Semiparametric Quantile Regression Research Articles

Smoothed quantile residual life regression analysis with application to the Korea HIV/AIDS cohort study

BackgroundThe residual life of a patient with human immunodeficiency virus (HIV) is of major interest to patients and their physicians. While existing analyses of HIV patient survival focus mostly on data collected at baseline, residual life analysis allows for dynamic analysis based on additional data collected over a period of time. As survival times typically exhibit a right-skewed distribution, the median provides a more useful summary of the underlying distribution than the mean. In this paper, we propose an efficient inference procedure that fits a semiparametric quantile regression model assessing the effect of longitudinal biomarkers on the residual life of HIV patients until the development of dyslipidemia, a disease becoming more prevalent among those with HIV.MethodsFor estimation of model parameters, we propose an induced smoothing method that smooths nonsmooth estimating functions based on check functions. For variance estimation, we propose an efficient resampling-based estimator. The proposed estimators are theoretically justified. Simulation studies are used to evaluate their finite sample performances, including their prediction accuracy. We analyze the Korea HIV/AIDS cohort study data to examine the effects of CD4 (cluster of differentiation 4) cell count on the residual life of HIV patients to the onset of dyslipidemia.ResultsThe proposed estimator is shown to be consistent and normally distributed asymptotically. Under various simulation settings, our estimates are approximately unbiased. Their variances estimates are close to the empirical variances and their computational efficiency is superior to that of the nonsmooth counterparts. Two measures of prediction performance indicate that our method adequately reflects the dynamic character of longitudinal biomarkers and residual life. The analysis of the Korea HIV/AIDS cohort study data shows that CD4 cell count is positively associated with residual life to the onset of dyslipidemia but the effect is not statistically significant.ConclusionsOur method enables direct prediction of residual lifetimes with a dynamic feature that accommodates data accumulated at different times. Our estimator significantly improves computational efficiency in variance estimation compared to the existing nonsmooth estimator. Analysis of the HIV/AIDS cohort study data reveals dynamic effects of CD4 cell count on the residual life to the onset of dyslipidemia.

Two-piece distribution based semi-parametric quantile regression for right censored data

Two-piece distribution based semi-parametric quantile regression for right censored data

Instrumental variable quantile regression under random right censoring

Summary This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the system of equations. We derive conditions under which the estimator is asymptotically normal and prove the validity of a bootstrap procedure for inference. The finite sample performance of the approach is evaluated through numerical simulations. An application to the national Job Training Partnership Act study illustrates the method.

A Bayesian Semi-parametric Quantile Regression Approach for Joint Modeling of Longitudinal Ordinal and Continuous Responses

Quantile regression (QR) models are one of the methods for longitudinal data analysis. When responses seemto be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. This paper developes the semi-parametric quantile regression model for analyzing longitudinal continuous and ordinal mixed responses. The latent variable model and some threshold parameters are used to perform the quantile regression model’s ordinal part. The error of the latent variable model has Asymmetric Laplace (AL) distribution. The error term’s distribution is assumed to be AL distribution to model the continuous responses. The correlations of longitudinal responses belong to the same individual and those of mixed continuous and ordinal responses are considered using a random-effects approach. The regression spline is used to approximate the non-parametric part of the model. The parameter estimation procedure is performed under aBayesian paradigm using the Gibbs sampling method. A simulation study is performed to demonstrate the proposed model’s performance where the relative biases, standard errors, and root of MSEs of estimated parameters are decreased in the semi- parametric QR joint model when the number of subjects is increased. In our application, it was found that the mother’s age and her child’s age have significant effects on reading ability, and antisocial behavior depends on the child’s gender.

Nonparametric and Semiparametric Quantile Regression via a New MM Algorithm

Quantile regression is a popular method with a wide range of scientific applications, but the computation for quantile regression is challenging. Hunter and Lange proposed an MM algorithm for solving optimization problems in parametric quantile regression models. For nonparametric and semiparametric quantile regression, their algorithm can be applied to estimate unknown quantile functions in a pointwise manner. However, the resulting estimates may suffer from drawbacks like nonsmooth with discontinuous points and unstable at extreme quantile levels. To remedy the above issues, we propose a new MM algorithm and show that it yields continuous, smoother, and faster estimated quantile functions. We systematically study the new MM algorithm using the local linear quantile regression model. We prove that the proposed algorithm preserves the monotone descent property in an asymptotic sense. We then extend it to some popular nonparametric and semiparametric quantile regression models. For semiparametric models, we propose new efficient backfitting algorithms based on the new MM algorithm. Compared to traditional backfitting algorithms, the new procedures can significantly reduce computational costs for fully iterative backfitting. The performance of the proposed algorithms is demonstrated via extensive simulation studies and a real data example. Supplementary materials for this article are available online.

Ownership Structure, Corporate Governance, and Performance of Listed Companies—An Empirical Application of a Semi-Parametric Quantile Regression Model

China’s listed companies have different ownership characteristics and market environments from those of other countries and thus exhibit vastly different changes. From the existing corporate life cycle perspective, companies differ in their different development stages, which makes each factor’s effect dynamic. How to adjust the governance mechanism to the requirements of the company’s stage of development is an urgent issue in sustainable corporate governance. To address the above issues, we establish a semi-parametric quantile regression model to analyze the relationship between the ownership structure and corporate performance based on the data of listed companies on the Shanghai Stock Exchange between 2013 and 2021. Moreover, corporate governance measures taken at different stages of the corporate life cycle are discussed to see whether they effectively improve corporate governance. We conclude that there are non-linear effects of ownership structure while dynamic changes in corporate governance mechanisms exist. Companies should be concerned about the non-linear effects of ownership structures while considering the company’s life cycle and choosing appropriate governance measures. The results will help develop a sustainable development strategy to ensure that the company can improve its profitability and mitigate agency problems.

Nonparametric inference on smoothed quantile regression process

This paper studies the global estimation in semiparametric quantile regression models. For estimating unknown functional parameters, an integrated quantile regression loss function with penalization is proposed. The first step is to obtain a vector-valued functional Bahadur representation of the resulting estimators, and then derive the asymptotic distribution of the proposed infinite-dimensional estimators. Furthermore, a resampling approach that generalizes the minimand perturbing technique is adopted to construct confidence intervals and to conduct hypothesis testing. Extensive simulation studies demonstrate the effectiveness of the proposed method, and applications to the real estate dataset and world happiness report data are provided.

Testing rank similarity in the local average treatment effects model

This paper develops a test for the rank similarity condition of the nonseparable instrumental variable quantile regression model using the local average treatment effect model. When the instrument takes more than two values or multiple binary instruments are available, there exist multiple complier groups for which the marginal distributions of potential outcomes are identified. A testable implication is obtained by comparing the distributions of ranks across complier groups. We propose a test procedure in a semiparametric quantile regression specification. We establish the weak convergence of the test statistic and the validity of the bootstrap critical value. We illustrate the test with an empirical example of the effects of fertility on women’s labor supply.

The determinants of IPO initial returns in emerging markets: a quantile regression

PurposeThis article investigates the determinants of cross-section variation of initial public offerings' (IPOs) first-day returns in a sample of 710 issues across seven emerging markets between 2013 and 2017.Design/methodology/approachOrdinary least squares regression (OLS) and the semi-parametric quantile regression (QR) technique are employed. QR enables to analyse beyond the explanatory variables' relative mean effect at various points in the endogenous variable distribution. Furthermore, parameter estimates under QR are robust to the existence of outliers and long tails in the data distribution.FindingsUnderpricing varies across countries with an average of 78%. According to the OLS results, independent variables explain 26% of the variation of IPOs' first-day returns. Findings show that employing QR is important, given the non-normality of the data and because each quantile is associated with a different effect of explanatory variables.Originality/valueIn addition to firm-specific, market-specific and issue-specific factors, the paper extends IPOs' underpricing literature through studying the impact of country-specific characteristics, largely neglected by literature, on IPO underpricing.

R&D expenditure and managerial ownership: evidence from firms of high-vs-low R&D intensity

PurposeCorporate managers spend on research and development (R&D) for reasons of growth and survival. However, they may be less willing to invest in R&D because of its long-term horizon, high failure rate and uncertain outcomes. This study aims to explore the extent to which managerial ownership influences R&D expenditure decisions.Design/methodology/approachApart from the linear regression models, this study uses a semi-parametric quantile regression analysis for a sample of German non-financial firms throughout 2009–2018.FindingsThis study finds a nonmonotonic sensitivity of R&D spending to the level of managerial ownership over various quantiles of R&D distribution. That is, managerial ownership increases the expenditure on R&D at low R&D intensity firms. However, it decreases the expenditure on R&D at high R&D intensity firms. These results suggest the presence of a maximum level of R&D expenditure, after which owner-managers would be unwilling to spend on R&D.Practical implicationsThe results confirm the importance of corporate ownership structure for firm R&D and innovation activities. It provides an implication for corporate policymakers to reform the corporate ownership structures to encourage corporate managers and owners to invest in R&D projects.Originality/valueThis study offers two distinct contributions study. First, it provides the first German shred of evidence on the nonlinear relationship between managerial ownership and R&D expenditure decisions by distinguishing between high and low R&D intensity firms. Second, unlike prior research, it uses a semi-parametric quantile regression analysis. This method is more efficient than least-squares estimators and produces robust estimators to heteroscedasticity of the residuals.

Panel semiparametric quantile regression neural network for electricity consumption forecasting

Addressing the forecasting issues is one of the core objectives of developing and restructuring of electric power industry in China. However, there are not enough efforts that have been made to develop an accurate electricity consumption forecasting procedure. In this paper, a panel semiparametric quantile regression neural network (PSQRNN) is developed by combining an artificial neural network and semiparametric quantile regression for panel data. By embedding penalized quantile regression with least absolute shrinkage and selection operator (LASSO), ridge regression and backpropagation, PSQRNN keeps the flexibility of nonparametric models and the interpretability of parametric models simultaneously. The prediction accuracy is evaluated based on China's electricity consumption data set, and the results indicate that PSQRNN performs better compared with three benchmark methods including BP neural network (BP), Support Vector Machine (SVM) and Quantile Regression Neural Network (QRNN).

Semiparametric Quantile Models for Ascending Auctions With Asymmetric Bidders

The article proposes a parsimonious and flexible semiparametric quantile regression specification for asymmetric bidders within the independent private value framework. Asymmetry is parameterized using powers of a parent private value distribution, which is generated by a quantile regression specification. As noted in Cantillon, this covers and extends models used for efficient collusion, joint bidding and mergers among homogeneous bidders. The specification can be estimated for ascending auctions using the winning bids and the winner’s identity. The estimation is in two stage. The asymmetry parameters are estimated from the winner’s identity using a simple maximum likelihood procedure. The parent quantile regression specification can be estimated using simple modifications of Gimenes. Specification testing procedures are also considered. A timber application reveals that weaker bidders have 30% less chances to win the auction than stronger ones. It is also found that increasing participation in an asymmetric ascending auction may not be as beneficial as using an optimal reserve price as would have been expected from a result of Bulow and Klemperer valid under symmetry.

Semiparametric quantile regression using family of quantile-based asymmetric densities

Quantile regression is an important tool in data analysis. Linear regression, or more generally, parametric quantile regression imposes often too restrictive assumptions. Nonparametric regression avoids making distributional assumptions, but might have the disadvantage of not exploiting distributional modelling elements that might be brought in. A semiparametric approach towards estimating conditional quantile curves is proposed. It is based on a recently studied large family of asymmetric densities of which the location parameter is a quantile (and not a mean). Passing to conditional densities and exploiting local likelihood techniques in a multiparameter functional setting then leads to a semiparametric estimation procedure. For the local maximum likelihood estimators the asymptotic distributional properties are established, and it is discussed how to assess finite sample bias and variance. Due to the appealing semiparametric framework, one can discuss in detail the bandwidth selection issue, and provide several practical bandwidth selectors. The practical use of the semiparametric method is illustrated in the analysis of maximum winds speeds of hurricanes in the North Atlantic region, and of bone density data. A simulation study includes a comparison with nonparametric local linear quantile regression as well as an investigation of robustness against miss-specifying the parametric model part.

Flexible Bayesian quantile curve fitting with shape restrictions under the Dirichlet process mixture of the generalized asymmetric Laplace distribution

We propose a flexible Bayesian semiparametric quantile regression model based on Dirichlet process mixtures of generalized asymmetric Laplace distributions for fitting curves with shape restrictions. The generalized asymmetric Laplace distribution exhibits more flexible tail behaviour than the frequently used asymmetric Laplace distribution in Bayesian quantile regression. In addition, nonparametric mixing over the shape and scale parameters with the Dirichlet process mixture extends its flexibility and improves the goodness of fit. By assuming the derivatives of the regression functions to be the squares of the Gaussian processes, our approach ensures that the resulting functions have shape restrictions such as monotonicity, convexity and concavity. The introduction of shape restrictions prevents overfitting and helps obtain smoother and more stable estimates of the quantile curves, especially in the tail quantiles for small and moderate sample sizes. Furthermore, the proposed shape‐restricted quantile semiparametric regression model deals with sparse estimation for regression coefficients using the horseshoe+ prior distribution, and it is extended to cases with group‐specific curve estimation and censored data. The usefulness of the proposed models is demonstrated using simulated datasets and real applications.

Does the Impact of Carbon Price Determinants Change with the Different Quantiles of Carbon Prices? Evidence from China ETS Pilots

Since carbon price volatility is critical to the risk management of the CO2 emissions trading market, research has focused on energy prices and macroeconomic drivers which cause changes in carbon prices and make the carbon market more volatile than other markets. However, they have ignored whether the impact of carbon price determinants changes when the carbon price is at different levels. To fill this gap, this paper applies a semiparametric quantile regression model to explore the effects of energy prices and macroeconomic drivers on carbon prices at different quantiles. The model combines the advantages of parameter estimation, nonparametric estimation and quantile regression to describe the nonlinear relationship between carbon price and its fundamentals, which do not need to make any assumptions about the random error. Carbon prices are high–tailed and exhibit higher kurtosis, the traditional models which tend to assume that data are normally distributed can’t perform well. Furthermore, the semiparametric model doesn’t need to assume that the data are normally distributed. Therefore, the semiparametric model can effectively model the data. Some new evidence from China’s emission trading scheme (ETS) pilots shows that energy prices and macroeconomic drivers have different effects on carbon prices at high or low quantiles. First, the negative impact of coal prices on carbon prices was greater at the lower quantile of carbon prices in the Shenzhen ETS pilot. However, the effects of coal prices were positive in the Beijing ETS pilot, which may be attributed to great demand for coal. Second, oil prices had greater negative effects on carbon prices at higher quantiles in Beijing and Hubei ETS pilots. This can be attributed to the fact that businesses use less oil when carbon prices are high. For the Shenzhen ETS pilot, the effects of oil prices were positive. Third, natural gas prices have a stronger effect on carbon prices as quantiles increased in the Beijing and Hubei ETS pilots. Lastly, the effects of macroeconomic drivers on carbon prices at low quantiles were stronger in the Shenzhen ETS pilots and higher at the medium quantiles in Beijing and Hubei ETS pilots. These findings suggest that the impact of determinants on the carbon prices at different levels is not constant. Ignoring this issue will lead to a missed warning about the risks of the carbon market. This study will be of positive significance for China’s emission trading scheme (ETS) pilots, in order to accurately monitor the effects of carbon prices determinants and effectively avoid carbon market risks.

Local Linear Quantile Regression for Time Series Under Near Epoch Dependence

This paper aims to establish asymptotic normality of the local linear kernel estimator for quantile regression under near epoch dependence, a useful concept in characterising time series dependence of extensive interests in Econometrics. In particular, near epoch dependence can cover a wide range of linear or nonlinear time series models that are even not of strong or $\alpha$-mixing property (a property usually assumed in the nonlinear time series literature). Under the mild conditions, the Bahadur representation of the quantile regression estimators is established in weak convergence sense. The method provides much richer information than mean regression and covers much more processes, which do not satisfy general mixing conditions. Simulation and application to a real data set are studied, which demonstrate the usefulness of the introduced method for analysis of time series. The theoretical results of this paper will be of widely potential interest for time series econometric semiparametric quantile regression modelling.

Real estate VaR estimation in Seoul and Busan, Korea

In this study, we estimtate the value-at-risk (VaR) of the 10-day average apartment prices of Gangnam-gu, Seoul and Haeundae-gu, Busan in Korea. For this purpose, we adopt the semiparametric quantile regression approach for the VaR calculation based on ARIMA-GARCH models, employing the well-known risk measures such as the conditional autoregressive value-at-risk (CAViaR) and conditional autoregressive expectile (CARE) methods. After conducting the unconditional coverage (UC) and conditional coverage (CC) tests on the estimated VaRs, we conclude that the two methods perform similarly for the Seoul case but the CARE method shows more stability than the CAViaR method in the Busan case.

Predicting pollution incidents through semiparametric quantile regression models

In this paper we present a method to forecast pollution episodes using measurements of the pollutant concentration along time. Specifically, we use a backfitting algorithm with local polynomial kernel smoothers to estimate a semiparametric additive quantile regression model. We also propose a statistical hypothesis test to determine critical values, i.e., the values of the concentration that are significant to forecast the pollution episodes. This test is based on a wild bootstrap approach modified to suit asymmetric loss functions, as occurs in quantile regression. The validity of the method was checked with both simulated and real data, the latter from $${\hbox {SO}}_{2}$$ emissions from a coal-fired power station located in Northern Spain.

Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk

This paper develops a Bayesian semiparametric quantile regression model for count data. The count responses are converted to continuous responses through the “jittered” method and a transform function. A Bayesian semiparametric quantile regression modeling approach is then developed. The error distribution in the quantile regression model is assumed to be a mixture of asymmetric Laplace distributions constructed with Dirichlet process. Historical death tolls of China caused by earthquakes from 1969 to 2006 are used for fitting, and a parametric model is employed for model comparison. The results of model comparison show that the proposed semiparametric quantile regression model outperforms the parametric model. The empirical analysis illustrates that the impact of earthquake magnitude on death tolls is significant. Moreover, the impact of the magnitude is more pronounced on higher percentiles of death tolls.

Fuzzy Quantile Linear Regression Model Adopted with a Semi-Parametric Technique based on Fuzzy Predictors and Fuzzy Responses

As an extension to statistical techniques, fuzzy regression analysis estimates the relationship between fuzzy independent variables and non-fuzzy and/or fuzzy dependent variables. However, facing skewed or non-normal data may lead to vague results if the conventional least square models are used. However, there are many situations in applications of intelligence systems where regression components are fuzzy quantities instead of exact values. The present work is aimed to propose a fuzzy semi-parametric quantile regression model with fuzzy predictors, a fuzzy smooth function, exact coefficients and fuzzy responses. The proposed method is based on a new class of novel kernel-based signed-distance measures in space of fuzzy numbers. Main features of the proposed signed-distance including its robustness were studied. It was shown that the proposed signed-distance measure is more reasonable and effective than a common signed-distance which extensively has been used in fuzzy set theory. This is the reason why we decided to apply the proposed signed-distance to extend the classical quantile regression model. Then, a hybrid algorithm was suggested to evaluate optimal bandwidth, non-fuzzy regression coefficients and fuzzy smooth function at a specific quantile level. The proposed method was then compared with some common fuzzy regression models based on two data sets including a simulation study and an applied example. The numerical results clearly indicated that the proposed fuzzy semi-parametric quantile linear regression model performs better than the other available methods in terms of some common goodness-of-fit criteria in cases where the data set includes skewness and/or some outlier data point. The main advantages of the proposed method are as follows: 1-it is not so sensitive to the outlier data points and/or skewed data, 2- it possesses better fitting effect compared to other existing fuzzy regression models. Thus, the proposed quantile regression model could be successfully applied in many practical studies of fuzzy regression model in real-world applications.