Nonparametric Quantile Regression Research Articles

Jump Aggregation, Volatility Prediction, and Nonlinear Estimation of Banks’ Sustainability Risk

Extreme financial events usually lead to sharp jumps in stock prices and volatilities. In addition, jump clustering and stock price correlations contribute to the risk amplification acceleration mechanism during the crisis. In this paper, four Jump-GARCH models are used to forecast the jump diffusion volatility, which is used as the risk factor. The linear and asymmetric nonlinear effects are considered, and the value at risk of banks is estimated by support vector quantile regression. There are three main findings. First, in terms of the volatility process of bank stock price, the Jump Diffusion GARCH model is better than the Continuous Diffusion GARCH model, and the discrete jump volatility is significant. Secondly, due to the difference of the sensitivity of abnormal information shock, the jump behavior of bank stock price is heterogeneous. Moreover, CJ-GARCH models are suitable for most banks, while ARJI-R2-GARCH models are more suitable for small and medium sized banks. Thirdly, based on the jump diffusion volatility information, the performance of the support vector quantile regression is better than that of the parametric quantile regression and nonparametric quantile regression.

A comparison of E. coli concentration estimates quantified by the EPA and a Michigan laboratory network using EPA Draft Method C

We evaluated data from 10 laboratories that analyzed water samples from 82 recreational water sites across the state of Michigan between 2016 and 2018. Water sample replicates were analyzed by experienced U.S. Environmental Protection Agency (EPA) analysts and Michigan laboratories personnel, many of whom were newly trained, using EPA Draft Method C—a rapid quantitative polymerase chain reaction (qPCR) technique that provides same day Escherichia coli (E. coli) concentration results. Beach management decisions (i.e. remain open or issue an advisory or closure) based on E. coli concentration estimates obtained by Michigan labs and by the EPA were compared; the beach management decision agreed in 94% of the samples analyzed. We used the Wilcoxon one-sample signed rank test and nonparametric quantile regression to assess (1) the degree of agreement between E. coli concentrations quantified by Michigan labs versus the EPA and (2) Michigan lab E. coli measurement precision, relative to EPA results, in different years and water body types. The median quantile regression curve for Michigan labs versus EPA approximated the 1:1 line of perfect agreement more closely as years progressed. Similarly, Michigan lab E. coli estimates precision also demonstrated yearly improvements. No meaningful difference was observed in the degree of association between Michigan lab and EPA E. coli concentration estimates for inland lake and Great Lakes samples (median regression curve average slopes 0.93 and 0.95, respectively). Overall, our study shows that properly trained laboratory personnel can perform Draft Method C to a degree comparable with experienced EPA analysts. This allows health departments that oversee recreational water quality monitoring to be confident in qPCR results generated by the local laboratories responsible for analyzing the water samples.

Approximate nonparametric quantile regression in reproducing kernel Hilbert spaces via random projection

Nonparametric quantile regression is a commonly used nonlinear quantile model. One general and popular approach is based on the use of kernels within a reproducing kernel Hilbert space (RKHS) framework, with the smoothing splines estimation as a special case. However, when the sample size n is large, the computational burden is heavy. Motivated by the recent advances in random projection for kernel nonparametric (mean) ridge regression (KRR), we consider an m-dimensional random projection approach for kernel quantile regression (KQR) with m≪n. We establish a theoretical result showing that the sketched KQR still achieves the minimax convergence rate when m is at least as large as the effective statistical dimension of the problem. Some Monte Carlo studies are carried out for illustration purposes.

Prescriptive Reference Standards of Third-Trimester Cerebroplacental Ratio and Its Physiological Determinants

Objective: To construct valid reference standards reflecting optimal cerebroplacental ratio and to explore its physiological determinants. Methods: A cohort of 391 low-risk pregnancies of singleton pregnancies of nonmalformed fetuses without maternal medical conditions and with normal perinatal outcomes was created. Doppler measurements of the middle cerebral artery and umbilical artery were performed at 24–42 weeks. Reference standards were produced, and the influence of physiological determinants was explored by nonparametric quantile regression. The derived standards were validated in a cohort of 200 low-risk pregnancies. Results: Maternal body mass index was significantly associated with the 5th centile of the cerebroplacental ratio. For each additional unit of body mass index, the 5th centile was on average 0.014 lower. The derived 5th, 10th, and 50th centiles selected in the validation cohort were 5, 9.5, and 51% of the measurements. Conclusions: This study provides methodologically sound prescriptive standards and suggests that maternal body mass index is a determinant of a cutoff commonly used for decision-making.

Estimasi Model Regresi Kuantil Spline Kuadratik pada Data Trombosit dan Hematokrit Pasien DBD

Nonparametric quantile regression is used to estimate the regression function when assumptions about the shape of the regression curve are unknown. It is only assumed to be subtle by involving quantile values. One estimator in nonparametric regression is spline. The segmented properties of the spline provide more flexibility than ordinary polynomials. Therefore, the nature of the spline makes it possible to adapt more effectively to the local characteristics of a function or data. This study proposes to get the results of the estimation platelet count model to the hematocrit value of DHF. The optimal model obtained from the estimation of quadratic spline quantile regression is at quantile 0.5 with one knot and the GCV value is 41.5. The results of the estimation show that there is a decrease in platelet counts as the percentage of hematocrit increase.

Comparison between the estimated of nonparametric methods by using the methodology of quantile regression models

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them.

Measuring Granger Causality in Quantiles

ABSTRACT We consider measures of Granger causality in quantiles, which detect and quantify both linear and nonlinear causal effects between random variables. The measures are based on nonparametric quantile regressions and defined as logarithmic functions of restricted and unrestricted expectations of quantile check loss functions. They can consistently be estimated by replacing the unknown expectations of check loss functions by their nonparametric kernel estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measures. We establish the asymptotic distribution of this estimator, which can be used to build tests for the statistical significance of the measures. Thereafter, we show the validity of a smoothed local bootstrap that can be used in finite-sample settings to perform statistical tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite-sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, we provide an empirical application to illustrate the usefulness of measuring Granger causality in quantiles. We quantify the degree of predictability of the quantiles of equity risk premium using the variance risk premium, unemployment rate, inflation, and the effective federal funds rate. The empirical results show that the variance risk premium and effective federal funds rate have a strong predictive power for predicting the risk premium when compared to that of the predictive power of the other two macro variables. In particular, the variance risk premium is able to predict the center, lower, and upper quantiles of the distribution of the risk premium; however, the effective federal funds rate predicts only the lower and upper quantiles. Nevertheless, unemployment and inflation rates have no effect on the risk premium.

Nonparametric quantile regression estimation for functional data with responses missing at random

This paper presents the nonparametric quantile regression estimation for the regression function operator when the functional data with the responses missing at random are considered. Then, the large sample properties of the proposed estimator are established under some mild conditions. Finally, a simulation study is conducted to investigate the finite sample properties of the proposed method.

A Nonparametric Measure of Heteroskedasticity

We introduce a nonparametric measure to quantify the degree of heteroskedasticity at a fixed quantile of the conditional distribution of a random variable. Our measure of heteroskedasticity is based on nonparametric quantile regressions and is expressed in terms of unrestricted and restricted expectations of quantile loss functions. It can be consistently estimated by replacing the unknown expectations by their nonparametric estimates. We derive a Bahadur-type representation for the nonparametric estimator of the measure. We provide the asymptotic distribution of this estimator, which one can use to build tests for the statistical significance of the measure. Thereafter, we establish the validity of a fixed regressor bootstrap that one can use in finite-sample settings to perform tests. A Monte Carlo simulation study reveals that the bootstrap-based test has a good finite sample size and power for a variety of data generating processes and different sample sizes. Finally, two empirical applications are provided to illustrate the importance of the proposed measure.

Multiple‐output quantile regression through optimal quantization

AbstractA new nonparametric quantile regression method based on the concept of optimal quantization was developed recently and was showed to provide estimators that often dominate their classical, kernel‐type, competitors. In the present work, we extend this method to multiple‐output regression problems. We show how quantization allows approximating population multiple‐output regression quantiles based on halfspace depth. We prove that this approximation becomes arbitrarily accurate as the size of the quantization grid goes to infinity. We also derive a weak consistency result for a sample version of the proposed regression quantiles. Through simulations, we compare the performances of our estimators with (local constant and local bilinear) kernel competitors. The results reveal that the proposed quantization‐based estimators, which are local constant in nature, outperform their kernel counterparts and even often dominate their local bilinear kernel competitors. The various approaches are also compared on artificial and real data.

CALIPER paediatric reference intervals for the urea creatinine ratio in healthy children & adolescents

BackgroundThe urea creatinine ratio (UCR) is important in the clinical assessment of several medical conditions, including acute kidney injury and gastrointestinal bleeding. However, accurate and robust paediatric reference intervals (RIs) for this ratio have not been well established. Here, we determined age- and sex-specific discrete and continuous RIs for UCR in the Canadian Laboratory Initiative on Paediatric Reference Intervals (CALIPER) cohort of healthy children and adolescents for the first time. MethodsUCR was calculated for approximately 1030 CALIPER participants using retrospective urea and creatinine (both Jaffe and enzymatic methods) normative data. Partitions were determined using the Harris & Boyd statistical method. Discrete RIs were established in accordance with the Clinical and Laboratory Standards Institute (CLSI) guidelines. Continuous RIs were established using nonparametric quantile regression. ResultsSeveral age- and sex-specific partitions were necessary to capture dynamic physiological trends associated with this ratio throughout childhood and adolescence, highlighting the benefit of continuous RI establishment. Established UCR RIs also demonstrated marked differences between Jaffe and enzymatic assay methods. ConclusionOur results clearly demonstrate the critical need for RI stratification by important covariates such as age, sex, and creatinine assay methodology for paediatric UCR test result interpretation. These data contribute to our understanding of normative UCR values in childhood and adolescence and can be expected to improve paediatric test result interpretation in clinical laboratories that report this ratio.

Exploración de la relación entre actitudes ante las ciencias y el rendimiento en el Programa Internacional para la evaluación de estudiantes (PISA)

The Program for International Student Assessment (PISA) 2006 and PISA 2015 is focused on students’ competency in science, providing wide data banks for the analysis of the interaction between science performance and attitudes toward science. The few attempts to study this relationship in other assessment studies suggest some positive correlations on the individual level and some unexpected negative correlations and a lack of scalar invariance across countries. The aim of this study is to contribute to the exploration of the generalizability of this relationship across countries and regions within nations. For this, the PISA 2015 data are analyzed using Ordinary Least Square and Quantile regression modelling techniques together with bivariate correlation matrix analysis. The relationship patterns between attitudes —such as self-efficacy, interest in science, participation in science activities, and enjoyment of science—and performance in science are explored at different scales; across 72 PISA participating countries and across 17 regions in Spain. Across countries, the relationship is unexpectedly negative for all attitudes, although high quantiles show a much less pronounced pattern. Across regions, only self-efficacy is significantly and positively correlated with science performance. Overall, positive non–linear relationships are distinguished for high performance values. The results of this study suggest the need of further research using non-parametric quantile regression modeling, and exploring attitudinal indices scaling when investigating potential universal/invariant models. This research should try to justify the comparison across countries/regions using aggregated scores, while incorporating differences in cultural, educational, and social influences on attitudes toward science.

Exploring the relationship between attitudes toward science and PISA scientific performance

The Program for International Student Assessment (PISA) 2006 and PISA 2015 are focused on students’ competency in science, providing wide data banks for the analysis of the interaction between science performance and attitudes toward science. The few attempts to study this relationship in other assessment studies suggest some positive correlations on the individual level and some unexpected negative correlations and a lack of scalar invariance across countries. The aim of this study is to contribute to the exploration of the generalizability of this relationship across countries and regions within nations. For this, the PISA 2015 data are analyzed using Ordinary Least Square and Quantile regression modelling techniques together with bivariate correlation matrix analysis. The relationship patterns between attitudes—such as self-efficacy, interest in science, participation in science activities, and enjoyment of science—and performance in science are explored at different scales; across 72 PISA participating countries and across 17 regions in Spain. Across countries, the relationship is unexpectedly negative for all attitudes, although high quantiles show a much less pronounced pattern. Across regions, only self-efficacy is significantly and positively correlated with science performance. Overall, positive non–linear relationships are distinguished for high performance values. The results of this study suggest the need of further research using non-parametric quantile regression modeling, and exploring attitudinal indices scaling when investigating potential universal/invariant models. This research should try to justify the comparison across countries/regions using aggregated scores, while incorporating differences in cultural, educational, and social influences on attitudes toward science.

Continuous reference intervals for 38 biochemical markers in healthy children and adolescents: Comparisons to traditionally partitioned reference intervals

BackgroundReference intervals have traditionally been partitioned by age based on statistical significance and physiological relevance. However, analyte concentration does not change abruptly with age, but rather dynamically. In this study, we establish biochemical marker continuous reference intervals for a Canadian population using healthy pediatric reference individuals and compare these to partitioned reference intervals. MethodsContinuous reference intervals spanning 1–18.5 years of age were established using data from healthy CALIPER children and adolescents aged 6 months- < 19 years. Continuous reference intervals (i.e. 2.5th and 97.5th quantiles) were generated by nonparametric quantile regression via penalized splines with non-crossing constraints. Abnormal flagging rates of established continuous reference intervals were compared to previously established age-partitioned CALIPER reference intervals for five biochemical markers using internal (CALIPER) and external (i.e. Canadian Health Measures Survey (CHMS)) datasets. ResultsContinuous reference intervals were determined for 38 biochemical markers, with 21 markers requiring sex-specific reference intervals. Despite similar total flagging rates to partitioned reference intervals, continuous reference intervals appeared to provide a more consistent and accurate estimation of reference limits for biomarkers with more complex age-related changes, including alkaline phosphatase and phosphate. ConclusionsThis is the first report of continuous biochemical marker reference intervals based on a healthy Canadian pediatric population. Reference limit point estimates based on continuous reference intervals are provided to aid clinical implementation. Continuous reference intervals offer a better estimation of dynamic changes in biochemical marker reference values with age, resulting in improved laboratory test result interpretation and clinical decision making in pediatrics.

Crude oil price and implied volatility

Purpose The purpose of this study is to investigate empirically the pattern of co-movement between prices and implied volatility in the future markets for crude oil. Design/methodology/approach The tool of non-parametric quantile regression is applied to daily price returns and implied volatility changes from 2007 to 2018. Findings For the total sample period, the link between price returns and forward-looking volatility expectations is contemporaneous, negative and asymmetric, and it exhibits an (approximately) inverted U-shaped pattern suggesting that: the pricing of implied volatility is heavier for large (in absolute value terms) changes relative to small ones and it is lighter for large positive changes relative to large negative ones. The pattern of co-movement, therefore, appears to be in line with the theoretical postulates of fear, exuberance and loss aversion. The main characteristics of the relationship are present in some (but not in all) sub-periods, which are also considered in this study. Originality/value Less than a handful of works have assessed the link between implied volatility and prices for commodity ETFs. This is the first one relying on flexible non-parametric quantile regressions.

Applications for Quantile Regression in Epidemiology

To illustrate the utility of quantile regression in epidemiology for outcomes that are continuous and when exposure effects may differ across the distribution of the outcome. Linear regression methods estimate only the effects at the mean level which may be an incomplete and biased summary of the effect of exposures for some continuous health outcomes. There are several variations of the quantile regression method including classical linear quantile regression, nonparametric quantile regression for growth trajectories, and the modified quantile regression for case–control designs. Such methods offer several applications including (1) the use of quantile regression to test whether the effects of exposure are similar across quantiles, (2) the use of quantile regression for risk prediction, and (3) the use of quantile regression to examine the effects of growth trajectories over time. Quantile regression is an important tool for understanding continuous health outcomes, especially outcomes that are not normally distributed, as it offers insight into the relation of exposures with respect to the distribution of the outcome. Quantile regression methods have the potential to deepen and expand the existing quantitative evidence from more common mean-based analyses.

Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions

This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative operator and hence an unknown degree of ill-posedness, making it difficult to know if the information bound is singular or not. In either case, we propose a penalized sieve generalized empirical likelihood (GEL) estimation and inference procedure, which is based on the unconditional WAD moment restriction and an increasing number of unconditional moments that are implied by the conditional NPQIV restriction, where the unknown quantile function is approximated by a penalized sieve. Under some regularity conditions, we show that the self-normalized penalized sieve GEL estimator of the WAD of a NPQIV is asymptotically standard normal. We also show that the quasi likelihood ratio statistic based on the penalized sieve GEL criterion is asymptotically chi-square distributed regardless of whether or not the information bound is singular.

Generalized random forests

We propose generalized random forests, a method for nonparametric statistical estimation based on random forests (Breiman [Mach. Learn. 45 (2001) 5–32]) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method considers a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dimensionality, we use an adaptive weighting function derived from a forest designed to express heterogeneity in the specified quantity of interest. We propose a flexible, computationally efficient algorithm for growing generalized random forests, develop a large sample theory for our method showing that our estimates are consistent and asymptotically Gaussian and provide an estimator for their asymptotic variance that enables valid confidence intervals. We use our approach to develop new methods for three statistical tasks: nonparametric quantile regression, conditional average partial effect estimation and heterogeneous treatment effect estimation via instrumental variables. A software implementation, grf for R and C++, is available from CRAN.

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.

Stochastic data envelopment analysis: A quantile regression approach to estimate the production frontier

Data Envelopment Analysis was developed as a deterministic model that assumed that deviations from the production frontier were one sided representing technical inefficiency. The model provides biased estimates of production and inefficiency if deviations from the frontier arise not only from inefficiency but also from statistical noise. Banker (1988, “Stochastic Data Envelopment Analysis,” Working Paper, Carnegie Mellon University) extended Data Envelopment Analysis with a stochastic model to allow not only inefficiency but also statistical noise. Banker's model can be considered a nonparametric quantile regression. Using the celebrated Afriat constraints, the model estimates a piecewise linear production function through the middle of the data. In this paper, we extend Banker's Stochastic DEA model by considering a semi-parametric model that identifies the most likely quantile based on assumptions of the composed error terms. We focus on the most common stochastic frontier model with an error structured constrained to a convolution of the normal and half-normal distributions. Using simulated data, we compare the model to the econometric stochastic frontier model under different distributional assumptions.