Asymptotic Theory for Regression Quantile Estimators in the Heteroscedastic Regression Model

1994 ◽  
pp. 151-161 ◽  
Author(s):  
Marc Aerts ◽  
Paul Janssen ◽  
NoëL Veraverbeke
Keyword(s):  
Regression Model ◽  
Asymptotic Theory ◽  
Heteroscedastic Regression ◽  
Regression Quantile ◽  
Quantile Estimators

scholarly journals A Shortcut to LAD Estimator Asymptotics

1991 ◽  
Vol 7 (4) ◽  
pp. 450-463 ◽  
Author(s):  
P.C.B. Phillips
Keyword(s):  
Asymptotic Expansion ◽  
Regression Model ◽  
Taylor Series ◽  
Asymptotic Theory ◽  
Random Variables ◽  
Generalized Functions ◽  
Infinite Variance ◽  
Series Expansions ◽  
Linear Functionals ◽  
Taylor Series Expansions

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

ROBUST TEST BASED ON NONLINEAR REGRESSION QUANTILE ESTIMATORS

2005 ◽  
Vol 20 (1) ◽  
pp. 145-159 ◽  
Author(s):  
SEUNG-HOE CHOI ◽  
KYUNG-JOONG KIM ◽  
MYUNG-SOOK LEE
Keyword(s):  
Nonlinear Regression ◽  
Robust Test ◽  
Regression Quantile ◽  
Quantile Estimators

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

Estimation in a Heteroscedastic Regression Model

1968 ◽  
Vol 63 (322) ◽  
pp. 552 ◽  
Author(s):  
Herbert C. Rutemiller ◽  
David A. Bowers
Keyword(s):  
Regression Model ◽  
Heteroscedastic Regression

scholarly journals Generalized Odd Power Cauchy Family and Its Associated Heteroscedastic Regression Model

2021 ◽  
Vol 9 (3) ◽  
pp. 516-528
Author(s):  
Emrah Altun EA ◽  
Morad Alizadeh ◽  
Thiago Ramires ◽  
Edwin Ortega
Keyword(s):  
Monte Carlo ◽  
Regression Model ◽  
Data Structures ◽  
Generating Functions ◽  
Shape Parameter ◽  
Model Parameters ◽  
Data Sets ◽  
Complex Data ◽  
Linear Representations ◽  
Heteroscedastic Regression

This study introduces a generalization of the odd power Cauchy family by adding one more shape parameter togain more flexibility modeling the complex data structures. The linear representations for the density, moments, quantile,and generating functions are derived. The model parameters are estimated employing the maximum likelihood estimationmethod. The Monte Carlo simulations are performed under different parameter settings and sample sizes for the proposedmodels. In addition, we introduce a new heteroscedastic regression model based on the special member of the proposedfamily. Three data sets are analyzed with competitive and proposed models.

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