scholarly journals Estimation for Extreme Conditional Quantiles of Functional Quantile Regression

2023 ◽  
Author(s):  
Hanbing Zhu ◽  
Riquan Zhang ◽  
Yehua Li ◽  
Weixin Yao
Keyword(s):  
Quantile Regression ◽  
Conditional Quantiles

scholarly journals Probabilistic Hydrological Post-Processing at Scale: Why and How to Apply Machine-Learning Quantile Regression Algorithms

Water ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 2126 ◽  
Author(s):  
Georgia Papacharalampous ◽  
Hristos Tyralis ◽  
Andreas Langousis ◽  
Amithirigala W. Jayawardena ◽  
Bellie Sivakumar ◽  
...  
Keyword(s):  
Machine Learning ◽  
Quantile Regression ◽  
Random Forests ◽  
Large Scale ◽  
Hydrological Model ◽  
Model Errors ◽  
Post Processing ◽  
Conditional Quantiles ◽  
Daily Streamflow ◽  
Regression Algorithms

We conduct a large-scale benchmark experiment aiming to advance the use of machine-learning quantile regression algorithms for probabilistic hydrological post-processing “at scale” within operational contexts. The experiment is set up using 34-year-long daily time series of precipitation, temperature, evapotranspiration and streamflow for 511 catchments over the contiguous United States. Point hydrological predictions are obtained using the Génie Rural à 4 paramètres Journalier (GR4J) hydrological model and exploited as predictor variables within quantile regression settings. Six machine-learning quantile regression algorithms and their equal-weight combiner are applied to predict conditional quantiles of the hydrological model errors. The individual algorithms are quantile regression, generalized random forests for quantile regression, generalized random forests for quantile regression emulating quantile regression forests, gradient boosting machine, model-based boosting with linear models as base learners and quantile regression neural networks. The conditional quantiles of the hydrological model errors are transformed to conditional quantiles of daily streamflow, which are finally assessed using proper performance scores and benchmarking. The assessment concerns various levels of predictive quantiles and central prediction intervals, while it is made both independently of the flow magnitude and conditional upon this magnitude. Key aspects of the developed methodological framework are highlighted, and practical recommendations are formulated. In technical hydro-meteorological applications, the algorithms should be applied preferably in a way that maximizes the benefits and reduces the risks from their use. This can be achieved by (i) combining algorithms (e.g., by averaging their predictions) and (ii) integrating algorithms within systematic frameworks (i.e., by using the algorithms according to their identified skills), as our large-scale results point out.

scholarly journals Statistical Downscaling of Extreme Precipitation Events Using Censored Quantile Regression

2007 ◽  
Vol 135 (6) ◽  
pp. 2365-2378 ◽  
Author(s):  
P. Friederichs ◽  
A. Hense
Keyword(s):  
Quantile Regression ◽  
Statistical Downscaling ◽  
Large Scale ◽  
Daily Precipitation ◽  
Skill Score ◽  
Reanalysis Data ◽  
Conditional Quantile ◽  
Conditional Quantiles ◽  
Censored Quantile Regression ◽  
Extreme Precipitation Events

Abstract A statistical downscaling approach for extremes using censored quantile regression is presented. Conditional quantiles of station data (e.g., daily precipitation sums) in Germany are estimated by means of the large-scale circulation as represented by the NCEP reanalysis data. It is shown that a mixed discrete–continuous response variable, such as a daily precipitation sum, can be statistically modeled by a censored variable. Furthermore, a conditional quantile skill score is formulated to assess the relative gain of a quantile forecast compared with a reference forecast. Just like multiple regression for expectation values, quantile regression provides a tool to formulate a model output statistics system for extremal quantiles.

scholarly journals Probability Density Forecasting of Wind Speed Based on Quantile Regression and Kernel Density Estimation

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6125
Author(s):  
Lei Zhang ◽  
Lun Xie ◽  
Qinkai Han ◽  
Zhiliang Wang ◽  
Chen Huang
Keyword(s):  
Wind Speed ◽  
Quantile Regression ◽  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Confidence Level ◽  
Kernel Density ◽  
Conditional Quantiles ◽  
Wind Speeds ◽  
Density Forecasting

Based on quantile regression (QR) and kernel density estimation (KDE), a framework for probability density forecasting of short-term wind speed is proposed in this study. The empirical mode decomposition (EMD) technique is implemented to reduce the noise of raw wind speed series. Both linear QR (LQR) and nonlinear QR (NQR, including quantile regression neural network (QRNN), quantile regression random forest (QRRF), and quantile regression support vector machine (QRSVM)) models are, respectively, utilized to study the de-noised wind speed series. An ensemble of conditional quantiles is obtained and then used for point and interval predictions of wind speed accordingly. After various experiments and comparisons on the real wind speed data at four wind observation stations of China, it is found that the EMD-LQR-KDE and EMD-QRNN-KDE generally have the best performance and robustness in both point and interval predictions. By taking conditional quantiles obtained by the EMD-QRNN-KDE model as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method, whose bandwidth is optimally determined according to the normal reference criterion. It is found that most actual wind speeds lie near the peak of predicted PDF curves, indicating that the probabilistic density prediction by EMD-QRNN-KDE is believable. Compared with the PDF curves of the 90% confidence level, the PDF curves of the 80% confidence level usually have narrower wind speed ranges and higher peak values. The PDF curves also vary with time. At some times, they might be biased, bimodal, or even multi-modal distributions. Based on the EMD-QRNN-KDE model, one can not only obtain the specific PDF curves of future wind speeds, but also understand the dynamic variation of density distributions with time. Compared with the traditional point and interval prediction models, the proposed QR-KDE models could acquire more information about the randomness and uncertainty of the actual wind speed, and thus provide more powerful support for the decision-making work.

Conditional Quantile Estimation and Inference for Arch Models

1996 ◽  
Vol 12 (5) ◽  
pp. 793-813 ◽  
Author(s):  
Roger Koenker ◽  
Quanshui Zhao
Keyword(s):  
Quantile Regression ◽  
Prediction Intervals ◽  
Quantile Estimation ◽  
Arch Models ◽  
Conditional Quantile ◽  
Regression Methods ◽  
Conditional Quantiles ◽  
Inference Methods

Quantile regression methods are suggested for a class of ARCH models. Because conditional quantiles are readily interpretable in semiparametric ARCH models and are inherendy easier to estimate robustly than population moments, they offer some advantages over more familiar methods based on Gaussian likelihoods. Related inference methods, including the construction of prediction intervals, are also briefly discussed.

A semiparametric nonlinear quantile regression model for financial returns

2017 ◽  
Vol 21 (1) ◽  
Author(s):  
Krenar Avdulaj ◽  
Jozef Barunik
Keyword(s):  
Quantile Regression ◽  
Value At Risk ◽  
Regression Models ◽  
Tail Dependence ◽  
Financial Economic ◽  
Financial Returns ◽  
Ample Evidence ◽  
Conditional Quantiles ◽  
Conditional Dependence ◽  
Quantile Regression Model

AbstractAccurately measuring and forecasting value-at-risk (VaR) remains a challenging task at the heart of financial economic theory. Recently, quantile regression models have been used successfully to capture the conditional quantiles of returns and to forecast VaR accurately. In this paper, we further explore nonlinearities in data and propose to couple realized measures with the nonlinear quantile regression framework to explain and forecast the conditional quantiles of financial returns. The nonlinear quantile regression models are implied by the copula specifications and allow us to capture possible nonlinearities, tail dependence, and asymmetries in the conditional quantiles of financial returns. Using high frequency data that covers most liquid US stocks in seven sectors, we provide ample evidence of asymmetric conditional dependence with different levels of dependence, which are characteristic for each industry. The backtesting results of estimated VaR favour our approach.

scholarly journals Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach

2021 ◽  
Vol 18 (24) ◽  
pp. 13277
Author(s):  
Yohann Moanahere Chiu ◽  
Fateh Chebana ◽  
Belkacem Abdous ◽  
Diane Bélanger ◽  
Pierre Gosselin
Keyword(s):  
Public Health ◽  
Quantile Regression ◽  
Cardiovascular Health ◽  
Meteorological Conditions ◽  
Significant Variable ◽  
Conditional Quantiles ◽  
Conditional Median ◽  
High Quantiles ◽  
Cardiovascular Morbidity And Mortality ◽  
Heavy Burden

Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.

A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS

2016 ◽  
Vol 19 (03) ◽  
pp. 1650016
Author(s):  
YUZHI CAI
Keyword(s):  
Quantile Regression ◽  
Potential Problem ◽  
Financial Returns ◽  
Financial Return ◽  
Regression Methods ◽  
Conditional Quantiles ◽  
Extreme Quantiles ◽  
Estimation Problems ◽  
The Impact ◽  
Quantile Regression Method

Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.

scholarly journals Bayesian quantile regression analysis for continuous data with a discrete component at zero

2017 ◽  
Vol 18 (1) ◽  
pp. 73-93 ◽  
Author(s):  
Bruno Santos ◽  
Heleno Bolfarine
Keyword(s):  
Regression Analysis ◽  
Quantile Regression ◽  
Durable Goods ◽  
Continuous Distribution ◽  
Real Data ◽  
Discrete Component ◽  
Bayesian Quantile Regression ◽  
Conditional Quantiles ◽  
Quantile Regression Analysis ◽  
Quantile Regression Method

In this work, we propose a Bayesian quantile regression method to response variables with mixed discrete-continuous distribution with a point mass at zero, where these observations are believed to be left censored or true zeros. We combine the information provided by the quantile regression analysis to present a more complete description of the probability of being censored given that the observed value is equal to zero, while also studying the conditional quantiles of the continuous part. We build up a Markov Chain Monte Carlo method from related models in the literature to obtain samples from the posterior distribution. We demonstrate the suitability of the model to analyse this censoring probability with a simulated example and two applications with real data. The first is a well-known dataset from the econometrics literature about women labour in Britain, and the second considers the statistical analysis of expenditures with durable goods, considering information from Brazil.

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