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.

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.

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.

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.   

scholarly journals Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
I-Chen Chen ◽  
Philip M. Westgate
Keyword(s):  
Parameter Estimation ◽  
Longitudinal Data ◽  
Quantile Regression ◽  
Mean Squared Error ◽  
Time Dependent ◽  
Regression Methods ◽  
Squared Error ◽  
Highly Correlated ◽  
Time Dependent Covariates ◽  
Independence Structure

AbstractWhen observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

Corporate social responsibility and debt financing of listed firms: a quantile regression approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kofi Mintah Oware ◽  
T. Mallikarjunappa
Keyword(s):  
Quantile Regression ◽  
Debt Financing ◽  
Short Term ◽  
Content Type ◽  
Leverage Ratio ◽  
Listed Firms ◽  
Conditional Mean ◽  
Natural Logarithm ◽  
Corporate Social

Purpose The purpose of the study is to examine the effect of corporate social responsibility (CSR) on debt financing (natural logarithm of debt and leverage ratios) of listed firms. Design/methodology/approach Using content analysis for data extraction, the study examines listed firms on the Bombay Stock Exchange (BSE) from 2010 to 2019 financial year. It uses a quantile regression and panel fixed effect regression as the model's application. Findings The study shows that CSR expenditure has a positive and strong correlation with debt financing (i.e. natural logarithm of long-term and short-term debts). The first findings show that CSR expenditure has a negative and statistically significant association with total leverage ratio, using conditional mean and median percentile. However, there is a positive and statistically significant association between CSR expenditure and long-term leverage ratio at the 25th and 50th percentile. The second findings show that CSR expenditure has a positive and statistically significant association with long-term debt but an insignificant association with short-term debt and total debt under a conditional mean average. The application of quantile regression addresses the values that fall outside the confidence interval and therefore document a positive and statistically significant association between CSR expenditure and debt financing (short-term debt, long-term debt and total debt) at the 25th, 50th and 75th percentile. Originality/value The introduction of quantile regression gives a novelty in CSR and debt financing study, which to the best of the authors’ knowledge, has not received any attention. Similarly, firms have better information on how to position their CSR expenditure to attract providers of debt financing.

Several weighted sum formulas of multiple zeta values

2017 ◽  
Vol 13 (09) ◽  
pp. 2253-2264 ◽  
Author(s):  
Minking Eie ◽  
Wen-Chin Liaw ◽  
Yao Lin Ong
Keyword(s):  
Real Number ◽  
Weighted Sum ◽  
Multiple Zeta Values ◽  
Explicit Evaluation ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Number Formula ◽  
Positive Integers ◽  
Special Case

For a real number [Formula: see text] and positive integers [Formula: see text] and [Formula: see text] with [Formula: see text], we evaluate the sum of multiple zeta values [Formula: see text] explicitly in terms of [Formula: see text] and [Formula: see text]. The special case [Formula: see text] gives an evaluation of [Formula: see text]. An explicit evaluation of the multiple zeta-star value [Formula: see text] is also obtained, as well as some applications to evaluation of multiple zeta values with even arguments.

Sign in / Sign up

Export Citation Format

Share Document