A Quantile Function Approach to the K-Sample Quantile Regression Problem.

1980 ◽  
Author(s):  
James Michael White
Keyword(s):  
Quantile Regression ◽  
Quantile Function ◽  
Function Approach ◽  
Sample Quantile ◽  
Regression Problem

scholarly journals Probabilistic Prediction of Separation Buffer to Compensate for the Closing Effect on Final Approach

Aerospace ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 29
Author(s):  
Stanley Förster ◽  
Michael Schultz ◽  
Hartmut Fricke
Keyword(s):  
Quantile Regression ◽  
Prediction Interval ◽  
Quantile Function ◽  
Air Traffic ◽  
Point Estimate ◽  
Probabilistic Prediction ◽  
Traffic System ◽  
Final Approach ◽  
Model Training ◽  
Prediction Approach

The air traffic is mainly divided into en-route flight segments, arrival and departure segments inside the terminal maneuvering area, and ground operations at the airport. To support utilizing available capacity more efficiently, in our contribution we focus on the prediction of arrival procedures, in particular, the time-to-fly from the turn onto the final approach course to the threshold. The predictions are then used to determine advice for the controller regarding time-to-lose or time-to-gain for optimizing the separation within a sequence of aircraft. Most prediction methods developed so far provide only a point estimate for the time-to-fly. Complementary, we see the need to further account for the uncertain nature of aircraft movement based on a probabilistic prediction approach. This becomes very important in cases where the air traffic system is operated at its limits to prevent safety-critical incidents, e.g., separation infringements due to very tight separation. Our approach is based on the Quantile Regression Forest technique that can provide a measure of uncertainty of the prediction not only in form of a prediction interval but also by generating a probability distribution over the dependent variable. While the data preparation, model training, and tuning steps are identical to classic Random Forest methods, in the prediction phase, Quantile Regression Forests provide a quantile function to express the uncertainty of the prediction. After developing the model, we further investigate the interpretation of the results and provide a way for deriving advice to the controller from it. With this contribution, there is now a tool available that allows a more sophisticated prediction of time-to-fly, depending on the specific needs of the use case and which helps to separate arriving aircraft more efficiently.

Fast learning rates for sparse quantile regression problem

2013 ◽  
Vol 108 ◽  
pp. 13-22 ◽  
Author(s):  
Shao-Gao Lv ◽  
Tie-Feng Ma ◽  
Liu Liu ◽  
Yun-Long Feng
Keyword(s):  
Quantile Regression ◽  
Regression Problem ◽  
Fast Learning ◽  
Learning Rates

scholarly journals Statistically Efficient Construction of α-Risk-Minimizing Portfolio

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hiroyuki Taniai ◽  
Takayuki Shiohama
Keyword(s):  
Monte Carlo ◽  
Quantile Regression ◽  
Asymptotic Normality ◽  
Asymptotic Properties ◽  
Regression Method ◽  
General Reference ◽  
Regression Problem ◽  
Efficient Construction ◽  
Consistency And Asymptotic Normality ◽  
Quantile Regression Method

We propose a semiparametrically efficient estimator for α-risk-minimizing portfolio weights. Based on the work of Bassett et al. (2004), an α-risk-minimizing portfolio optimization is formulated as a linear quantile regression problem. The quantile regression method uses a pseudolikelihood based on an asymmetric Laplace reference density, and asymptotic properties such as consistency and asymptotic normality are obtained. We apply the results of Hallin et al. (2008) to the problem of constructing α-risk-minimizing portfolios using residual signs and ranks and a general reference density. Monte Carlo simulations assess the performance of the proposed method. Empirical applications are also investigated.

qmodel: A command for fitting parametric quantile models

2019 ◽  
Vol 19 (2) ◽  
pp. 261-293 ◽  
Author(s):  
Matteo Bottai ◽  
Nicola Orsini
Keyword(s):  
Quantile Regression ◽  
Simulated Data ◽  
Quantile Function ◽  
Parametric Models ◽  
Outcome Variable ◽  
Simple Type ◽  
Conditional Quantile ◽  
Quantile Functions ◽  
Conditional Quantile Function ◽  
Insight Into

In this article, we introduce the qmodel command, which fits parametric models for the conditional quantile function of an outcome variable given covariates. Ordinary quantile regression, implemented in the qreg command, is a popular, simple type of parametric quantile model. It is widely used but known to yield erratic estimates that often lead to uncertain inferences. Parametric quantile models overcome these limitations and extend modeling of conditional quantile functions beyond ordinary quantile regression. These models are flexible and efficient. qmodel can estimate virtually any possible linear or nonlinear parametric model because it allows the user to specify any combination of qmodel-specific built-in functions, standard mathematical and statistical functions, and substitutable expressions. We illustrate the potential of parametric quantile models and the use of the qmodel command and its postestimation commands through realand simulated-data examples that commonly arise in epidemiological and pharmacological research. In addition, this article may give insight into the close connection that exists between quantile functions and the true mathematical laws that generate data.

Model-robust designs for nonlinear quantile regression

2020 ◽  
pp. 096228022094815
Author(s):  
Selvakkadunko Selvaratnam ◽  
Linglong Kong ◽  
Douglas P Wiens
Keyword(s):  
Quantile Regression ◽  
Mean Squared Error ◽  
Quantile Function ◽  
Adaptive Method ◽  
Scale Function ◽  
Sequential Method ◽  
Sequential Approach ◽  
Design Point ◽  
Scale Functions ◽  
Robust Designs

We construct robust designs for nonlinear quantile regression, in the presence of both a possibly misspecified nonlinear quantile function and heteroscedasticity of an unknown form. The asymptotic mean-squared error of the quantile estimate is evaluated and maximized over a neighbourhood of the fitted quantile regression model. This maximum depends on the scale function and on the design. We entertain two methods to find designs that minimize the maximum loss. The first is local – we minimize for given values of the parameters and the scale function, using a sequential approach, whereby each new design point minimizes the subsequent loss, given the current design. The second is adaptive – at each stage, the maximized loss is evaluated at quantile estimates of the parameters, and a kernel estimate of scale, and then the next design point is obtained as in the sequential method. In the context of a Michaelis–Menten response model for an estrogen/hormone study, and a variety of scale functions, we demonstrate that the adaptive approach performs as well, in large study sizes, as if the parameter values and scale function were known beforehand and the sequential method applied. When the sequential method uses an incorrectly specified scale function, the adaptive method yields an, often substantial, improvement. The performance of the adaptive designs for smaller study sizes is assessed and seen to still be very favourable, especially so since the prior information required to design sequentially is rarely available.

scholarly journals A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 682
Author(s):  
Josmar Mazucheli ◽  
Víctor Leiva ◽  
Bruna Alves ◽  
André F. B. Menezes
Keyword(s):  
Quantile Regression ◽  
Real Data ◽  
Quantile Function ◽  
R Package ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Continuous Variables ◽  
Estimation Model ◽  
Response Distribution ◽  
Bounded Data

Quantile regression provides a framework for modeling the relationship between a response variable and covariates using the quantile function. This work proposes a regression model for continuous variables bounded to the unit interval based on the unit Birnbaum–Saunders distribution as an alternative to the existing quantile regression models. By parameterizing the unit Birnbaum–Saunders distribution in terms of its quantile function allows us to model the effect of covariates across the entire response distribution, rather than only at the mean. Our proposal, especially useful for modeling quantiles using covariates, in general outperforms the other competing models available in the literature. These findings are supported by Monte Carlo simulations and applications using two real data sets. An R package, including parameter estimation, model checking as well as density, cumulative distribution, quantile and random number generating functions of the unit Birnbaum–Saunders distribution was developed and can be readily used to assess the suitability of our proposal.

scholarly journals Utilizing a Quantile Function Approach to Obtain Exact Bootstrap Solutions

2003 ◽  
Vol 18 (2) ◽  
pp. 231-240 ◽  
Author(s):  
Alan D. Hutson ◽  
Michael D. Ernst
Keyword(s):  
Quantile Function ◽  
Function Approach
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