Quantile Regression Framework Research Articles

Partial Quantile Tensor Regression

Tensors, characterized as multidimensional arrays, are frequently encountered in modern scientific studies. Quantile regression has the unique capacity to explore how a tensor covariate influences different segments of the response distribution. In this work, we propose a partial quantile tensor regression (PQTR) framework, which novelly applies the core principle of the partial least squares technique to achieve effective dimension reduction for quantile regression with a tensor covariate. The proposed PQTR algorithm is computationally efficient and scalable to a large tensor covariate. Moreover, we uncover an appealing latent variable model representation for the PQTR algorithm, justifying a simple population interpretation of the resulting estimator. We further investigate the connection of the PQTR procedure with an envelope quantile tensor regression (EQTR) model, which defines a general set of sparsity conditions tailored to quantile tensor regression. We prove the root-n consistency of the PQTR estimator under the EQTR model, and demonstrate its superior finite-sample performance compared to benchmark methods through simulation studies. We demonstrate the practical utility of the proposed method via an application to a neuroimaging study of post traumatic stress disorder (PTSD). Results derived from the proposed method are more neurobiologically meaningful and interpretable as compared to those from existing methods.

Marketing inputs and outcome heterogeneity: Using a quantile regression framework in the entertainment industry

AbstractThe success of entertainment products such as movies or books varies tremendously, and managers strive to increase the odds by deciding on the right marketing input. Aiming to improve managerial decision making, we suggest and test a quantile regression framework to detect outcome heterogeneity effects of marketing inputs in the entertainment industry. By analyzing the spread of the .9 and the .1 conditioned quantile to the .5 (median) conditioned quantile, we study how much an increase (decrease) of an input factor (star power and quality) changes the spread of the expected outcome (revenues and sales). The spread serves as an indicator for the heterogeneity effect of the input factor regarding the outcome. In two empirical studies, we show how marketing instruments increase (or decrease) outcome heterogeneity by estimating quantile regressions and provide generalizable findings regarding the outcome heterogeneity effects of star power (increases outcome heterogeneity) and quality evaluations (reduces outcome heterogeneity) in the entertainment industry.

A distribution-free method for reliability improvement based on design of experiments

Given growing consumer expectations for enhanced product lifespans, there is a particular focus on improving product reliability. Design of Experiments (DOE) is a useful tool for identifying significant factors and determining factor levels to enhance product reliability. Current research commonly assumes that the lifetime data follows a specific distribution. This overlooks the possibility that erroneous assumptions about the data distribution may lead to imprecise factors identification. Additionally, factorial effect principles are often disregarded in factors effects identification. In this paper, a distribution-free method named Factor-Effect Bayesian Quantile Regression (FEBQR) is proposed to address the aforementioned issues. We first construct a new set of factor indicator variables, considering the principles of effect sparsity, weak effect hierarchy, and effect heredity. Then we develop a novel model that extends the Bayesian quantile regression framework by incorporating the principle of factor effects to describe the relationship between percentile lifetimes and factor effects. Unknown parameter estimates are obtained through the Gibbs sampling algorithm, and significant factors are identified based on the posterior mean of the proposed factor indicator variables. Two practical examples are illustrated using the proposed method. Compared with traditional methods, the proposed method provides more accurate factor identification results.

Quantile regression based method for characterizing risk-specific behavioral patterns in relation to longitudinal left-censored biomarker data collected from heterogeneous populations

There are many studies aimed at promoting positive lifestyle behaviors to reduce lifetime risk of cancer and related diseases. However, assessing these modifiable behaviors through statistical modeling is challenging because of the multidimensionality of interrelated measurements that may dramatically differ between at-risk individuals. Taking into account this heterogeneity while considering the multidimensionality of behavior changes is fundamental to tailoring interventions to their needs. Biomarkers that identify high-risk individuals may help validate proximal measures, but the number of validated methods that link biomarkers to multiple behavioral measurements by determining their dynamic relations with disease risks is limited to just a few, since it requires an advanced statistical methodology to address challenges in analyzing biomarker data, including left-censoring due to limits of detection. To address these challenges, we propose a method that constructs a quantile-specific weighted index of multiple behavioral measurements. Under the quantile regression framework, the proposed method renders a multidimensional view of risk-specific behavioral patterns by connecting them with biomarker levels to provide better insights into heterogeneous behavioral profiles among at-risk populations. We evaluate performances of the proposed method through simulations, and illustrate its applications to the Tu Salud ¡Sí Cuenta! data by examining behavior changes among Mexican-American adults.

Pinball boosting of regression quantiles

An algorithm for boosting regression quantiles using asymmetric least absolute deviations, better known as pinball loss, is proposed. Existing approaches for boosting regression quantiles are essentially equal to least squares boosting of regression means with the single difference that their working residuals are based on pinball loss. All steps of our boosting algorithm are embedded in the well-established framework of quantile regression, and its main components – sequential base learning, fitting, and updating – are based on consistent scoring rules for regression quantiles. The Monte Carlo simulations performed indicate that the pinball boosting algorithm is competitive with existing approaches for boosting regression quantiles in terms of estimation accuracy and variable selection, and that its application to the study of regression quantiles of hedonic price functions allows the estimation of previously infeasible high-dimensional specifications.

TENSOR QUANTILE REGRESSION WITH LOW-RANK TENSOR TRAIN ESTIMATION.

Neuroimaging studies often involve predicting a scalar outcome from an array of images collectively called tensor. The use of magnetic resonance imaging (MRI) provides a unique opportunity to investigate the structures of the brain. To learn the association between MRI images and human intelligence, we formulate a scalar-on-image quantile regression framework. However, the high dimensionality of the tensor makes estimating the coefficients for all elements computationally challenging. To address this, we propose a low-rank coefficient array estimation algorithm based on tensor train (TT) decomposition which we demonstrate can effectively reduce the dimensionality of the coefficient tensor to a feasible level while ensuring adequacy to the data. Our method is more stable and efficient compared to the commonly used, Canonic Polyadic rank approximation-based method. We also propose a generalized Lasso penalty on the coefficient tensor to take advantage of the spatial structure of the tensor, further reduce the dimensionality of the coefficient tensor, and improve the interpretability of the model. The consistency and asymptotic normality of the TT estimator are established under some mild conditions on the covariates and random errors in quantile regression models. The rate of convergence is obtained with regularization under the total variation penalty. Extensive numerical studies, including both synthetic and real MRI imaging data, are conducted to examine the empirical performance of the proposed method and its competitors.

Role of walkability, bike infrastructure, and greenspace in combatting chronic diseases: A heterogeneous ecological analysis in the United States

Associations of built and natural environment and bike infrastructure features with neighborhood-level hypertension and obesity prevalence across the U.S. are not well explored. Identifying the environmental determinants of neighborhood-level disease prevalence can support community-based nonpharmacologic interventions. Additionally, little is known about the extent of heterogeneity in built and natural environment impacts. Quantifying heterogeneity can help identify places where the greatest health gains can be obtained from infrastructural investments. Using a new neighborhood-level database, we assessed heterogeneous associations of neighborhood built and natural environment and bike infrastructure features with nationwide hypertension and obesity rates using a simultaneous quantile regression framework. A walkability index, access to green space, and bicycle infrastructure were negatively correlated with hypertension and obesity after controlling for social vulnerability. The associations of key environmental and bike infrastructure factors exhibited considerable heterogeneity. For a unit increase in the walkability index, the potential reduction in hypertension prevalence at the 10th percentile was 3.4 times the reduction at the 95th percentile. Likewise, the potential reduction in obesity prevalence at the 10th percentile was 1.8 times the reduction at the 95th percentile. Provision of on-street and off-street bike lanes was correlated with lower hypertension and obesity, although the impacts varied across the quantiles of health outcomes. Urban design policies promoting walkability, providing on-street and off-street bicycle facilities, and enhancing greenspace can be important strategies to combat hypertension and obesity. Our study underscores the importance of incorporating environmental features into future iterations of national disease prevalence data programs in the U.S.

Joint quantile disease mapping with application to malaria and G6PD deficiency.

Statistical analysis based on quantile methods is more comprehensive, flexible and less sensitive to outliers when compared to mean methods. Joint disease mapping is useful for inferring correlation between different diseases. Most studies investigate this link through multiple correlated mean regressions. We propose a joint quantile regression framework for multiple diseases where different quantile levels can be considered. We are motivated by the theorized link between the presence of malaria and the gene deficiency G6PD, where medical scientists have anecdotally discovered a possible link between high levels of G6PD and lower than expected levels of malaria initially pointing towards the occurrence of G6PD inhibiting the occurrence of malaria. Thus, the need for flexible joint quantile regression in a disease mapping framework arises. Our model can be used for linear and nonlinear effects of covariates by stochastic splines since we define it as a latent Gaussian model. We perform Bayesian inference using the R integrated nested Laplace approximation, suitable even for large datasets. Finally, we illustrate the model's applicability by considering data from 21 countries, although better data are needed to prove a significant relationship. The proposed methodology offers a framework for future studies of interrelated disease phenomena.

Spatiotemporal interaction characteristics and transition mechanism of tourism environmental efficiency in China

High-quality development is the theme of China’s economic and social development in the new era, and it is also an objective need for tourism development in the 14th Five-Year Plan period. This study presents an investigation of China’s patterns of tourism environmental efficiency from the perspective of spatiotemporal interactions. A nested analytical framework of quantile regression and spatiotemporal leaps was used to explore the driving mechanism patterns of tourism environmental efficiency under different leap types. Based on various spatial analysis methods, we posit that the patterns of tourism environmental efficiency differ through spatial associations, dynamic evolutions, and transition mechanisms. Our results indicate that there is a dynamic convergence trend of the overall differences in tourism environmental efficiency in China from 2000 to 2020 where a significant clustering phenomenon is observed in space and the level of spatial clustering gradually tends to be stable. In terms of local spatial structures and the dependence directions of tourism environmental efficiency, China’s northwest and northeast regions are more volatile, while eastern coastal regions are relatively stable. Spatiotemporal leaps of tourism environmental efficiency show certain transfer inertia with strong spatial dependence or path-locked characteristics, among which most central and western regions always maintain high carbon emission attributes. These regions are the most limited in the synergy of tourism environmental efficiency. The spatiotemporal network patterns of tourism environmental efficiency are mainly based on positive correlations and show strong spatial integration. However, a few neighboring provinces still have a certain degree of spatiotemporal competition. Driving patterns of the spatiotemporal leaps in tourism environmental efficiency among regions differ greatly. The eastern coastal provinces are driven by population-urbanization constraint patterns, and the northwest, southwest, and northeast regions are driven by technology regulation patterns. From the southeast to the northwest, the leap in the environmental efficiency of China's tourism gradually shows a stepwise pattern of "congruent constraint-reverse development-congruent development.” Therefore, the government should not only consider these various driving/constraining factors but also combine different environmentally-efficient tourism clustering types and transition paths to emphasize differentiated environmental tourism measures. This can help avoid the closure of inter-provincial tourism policies through inter-regional synergy.

Euro area uncertainty and Euro exchange rate volatility: Exploring the role of transnational economic policy

This study examines the relationship between economic policy uncertainty and Euro area exchange rate volatility, focusing on transnational Euro area uncertainty. The study introduces a novel index that captures uncertainty related to Euro area integration. The index is constructed using both traditional and advanced textual analysis methods. By employing a quantile regression framework, findings show that Euro area uncertainty significantly impacts the euro exchange rate's volatility, while national economic policy uncertainty is generally insignificant. The study emphasizes the importance of considering both national and supranational uncertainties when analysing exchange rate volatility, contributing to the existing literature on this subject.

The Influence of Equity Market Sentiment on Credit Default Swap Markets: Evidence from Wavelet Quantile Regression

Previous studies focused on the fundamental channels of the interaction between the equity market and credit default swap (CDS) market. This paper finds another channel, investor sentiment, that contributes to the impact of the equity market on the CDS market under different time horizons and market conditions within the framework of wavelet quantile regression. It absorbs both the merits of wavelet transform and quantile regression and is advantageous in analyzing heterogeneous time horizons and full conditional distributions. Empirical results show that investor attitude turning optimistic has a negative influence on the deviation of CDS market spread from theoretical value, while the intensification of fear among equity market will enlarge this deviation. Besides, we discovered that the influence of equity market sentiment on the CDS market first increases and then decreases as the time horizon lengthens and that the greater the deviation of CDS spreads from intrinsic value is, the more irrational the CDS market participants are. These findings suggest that the influence of investor sentiment on the credit default swap market is self-reinforced. Our results are robust after controlling for macroeconomic conditions and under different wavelet decompositions. Reasonable suggestions are given to financial institutions, investors, and policy makers based on our findings.

Estimation and variable selection of quantile partially linear additive models for correlated data

Longitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application.

Environmental Sustainability Analysis Using Moderation of Transport Competitiveness for Industrial-Induced EKC

Combating adversities of climate change and promoting clean energy are two important goals of the Sustainable Development Goals (SDGs). The nations of the World have developed various commitments to reduce global warming. The transportation sector share is above twenty percent in total global Greenhouse Gas emissions which is continuously rising over time. The Intergovernmental Panel on Climate Change (IPCC) in its recent report conducted a scenario analysis and suggested reducing net emissions by 2050. The transport competitiveness index indicates the quality and expansion of transport services. Accordingly, this research study uses the data of 121 countries for which transport competitiveness is documented by the World Economic Forum (WEF). The period of the study is confined to 2008-2018. The sample countries are segregated into four groups on the basis of transport sector emissions. The study uses Panel Quantile Regression (PQR) framework to estimate results and to validate the industrial Environmental Kuznets Curve (EKC). The findings indicate that transport competitiveness mitigates transport sector emissions in the majority of groups/categories. Inverted U shape industrial EKC has been authenticated in group-1 and U shape industrial EKC for the other three groups. The moderation of transportation competitiveness specified the flattening of industrial EKC across all quantile groups. The empirical findings indicate that moderation results in the sustainability of industrial EKC at higher levels of industrial growth. Among other variables, the governing ability of institutions and planned population expansion are observed in mitigating emissions. The policy options are discussed depending on the results of the groups.

Neural networks for quantile claim amount estimation: a quantile regression approach

AbstractIn this paper, we discuss the estimation of conditional quantiles of aggregate claim amounts for non-life insurance embedding the problem in a quantile regression framework using the neural network approach. As the first step, we consider the quantile regression neural networks (QRNN) procedure to compute quantiles for the insurance ratemaking framework. As the second step, we propose a new quantile regression combined actuarial neural network (Quantile-CANN) combining the traditional quantile regression approach with a QRNN. In both cases, we adopt a two-part model scheme where we fit a logistic regression to estimate the probability of positive claims and the QRNN model or the Quantile-CANN for the positive outcomes. Through a case study based on a health insurance dataset, we highlight the overall better performances of the proposed models with respect to the classical quantile regression one. We then use the estimated quantiles to calculate a loaded premium following the quantile premium principle, showing that the proposed models provide a better risk differentiation.

Threshold quantile regression neural network

ABSTRACT For modelling the threshold effect in parameters of the quantile neural network models, this paper introduces a model called threshold quantile regression neural network (TQRNN), which allows a threshold effect in the quantile regression neural network (QRNN). We develop the estimation procedure of the proposed model and suggest test statistics for threshold effect and the linear setting used typically in the quantile regression framework. We conduct Monte Carlo simulations to assess the performance of estimation and testing procedures, and compare the forecasting performance of the TQRNN model relative to the QRNN model. Through Monte Carlo simulations, we show that the estimation and testing procedures work well in finite samples, and there is little loss in forecast accuracy by employing the suggested TQRNN model even when the true data is generated from a QRNN model; on the contrary, ignoring an existing threshold effect can deteriorate the forecast accuracy of the QRNN model. All the simulation results support the usefulness of the TQRNN model.

Identifying important gene signatures of BMI using network structure-aided nonparametric quantile regression.

We focus on identifying genomics risk factors of higher body mass index (BMI) incorporating a priori information, such as biological pathways. However, the commonly used methods to incorporate prior information provide a model for the mean function of the outcome and rely on unmet assumptions. To address these concerns, we propose a method for nonparametric additive quantile regression with network regularization to incorporate the information encoded by known networks. To account for nonlinear associations, we approximate the unknown additive functional effect of each predictor with the expansion of a B-spline basis. We implement the group Lasso penalty to obtain a sparse model. We define the network-constrained penalty by the total norm of the difference between the effect functions of any two linked genes in the known network. We further propose an efficient computation procedure to solve the optimization problem that arises in our model. Simulation studies show that our proposed method performs well in identifying more truly associated genes and less falsely associated genes than alternative approaches. We apply the proposed method to analyze the microarray gene-expression dataset in the Framingham Heart Study and identify several 75 percentile BMI associated genes. In conclusion, our proposed approach efficiently identifies the outcome-associated variables in a nonparametric additive quantile regression framework by leveraging known network information.

Extreme spillover effect of COVID-19 pandemic-related news and cryptocurrencies on green bond markets: A quantile connectedness analysis

We provide the first empirical study on the role of panic and stress related to the COVID-19 pandemic, including six uncertainties and the four most traded cryptocurrencies, on three green bond market volatilities. Based on daily data covering the period from January 1, 2020 to January 31, 2022, we combine Diebold and Yilmaz's (2012, 2014) time domain spillover approach and Ando et al.'s (2022) quantile regression framework to investigate the time-frequency spillover connectedness among markets and measure the direction and intensity of the net transmission effect under extreme negative and positive event conditions, and normal states. We further provide novel insights into the green finance literature by examining sensitivity to quantile analysis of the net transfer mechanism between green bonds, cryptocurrencies, and pandemic uncertainty. Regarding the network connectedness analysis, the results reveal strong net information spillover transmission among markets under the bearish market. In extremely negative event circumstances, the MSCI Euro green bond acts as the leading net shock receiver in the system, whereas COVID-19 fake news appears as the largest net shock contributor, followed by BTC. According to sensitivity to quantile analysis, the net dynamic shock transfer mechanism is time-varying and quantile-dependent. Overall, our work uncovers crucial implications for investors and policymakers.

Globally Adaptive Longitudinal Quantile Regression with High Dimensional Compositional Covariates.

In this work, we propose a longitudinal quantile regression framework that enables a robust characterization of heterogeneous covariate-response associations in the presence of high-dimensional compositional covariates and repeated measurements of both response and covariates. We develop a globally adaptive penalization procedure, which can consistently identify covariate sparsity patterns across a continuum set of quantile levels. The proposed estimation procedure properly aggregates longitudinal observations over time, and ensures the satisfaction of the sum-zero coefficient constraint that is needed for proper interpretation of the effects of compositional covariates. We establish the oracle rate of uniform convergence and weak convergence of the resulting estimators, and further justify the proposed uniform selector of the tuning parameter in terms of achieving global model selection consistency. We derive an efficient algorithm by incorporating existing R packages to facilitate stable and fast computation. Our extensive simulation studies confirm the theoretical findings. We apply the proposed method to a longitudinal study of cystic fibrosis children where the association between gut microbiome and other diet-related biomarkers is of interest.

The heterogeneous effect of economic growth on the ecological footprint in OECD countries

Organisation for Economic Co-operation and Development (OECD) countries are always being a concern of policymakers because of their high growth and high greenhouse emissions. The objective of this study is to investigate the heterogeneous effect of economic growth on the ecological footprint (EF) in OECD countries, spanning from the year 1995 to 2017. Based on a sample of 36 countries from OECD countries by using distributional heterogeneity in panel quantile regression framework, the result shows there is a non-linear relationship between economic growth and EF across different EF levels. Furthermore, an inverted U-shape exists in the relationship between economic growth and EF which supports the theory of Environmental Kuznets Curve (EKC). These results indicate that the economic growth of these countries increases the environmental pollution initially but reduces it after a certain level of economic growth. The novelty of this study shows that the effects of economic growth on ecological footprint can differ across countries along the line of their ecological footprint level.

Tensor response quantile regression with neuroimaging data.

Collecting neuroimaging data in the form of tensors (i.e. multidimensional arrays) has become more common in mental health studies, driven by an increasing interest in studying the associations between neuroimaging phenotypes and clinical disease manifestation. Motivated by a neuroimaging study of post-traumatic stress disorder (PTSD) from the Grady Trauma Project, we study a tensor response quantile regression framework, which enables novel analyses that confer a detailed view of the potentially heterogeneous association between a neuroimaging phenotype and relevant clinical predictors. We adopt a sensible low-rank structure to represent the association of interest, and propose a simple two-step estimation procedure which is easy to implement with existing software. We provide rigorous theoretical justifications for the intuitive two-step procedure. Simulation studies demonstrate good performance of the proposed method with realistic sample sizes in neuroimaging studies. We conduct the proposed tensor response quantile regression analysis of the motivating PTSD study to investigate the association between fMRI resting-state functional connectivity and PTSD symptom severity. Our results uncover non-homogeneous effects of PTSD symptoms on brain functional connectivity, which cannot be captured by existing tensor responsemethods.