make valid inference, we construct the confidence intervals that based on the asymptotic distribution. Besides, we also explore the asymptotic relative efficiency of the CSQR estimator with respect to the standard CQR estimator. At last, we provide extensive numerical experiments on both simulated and real data to demonstrate the good performance of our CSQR estimator compared with some baselines.

High-dimensional composite quantile regression: Optimal statistical guarantees and fast algorithms

High-dimensional composite quantile regression: Optimal statistical guarantees and fast algorithms

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

Accurate global horizontal irradiance (GHI) forecasting promotes power grid stability. Most of the research on solar irradiance forecasting has been based on a single-site analysis. It is crucial to explore multisite modeling to capture variations in weather conditions between various sites, thereby producing a more robust model. In this research, we propose the use of spatial regression coupled with Gaussian Process Regression (GP Spatial) and the GP Autoregressive Spatial model (GP-AR Spatial) for the prediction of GHI using data from seven radiometric stations from South Africa and one from Namibia. The results of the proposed methods were compared with a benchmark model, the Linear Spatial Temporal Regression (LSTR) model. Five validation sets each comprised of three stations were chosen. For each validation set, the remaining five stations were used for training. Based on root mean square error, the GP model gave the most accurate forecasts across the validation sets. These results were confirmed by the statistical significance tests using the Giacommini–White test. In terms of coverage probability, there was a 100% coverage on three validation sets and the other two had 97% and 99%. The GP model dominated the other two models. One of the study’s contributions is using standardized forecasts and including a nonlinear trend covariate, which improved the accuracy of the forecasts. The forecasts were combined using a monotone composite quantile regression neural network and a quantile generalized additive model. This modeling framework could be useful to power utility companies in making informed decisions when planning power grid management, including large-scale solar power integration onto the power grid.