Nonparametric Quantile Regression Models Research Articles

How Has Climate Change Driven the Evolution of Rice Distribution in China?

Estimating the impact of climate change risks on rice distribution is one of the most important elements of climate risk management. This paper is based on the GEE (Google Earth Engine) platform and multi-source remote sensing data; the authors quantitatively extracted rice production distribution data in China from 1990 to 2019, analysed the evolution pattern of rice distribution and clusters and explored the driving effects between climatic and environmental conditions on the evolution of rice production distribution using the non-parametric quantile regression model. The results show that: The spatial variation of rice distribution is significant, mainly concentrated in the northeast, south and southwest regions of China; the distribution of rice in the northeast is expanding, while the distribution of rice in the south is extending northward, showing a spatial evolution trend of "north rising and south retreating". The positive effect of precipitation on the spatial distribution of rice has a significant threshold. This shows that when precipitation is greater than 800 mm, there is a significant positive effect on the spatial distribution of rice production, and this effect will increase with precipitation increases. Climate change may lead to a continuous northward shift in the extent of rice production, especially extending to the northwest of China. This paper's results will help implement more spatially targeted climate change adaptation measures for rice to cope with the changes in food production distribution caused by climate change.

Rare disaster risks and gold over 700 years: Evidence from nonparametric quantile regressions

Using annual data on real gold returns and measures of rare disaster risks over the period of 1280–2016, we show the existence of nonlinearity and regime changes in the relationship between the two variables of concern, over and above the existence of non-normality in the data. In light of these issues, we rely on a nonparametric quantile regression model to show that real gold returns can hedge against such risks, but only when the market is in its bullish-state, with it being negatively impacted in its bearish-phase. Understandably, our results have important implications for investors seeking refuge in the safe haven of gold during rare disaster events. In addition, our findings, would require theoreticians to develop new asset pricing models, which would incorporate the state-specific impact of rare disaster risks on gold.

Effects of omega-3 fatty acids supplementation on perioperative blood loss and complications after radical prostatectomy.

Many dietary supplements, including omega-3 fatty acids (ω3), are suspected to affect blood coagulation and platelet function. Despite no clinical evidence, discontinuation is recommended before radical prostatectomy. However, long-chain ω3 (LCω3) appear beneficial against prostate cancer progression. Here, we aim to determine the effect of LCω3 supplements on perioperative bleeding, hemoglobin, platelets, and postoperative complications after radical prostatectomy. This is a planned exploratory analysis of 130 patients diagnosed with prostate cancer grade group 2 or greater enrolled in a randomized controlled trial (NCT02333435) testing the effects of LCω3, on prostate cancer biological and pathological outcomes at radical prostatectomy as main outcomes. The LCω3 intervention (MAG-EPA 3g daily) or equivalent placebo was given 4-10 weeks prior to radical prostatectomy. An intention-to-treat analysis approach was used with bi-variate statistical testing of bleeding and complications outcomes. We also estimated the difference between groups using linear regression and non-parametric quantile regression models. All models were adjusted for confounding variables selected on clinical relevance. We found no clinically significant effect of LCω3 versus placebo on perioperative bleeding, laboratory tests or postoperative complications. In contrast, as expected, we found a significant increase in perioperative bleeding in open retropubic radical prostatectomy compared to robot-assisted radical prostatectomy (adjusted difference 115.8mL, p=0.04). Our results suggest that ω3 supplements can be safely taken before radical prostatectomy without increasing surgical bleeding risk. These findings are relevant since ω3 may beneficially affect prostate cancer evolution.

Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

In this article, we focus on the efficient estimators of the derivative of the nonparametric function in the nonparametric quantile regression model. We develop two ways of combining quantile regression information to derive the estimators. One is the weighted composite quantile regression estimator based on the quantile weighted loss function; the other is the weighted quantile average estimator based on the weighted average of quantile regression estimators at a single quantile. Furthermore, by minimizing the asymptotic variance, the optimal weight vector is computed, and consequently, the optimal estimator is obtained. Furthermore, we conduct some simulations to evaluate the performance of our proposed estimators under different symmetric error distributions. Simulation studies further illustrate that both estimators work better than the local linear least square estimator for all the symmetric errors considered except the normal error, and the weighted quantile average estimator performs better than the weighted composite quantile regression estimator in most situations.

Contribution of Organized Sport Participation to Health-Related Fitness in Adolescents.

The purpose of this study was to investigate the relationship between organized sport (OS) participation and health-related fitness (HRF) in adolescents. A total of 320 adolescents (176 boys) aged between 10 and 16 years reported their engagement in OS and were assessed on 5 components of HRF (cardiovascular endurance, push-ups, curl-ups, flexibility, and body mass index). Data on OS participation frequency and duration were collected through a self-reported questionnaire. Adolescents were stratified by OS participation (engaged, n = 113; nonengaged, n = 220; 55% boys). Nonparametric quantile regression models were used to estimate the differences in HRF by participation group. Less than 30% of the participants reported they were regularly engaged in OS. Frequency of participation ranged from 2 to 5 days per week (median = 2; SD = 3), and duration of participation ranged from 45 to 180 minutes per week (median = 81.7; SD = 32.4). Adolescents who participated in OS displayed better cardiovascular endurance (+4.1 laps completed), with no statistically significant difference detected on any other HRF component. Our results highlight engagement in OS as a promising strategy for achieving cardiovascular endurance. Engagement in OS alone does not seem to be sufficient to enhance fitness components other than cardiovascular endurance.

A nonparametric approach for quantile regression

Quantile regression estimates conditional quantiles and has wide applications in the real world. Estimating high conditional quantiles is an important problem. The regular quantile regression (QR) method often designs a linear or non-linear model, then estimates the coefficients to obtain the estimated conditional quantiles. This approach may be restricted by the linear model setting. To overcome this problem, this paper proposes a direct nonparametric quantile regression method with five-step algorithm. Monte Carlo simulations show good efficiency for the proposed direct QR estimator relative to the regular QR estimator. The paper also investigates two real-world examples of applications by using the proposed method. Studies of the simulations and the examples illustrate that the proposed direct nonparametric quantile regression model fits the data set better than the regular quantile regression method.

A Bootstrap Method for Constructing Pointwise and Uniform Confidence Bands for Conditional Quantile Functions

This paper is concerned with inference about the conditional quantile function in a nonparametric quantile regression model. Any method for constructing a confidence interval or band for this function must deal with the asymptotic bias of nonparametric estimators of the function. In estimation methods such as local polynomial estimation, this is usually done through undersmoothing or explicit bias correction. The latter usually requires oversmoothing. However, there are no satisfactory empirical methods for selecting bandwidths that under- or oversmooth. This paper extends the bootstrap method of Hall and Horowitz (2013) for conditional mean functions to conditional quantile functions. The paper also shows how the bootstrap method can be used to obtain uniform confidence bands. The bootstrap method uses only bandwidths that are selected by standard methods such as cross validation and plug-in. It does not use under- or oversmoothing. The results of Monte Carlo experiments illustrate the numerical performance of the bootstrap method.

The independence process in conditional quantile location-scale models and an application to testing for monotonicity

In this paper the nonparametric quantile regression model is considered in a locationscale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular an asymptotic expansion and weak convergence to a Gaussian process are proved. The results can, on the one hand, be applied to test for validity of the location-scale model. On the other hand, they allow to derive various specification tests in conditional quantile location-scale models. In detail a test for monotonicity of the conditional quantile curve is investigated. For the test for validity of the location-scale model as well as for the monotonicity test smooth residual bootstrap versions of Kolmogorov-Smirnov type test statistics are suggested. We give rigorous proofs for bootstrap versions of the weak convergence results. The performance of the tests is demonstrated in a simulation study. AMS Classification: 62G10, 62G08, 62G30

Imputation in nonparametric quantile regression with complex data

This paper considers nonparametric quantile regression models for complex data of mixed categorical and continuous variables together with missing values at random (MAR). In consideration of the increasingly popular application of multiple imputation for handling missing data and the advantages of nonparametric quantile regression, we propose an effective and accurate multiple imputation method. The estimation procedure not only does well in modeling with mixed categorical and continuous data, but also makes full use of the entire data set to achieve increased efficiency. The proposed estimator is asymptotically normal. In simulation study, we compare the performance of the multiple imputation method with complete case (CC), Regression imputation and nearest-neighbor imputation methods, and outline advantages and drawbacks of the different methods. Simulation studies show that the proposed multiple imputation method performs better.

Nonparametric Inference for Time-Varying Coefficient Quantile Regression

The article considers nonparametric inference for quantile regression models with time-varying coefficients. The errors and covariates of the regression are assumed to belong to a general class of locally stationary processes and are allowed to be cross-dependent. Simultaneous confidence tubes (SCTs) and integrated squared difference tests (ISDTs) are proposed for simultaneous nonparametric inference of the latter models with asymptotically correct coverage probabilities and Type I error rates. Our methodologies are shown to possess certain asymptotically optimal properties. Furthermore, we propose an information criterion that performs consistent model selection for nonparametric quantile regression models of nonstationary time series. For implementation, a wild bootstrap procedure is proposed, which is shown to be robust to the dependent and nonstationary data structure. Our method is applied to studying the asymmetric and time-varying dynamic structures of the U.S. unemployment rate since the 1940s. Supplementary materials for this article are available online.

Non- and Semi-Parametric Quantile Models for Recovery Rate

This paper proposes a nonparametric quantile regression (NP-QR) and a partially linear additive QR (PLA-QR) for modelling recovery rates (RR). Using Moody’s Recovery Database, we uncover two novelties of the NP-QR model. First, the local constant estimation of NP-QR model captures the key empirical feature of RR data being bounded in [0,1] interval. Second, the heterogeneity in the impact of borrower characteristics with clarity can be estimated. For example, we show that the way in which the impact of debt cushion on RR depends on the other characteristics, such as collateralisation and the degree of instrument rank of loans, during various economic conditions. By contrast such heterogeneity is reduced to a single dimension in the parametric regression model. Furthermore, accommodating bimodality and heteroscedastic errors, the NP-QR also provides the heterogeneity of these impacts across the various quantiles of the conditional RR distribution. On the other hand, the idiosyncratic marginal effects of borrower characteristics are estimated using the PLA-QR model over the various quantiles of the conditional RR distribution. For example, for loans with very low risk, we find that the RR is less sensitive to the change in debt cushion at the lower quantiles than that at the upper quantile, particularly when the debt cushion is less than 30%, during economic downturns. The findings of this study have implication for lenders designing an optimum treatment rule for borrowers.

Reference Charts for Fetal Cerebellar Vermis Height: A Prospective Cross-Sectional Study of 10605 Fetuses.

ObjectiveTo establish reference charts for fetal cerebellar vermis height in an unselected population.MethodsA prospective cross-sectional study between September 2009 and December 2014 was carried out at ALTAMEDICA Fetal–Maternal Medical Centre, Rome, Italy. Of 25203 fetal biometric measurements, 12167 (48%) measurements of the cerebellar vermis were available. After excluding 1562 (12.8%) measurements, a total of 10605 (87.2%) fetuses were considered and analyzed once only. Parametric and nonparametric quantile regression models were used for the statistical analysis. In order to evaluate the robustness of the proposed reference charts regarding various distributional assumptions on the ultrasound measurements at hand, we compared the gestational age-specific reference curves we produced through the statistical methods used. Normal mean height based on parametric and nonparametric methods were defined for each week of gestation and the regression equation expressing the height of the cerebellar vermis as a function of gestational age was calculated. Finally the correlation between dimension/gestation was measured.ResultsThe mean height of the cerebellar vermis was 12.7mm (SD, 1.6mm; 95% confidence interval, 12.7–12.8mm). The regression equation expressing the height of the CV as a function of the gestational age was: height (mm) = -4.85+0.78 x gestational age. The correlation between dimension/gestation was expressed by the coefficient r = 0.87.ConclusionThis is the first prospective cross-sectional study on fetal cerebellar vermis biometry with such a large sample size reported in literature. It is a detailed statistical survey and contains new centile-based reference charts for fetal height of cerebellar vermis measurements.

Reference charts for fetal corpus callosum length: a prospective cross-sectional study of 2950 fetuses.

The purpose of this study was to establish reference charts for fetal corpus callosum length in a convenience sample. A prospective cross-sectional study was conducted at the Artemisia Fetal-Maternal Medical Center between December 2008 and January 2012. Among 16,975 fetal biometric measurements between 19 weeks and 37 weeks 6 days' gestation, 3438 measurements of the corpus callosum (20.3%) were available. After excluding 488 measurements (14.2%), a total of 2950 fetuses (85.8%) were considered and analyzed only once. Parametric and nonparametric quantile regression models were used for the statistical analysis. To evaluate the robustness of the proposed reference charts with respect to various distributional assumptions on the sonographic measurements at hand, we compared the gestational age (GA)-specific reference curves produced by the statistical methods used. The mean corpus callosum length was 26.18 mm (SD, 4.5 mm; 95% confidence interval, 26.01-26.34 mm). The linear regression equation expressing the length of the corpus callosum as a function of GA was length (mm) = -11.17 + 1.62 × GA. The correlation between the dimension and gestation was expressed by the coefficient r = 0.83. Normal mean lengths according the parametric and nonparametric methods were defined for each week of gestation. This work provides new quantile-based reference charts for corpus callosum length measurements that may be useful for diagnosis of congenital corpus callosum anomalies in fetal life.

Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression

We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting.In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies.In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.

AN EFFECTIVE TECHNIQUE OF MULTIPLE IMPUTATION IN NONPARAMETRIC QUANTILE REGRESSION

In this study, we consider the nonparametric quantile regression model with the covariates Missing at Random (MAR). Multiple imputation is becoming an increasingly popular approach for analyzing missing data, which combined with quantile regression is not well-developed. We propose an effective and accurate two-stage multiple imputation method for the model based on the quantile regression, which consists of initial imputation in the first stage and multiple imputation in the second stage. The estimation procedure makes full use of the entire dataset to achieve increased efficiency and we show the proposed two-stage multiple imputation estimator to be asymptotically normal. In simulation study, we compare the performance of the proposed imputation estimator with Complete Case (CC) estimator and other imputation estimators, e.g., the regression imputation estimator and k-Nearest-Neighbor imputation estimator. We conclude that the proposed estimator is robust to the initial imputation and illustrates more desirable performance than other comparative methods. We also apply the proposed multiple imputation method to an AIDS clinical trial data set to show its practical application.

Comments on: An updated review of Goodness-of-Fit tests for regression models

A survey on the new developments in goodness-of-fit testing in regression models isvery welcome and the authors have done an excellent job reviewing the recent litera-ture. I would like to complement this nearly exhaustive exposition by focusing on twofurther issues in the context of testing model assumptions for regression models. Thefirst refers to hypothesis testing in nonparametric quantile regression models, whilethe second discusses goodness-of-fit tests in inverse regression models.

QUANTILE REGRESSION WITH MISMEASURED COVARIATES

This paper establishes that the availability of instrumental variables enables the identification and the consistent estimation of nonparametric quantile regression models in the presence of measurement error in the regressors. The proposed estimator takes the form of a nonlinear functional of derivatives of conditional expectations and is shown to provide estimated quantile functions that are uniformly consistent over a compact set.