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About 5,533 papers for “Quantile function”

FUNCTION-ON-FUNCTION LINEAR QUANTILE REGRESSION

Ufuk Beyaztaş, Han Lin Shang · Mathematical Modelling and Analysis · 2022

In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finitedimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models.

Cited by 6Open access

Reconditioning your quantile function

Keith Pedersen · arXiv (Cornell University) · 2017

Monte Carlo simulation is an important tool for modeling highly nonlinear systems (like particle colliders and cellular membranes), and random, floating-point numbers are their fuel. These random samples are frequently generated via the inversion method, which harnesses the mapping of the quantile function Q(u) (e.g. to generate proposal variates for rejection sampling). Yet the increasingly large sample size of these simulations makes them vulnerable to a flaw in the inversion method; Q(u) is ill-conditioned in a distribution's tails, stripping precision from its sample. This flaw stems from limitations in machine arithmetic which are often overlooked during implementation (e.g. in popular C++ and Python libraries). This paper introduces a robust inversion method, which reconditions Q(u) by carefully drawing and using uniform variates. pqRand, a free C++ and Python package, implements this novel method for a number of popular distributions (exponential, normal, gamma, and more).

Cited by 0Open access

Multivariate Quantile Function Forecaster

Kelvin K.W. Kan, François-Xavier Aubet, Tim Januschowski et al. · arXiv (Cornell University) · 2022

We propose Multivariate Quantile Function Forecaster (MQF$^2$), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF$^2$ combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF$^2$: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure.

Cited by 8Open access

Nonparametric Estimation of Quantile and Quantile Density Function

Xiye Yang, Hutson AD, D Wang · Journal of Biometrics & Biostatistics · 2017

In this article, we derive a new and unique method of estimating quantile and quantile density function, which is based on moments of fractional order statistics. A comparison of the proposed estimators is made with existing popular nonparametric quantile and quantile density estimators, in terms of mean squared error (MSE) for censored and uncensored data. Recommendations for the choice of quantile and/or quantile density estimators are given.

Cited by 5

On function-on-function linear quantile regression

Muge Mutis, Ufuk Beyaztaş, Filiz Karaman et al. · Journal of Applied Statistics · 2024

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated using a basis expansion approach. Consequently, we approximate the infinite-dimensional function-on-function linear quantile regression model using a multivariate quantile regression model constructed from these partial quantile regression components. To evaluate the efficacy of our proposed techniques, we conduct a series of Monte Carlo experiments and analyze an empirical dataset, demonstrating superior performance compared to existing methods in finite-sample scenarios. Our techniques have been implemented in the ffpqr package in .

Cited by 7Open access

On function-on-function linear quantile regression

Mutis, Muge, Beyaztas, Ufuk, Karaman, Filiz et al. · ArXiv.org · 2025

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated using a basis expansion approach. Consequently, we approximate the infinite-dimensional function-on-function linear quantile regression model using a multivariate quantile regression model constructed from these partial quantile regression components. To evaluate the efficacy of our proposed techniques, we conduct a series of Monte Carlo experiments and analyze an empirical dataset, demonstrating superior performance compared to existing methods in finite-sample scenarios. Our techniques have been implemented in the ffpqr package in R.

Cited by 0Open access

Penalized function-on-function linear quantile regression

Ufuk Beyaztaş, Han Lin Shang, Semanur Sarıçam · ArXiv.org · 2025

We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic $B$-splines expansion is used to represent the regression parameter functions, where a derivative-free optimization algorithm is used to obtain the estimates. Quadratic roughness penalties are applied to the coefficients to control the smoothness of the estimates. The optimal degree of smoothness depends on the quantile of interest. An automatic grid-search algorithm based on the Bayesian information criterion is used to estimate the optimum values of the smoothing parameters. Via a series of Monte-Carlo experiments and an empirical data analysis using Mary River flow data, we evaluate the estimation and predictive performance of the proposed method, and the results are compared favorably with several existing methods.

Cited by 0Open access

Control function quantile hedonic pricing

Omid M. Ardakani, Jason Beck, Suyong Song · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2025

Abstract This paper addresses two persistent challenges in hedonic price analysis: endogeneity of marketing time and heterogeneity in attribute valuations, using a novel control function quantile regression framework. By exploiting characteristic-induced heteroskedasticity for identification, we address simultaneity bias without exclusion restrictions and recover heterogeneous effects across the price distribution. We find a U-shaped relationship between marketing duration and sale prices in Multiple Listing Service data. High-end properties at the 95th price percentile show 2.5% price premiums per 100 days of marketing time, three times greater than the effect at the median price level. Control function adjustments show that conventional instrumental variable approaches underestimate premiums, with bias greater in upper quantiles. The estimator accommodates both conditional and unconditional quantile specifications and remains robust to parametric variance assumptions using series estimation. Our results highlight the role of distributional analysis in housing markets, where seller patience and buyer bargaining power interact asymmetrically across price segments.

Cited by 0

quantsig: Sigmoidal Quantile Function Estimator

Alan D. Hutson · 2024

A sigmoidal quantile function estimator based on a newly defined generalized expectile function. The generalized sigmoidal quantile function can estimate quantiles beyond the range of the data, which is important for certain applications given smaller sample sizes. The package is based on the method introduced in Hutson (2024) &lt;<a href="https://doi.org/10.1080%2F03610918.2022.2032161" target="_top">doi:10.1080/03610918.2022.2032161</a>&gt;.

Cited by 0Open access

The generalized sigmoidal quantile function

Alan D. Hutson · Communications in Statistics - Simulation and Computation · 2022

In this note we introduce a new smooth nonparametric quantile function estimator based on a newly defined generalized expectile function and termed the sigmoidal quantile function estimator. We also introduce a hybrid quantile function estimator, which combines the optimal properties of the classic kernel quantile function estimator with our new generalized sigmoidal quantile function estimator. The generalized sigmoidal quantile function can estimate quantiles beyond the range of the data, which is important for certain applications given smaller sample sizes. This property of extrapolation is illustrated in order to improve standard bootstrap smoothing resampling methods.

Cited by 2Open access