Composite Quantile Regression Method Research Articles

Estimation for generalized linear cointegration regression models through composite quantile regression approach

This paper introduces a meaningful approach employing composite quantile regression (CQR) to estimate generalized linear cointegration regression models. We elucidate the fundamental structure of the proposed model by presenting its underlying expressions and derive the asymptotic distribution of the estimates of model parameters. Through extensive simulations, our findings demonstrate the superior robustness and precision of the CQR method compared to ordinary least squares (OLS) and quantile regression (QR) approaches. The application of the model to economic and financial variables highlights its significant academic and practical value.

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.

Doubly robust weighted composite quantile regression based on SCAD‐L2

In this article, a robust variable selection procedure based on the weighted composite quantile regression (WCQR) is proposed. Compared with the composite quantile regression (CQR), WCQR is robust to heavy‐tailed errors and outliers in the explanatory variables. For the choice of the weights in the WCQR, we employ a weighting scheme based on the principal component method. To select variables with grouping effect, we consider WCQR with SCAD‐L2 penalization. Furthermore, under some suitable assumptions, the theoretical properties, including the consistency and oracle property of the estimator, are established with a diverging number of parameters. In addition, we study the numerical performance of the proposed method in the case of ultrahigh‐dimensional data. Simulation studies and real examples are provided to demonstrate the superiority of our method over the CQR method when there are outliers in the explanatory variables and/or the random error is from a heavy‐tailed distribution.

Single-index composite quantile regression for massive data

Composite quantile regression (CQR) is becoming increasingly popular due to its robustness from quantile regression. Recently, the CQR method has been studied extensively with single-index models. However, the numerical inference of CQR methods for single-index models must involve iteration. In this study, we propose a non-iterative CQR (NICQR) estimation algorithm and derive the asymptotic distribution of the proposed estimator. Moreover, we extend the NICQR method to the analysis of massive datasets via a divide-and-conquer strategy. The proposed approach significantly reduces the computing time and the required primary memory. Simulation studies and two real data applications are conducted to illustrate the finite sample performance of the proposed methods.

Penalized weighted composite quantile regression for partially linear varying coefficient models with missing covariates

In this paper we study partially linear varying coefficient models with missing covariates. Based on inverse probability-weighting and B-spline approximations, we propose a weighted B-spline composite quantile regression method to estimate the non-parametric function and the regression coefficients. Under some mild conditions, we establish the asymptotic normality and Horvitz–Thompson property of the proposed estimators. We further investigate a variable selection procedure by combining the proposed estimation method with adaptive LASSO. The oracle property of the proposed variable selection method is studied. Under a missing covariate scenario, two simulations with various non-normal error distributions and a real data application are conducted to assess and showcase the finite sample performance of the proposed estimation and variable selection methods.

An improvement on the efficiency of complete-case-analysis with nonignorable missing covariate data

This paper develops a weighted composite quantile regression method for linear models where some covariates are missing not at random but the missingness is conditionally independent of the response variable. It is known that complete case analysis (CCA) is valid under these missingness assumptions. By fully utilizing the information from incomplete data, empirical likelihood-based weights are obtained to conduct the weighted composite quantile regression. Theoretical results show that the proposed estimator is more efficient than the CCA one if the probability of missingness on the fully observed variables is correctly specified. Besides, the proposed algorithm is computationally simple and easy to implement. The methodology is illustrated on simulated data and a real data set.

Shrinkage estimation for identification of linear components in composite quantile additive models

In this paper, we consider a new robust identification of linear parts in additive models. A one-step sparse algorithm based on local linear approximation is used for minimizing the proposed composite quantile regression (CQR) objective function. Under some mild conditions, the theoretical properties of the proposed CQR method are obtained. We also present some simulation studies and real data analysis to show the performance of the proposed procedure.

Composite quantile regression for massive datasets

ABSTRACTAnalysis of massive datasets is challenging owing to limitations of computer primary memory. Composite quantile regression (CQR) is a robust and efficient estimation method. In this paper, we extend CQR to massive datasets and propose a divide-and-conquer CQR method. The basic idea is to split the entire dataset into several blocks, applying the CQR method for data in each block, and finally combining these regression results via weighted average. The proposed approach significantly reduces the required amount of primary memory, and the resulting estimate will be as efficient as if the entire data set is analysed simultaneously. Moreover, to improve the efficiency of CQR, we propose a weighted CQR estimation approach. To achieve sparsity with high-dimensional covariates, we develop a variable selection procedure to select significant parametric components and prove the method possessing the oracle property. Both simulations and data analysis are conducted to illustrate the finite sample performance of the proposed methods.

Estimation and variable selection for partially functional linear models

In this paper, a new estimation procedure based on composite quantile regression and functional principal component analysis (PCA) method is proposed for the partially functional linear regression models (PFLRMs). The proposed estimation method can simultaneously estimate both the parametric regression coefficients and functional coefficient components without specification of the error distributions. The proposed estimation method is shown to be more efficient empirically for non-normal random error, especially for Cauchy error, and almost as efficient for normal random errors. Furthermore, based on the proposed estimation procedure, we use the penalized composite quantile regression method to study variable selection for parametric part in the PFLRMs. Under certain regularity conditions, consistency, asymptotic normality, and Oracle property of the resulting estimators are derived. Simulation studies and a real data analysis are conducted to assess the finite sample performance of the proposed methods.

A robust and efficient estimation method for partially nonlinear models via a new MM algorithm

When the observed data set contains outliers, it is well known that the classical least squares method is not robust. To overcome this difficulty, Wang et al. (J Am Stat Assoc 108(502): 632–643, 2013) proposed a robust variable selection method by using the exponential squared loss (ESL) function with a tuning parameter. Although many important statistical models are investigated, to date, in the presence of outliers there is no paper to study the partially nonlinear model by using the ESL function. To fill in this gap, in this paper, we propose a robust and efficient estimation method for the partially nonlinear model based on the ESL function. Under certain conditions, we have shown that the proposed estimators can achieve the best convergence rates. Next, the asymptotic normality of the proposed estimators is established. In addition, we develop a new minorization–maximization algorithm to calculate the estimates for both non-parametric and parametric parts and present a procedure for deriving initial values. Finally, we provide a data-driven approach to select the tuning parameters. Numerical simulations and a real data analysis are used to illustrate that when there are outliers, the proposed ESL method is more robust and efficient for partially nonlinear models than the existing linear approximation method and the composite quantile regression method.

Single-index composite quantile regression with heteroscedasticity and general error distributions

It is known that composite quantile regression (CQR) could be much more efficient and sometimes arbitrarily more efficient than the least squares estimator. Based on CQR method, we propose a weighted CQR (WCQR) method for single-index models with heteroscedasticity and general error distributions. Because of the use of weights, the estimation bias is eliminated asymptotically. By comparing asymptotic relative efficiency, WCQR estimation outperforms the CQR estimation and least squares estimation. The simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods.

Composite quantile regression for linear errors-in-variables models

Composite quantile regression can be more efficient and sometimes arbitrarily more efficient than least squares for non-normal random errors, and almost as efficient for normal random errors. Therefore, we extend composite quantile regression method to linear errors-in-variables models, and prove the asymptotic normality of the proposed estimators. Simulation results and a real dataset are also given to illustrate our the proposed methods.

Weighted composite quantile regression estimation of DTARCH models

In modelling volatility in financial time series, the double‐threshold autoregressive conditional heteroscedastic (DTARCH) model has been demonstrated as a useful variant of the autoregressive conditional heteroscedastic (ARCH) models. In this paper, we propose a weighted composite quantile regression method for simultaneously estimating the autoregressive parameters and the ARCH parameters in the DTARCH model. This method involves a sequence of weights and takes a data‐driven weighting scheme to maximize the asymptotic efficiency of the estimators. Under regularity conditions, we establish asymptotic distributions of the proposed estimators for a variety of heavy‐ or light‐tailed error distributions. Simulations are conducted to compare the performance of different estimators, and the proposed approach is used to analyse the daily S&P 500 Composite index, both of which endorse our theoretical results.

Asymptotic normality for a local composite quantile regression estimator of regression function with truncated data

In this paper, we construct a local linear composite quantile regression (CQR) estimator of regression function for left-truncated data, which extends the CQR method to the left-truncated model. The asymptotic normality of the proposed estimator is also established. The estimator is much more efficient than the local linear regression estimator for commonly-used non-normal error distributions via simulations.