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About 5,533 papers for “quantile function”

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

J. Michael White · 1980

Abstract : A procedure for estimating the parameters of a quantile regression function is investigated. The procedure is based on the work of Parzen (1979a) in the theory of quantile functions and is applicable to a wide range of distributional families. The procedure assumes the quantile functions of k populations to be location-scale shifts of a common quantile function. First, a goodness-of-fit procedure for determining the common distributional shape of the k populations generalizes the one-population data modeling techniques of Parzen (1979a). An estimator of the shape parameter of a distribution is also investigated. The methods of Ogawa (1951) and Eubank (1979) are then used for estimating the location and scale parameters of the k populations. A regression model for the location and scale parameters is specified, and the resulting estimators of the regression parameters are used to determine a regression function for any quantiles of the observed data. Finally it is shown that inferences about the quantile relationships can be based on the asymptotic normality of the estimated parameters. The procedures are applied to some published data sets.

Cited by 1

Estimation of conditional quantile density function

Xiaojing Xiang · Journal of nonparametric statistics · 1995

In this article, we establish the asymptotic normality and a law of the iterated logarithm for a kernel estimator of conditional quantile density function. The optimal bandwidths are obtained with respect to weak and almost sure convergences.

Cited by 7

Nonparametric estimation of hazard quantile function

P. G. Sankaran, N. Unnikrishnan Nair · Journal of nonparametric statistics · 2009

In this paper, we study the estimation of the hazard quantile function based on right censored data. Two nonparametric estimators, one based on the empirical quantile density function and the other using the kernel smoothing method, are proposed. Asymptotic properties of the kernel-based estimator are discussed. Monte Carlo simulation studies are conducted to compare the two estimators. The method is illustrated for a real data set.

Cited by 35

An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage

Lai Wei, Dongliang Wang, Alan D. Hutson · Communication in Statistics- Theory and Methods · 2014

In this article, we investigate the limitations of traditional quantile function estimators and introduce a new class of quantile function estimators, namely, the semi-parametric tail-extrapolated quantile estimators, which has excellent performance for estimating the extreme tails with finite sample sizes. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of confidence intervals. Through a comprehensive simulation study to compare the confidence interval estimations of various quantile estimators, we discuss the preferred quantile estimator in conjunction with the confidence interval estimation method to use under different circumstances. Data examples are given to illustrate the superiority of the semi-parametric tail-extrapolated quantile estimators. The new class of quantile estimators is obtained by slight modification of traditional quantile estimators, and therefore, should be specifically appealing to researchers in estimating the extreme tails.

Cited by 11

Spatial Scalar-on-Function Quantile Regression Model

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

This paper introduces a novel spatial scalar-on-function quantile regression model that extends classical scalar-on-function models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterizes the entire conditional distribution of a scalar outcome given a functional predictor. To address the endogeneity induced by the spatial lag term, we develop two robust estimation procedures based on instrumental variable strategies. $\sqrt{n}$-consistency and asymptotic normality of the proposed estimators are established under mild regularity conditions. We demonstrate through extensive Monte Carlo simulations that the proposed estimators outperform existing mean-based and robust alternatives, particularly in settings with strong spatial dependence and outlier contamination. We apply our method to high-resolution environmental data from the Lombardy region in Italy, using daily ozone trajectories to predict daily mean particulate matter with a diameter of less than 2.5 micrometers concentrations. The empirical results confirm the superiority of our approach in predictive accuracy, robustness, and interpretability across various quantile levels. Our method has been implemented in the \texttt{ssofqrm} R package.

Cited by 0Open access

Quantile regression with generalized multiquadric loss function

Wenwu Gao, Dongyi Zheng, Hanbing Zhu · ArXiv.org · 2025

Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared with classical least squares regression. However, the non-differentiability of the check loss function precludes the use of gradient-based methods to solve the optimization problem in quantile regression estimation. To this end, This paper constructs a smoothed loss function based on multiquadric (MQ) function. The proposed loss function leads to a globally convex optimization problem that can be efficiently solved via (stochastic) gradient descent methods. As an example, we apply the Barzilai-Borwein gradient descent method to obtain the estimation of quantile regression. We establish the theoretical results of the proposed estimator under some regularity conditions, and compare it with other estimation methods using Monte Carlo simulations.

Cited by 0Open access

A Software Reliability Model Using Quantile Function

Bijamma Thomas, N.N. Midhu, Sankaran Godan Paduthol · Journal of Probability and Statistics · 2014

We study a class of software reliability models using quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. Inference procedures on parameters of the model based on L-moments are studied. We apply the proposed model to a real data set.

Cited by 0Open access

Smooth Approximation of the Quantile Function Derivatives

Vitaliy Sobol, R.O. Torishnyy · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · 2022

V.R. Sobol1, R.O. Torishnyy1 1Moscow Aviation Institute, Moscow, Russian Federation E-mail: vitsobol@mail.ru, arenas-26@yandex.ru Виталий Романович Соболь, кандидат физико-математических наук, доцент, кафедра теории вероятностей и компьютерного моделирования, Московский авиационный институт (национальный исследовательский университет) (г. Москва, Российская Федерация), vitsobol@mail.ru. Роман Олегович Торишный, ассистент, кафедра теории вероятностей и компьютерного моделирования, Московский авиационный институт (национальный исследовательский университет) (г. Москва, Российская Федерация), arenas-26@yandex.ru.

Cited by 1Open access

Robust scalar-on-function partial quantile regression

Ufuk Beyaztaş, Müjgan Tez, Han Lin Shang · Journal of Applied Statistics · 2023

Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.

Cited by 4Open access