A Simple Nonparametric Approach for Estimation and Inference of Conditional Quantile Functions

2018 ◽  
Author(s):  
Zheng Fang ◽  
Qi Li ◽  
Karen Yan
Keyword(s):  
Conditional Quantile ◽  
Nonparametric Approach ◽  
Quantile Functions

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.

scholarly journals Quantile Regression

2001 ◽  
Vol 15 (4) ◽  
pp. 143-156 ◽  
Author(s):  
Roger Koenker ◽  
Kevin F Hallock
Keyword(s):  
Quantile Regression ◽  
Weighted Sum ◽  
Median Regression ◽  
Conditional Quantile ◽  
Conditional Mean ◽  
Regression Methods ◽  
Ceo Pay ◽  
Food Expenditure ◽  
Quantile Functions ◽  
Special Case

Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

scholarly journals A SIMPLE NONPARAMETRIC APPROACH FOR ESTIMATION AND INFERENCE OF CONDITIONAL QUANTILE FUNCTIONS

2021 ◽  
pp. 1-31
Author(s):  
Zheng Fang ◽  
Qi Li ◽  
Karen X. Yan
Keyword(s):  
Mean Squared Error ◽  
Bootstrap Method ◽  
Quantile Function ◽  
Confidence Bands ◽  
Convergence Theory ◽  
Conditional Quantile ◽  
Nonparametric Approach ◽  
Coverage Probabilities ◽  
Adequate Coverage ◽  
Conditional Quantile Function

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.

scholarly journals Efficiency of Bayesian Approaches in Quantile Regression with Small Sample Size

2018 ◽  
pp. 1-13
Author(s):  
Neveen Sayed-Ahmed
Keyword(s):  
Variable Selection ◽  
Quantile Regression ◽  
Full Range ◽  
Small Sample ◽  
Adaptive Lasso ◽  
Sample Sizes ◽  
Bayesian Approaches ◽  
Conditional Quantile ◽  
Quantile Functions ◽  
Small Sample Sizes

Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Just as the classical linear regression methods estimate model for the conditional mean function, quantile regression offers a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. In the Bayesian approach to variable selection prior distributions representing the subjective beliefs about the parameters are assigned to the regression coefficients. The estimation of parameters and the selection of the best subset of variables is accomplished by using adaptive lasso quantile regression. In this paper we describe, compare, and apply the two suggested Bayesian approaches. The two suggested Bayesian suggested approaches are used to select the best subset of variables and estimate the parameters of the quantile regression equation when small sample sizes are used.  Simulations show that the proposed approaches are very competitive in terms of variable selection, estimation accuracy and efficient when small sample sizes are used.   

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