Ghent University Academic Bibliography

Advanced

Essays on Bayesian quantile regression using Laplace-like distributions with applications in economics

Dries Benoit UGent (2011) PhD Series. Ghent University.
abstract
The classical theory of linear models focuses on the conditional mean function, i.e. the function that describes how the mean of y changes with the vector of covariates x. Quantile regression extends the mean regression model to conditional quantiles of the response variable, such as the median. This approach provides a more nuanced view of the relationship of the dependent variable and the covariates, since it allows the user to examine the relationship between a set of covariates and the different parts of the distribution of the response variable. An additional advantage is that quantile regression parameter estimates are not biased by heteroskedasticity. The classical approach is to optimize an objective function and conduct inference using the bootstrap, as the sampling distribution is difficult to deduct analytically. The most popular Bayesian approach starts from a different point of view. The Bayesian approach is to employ a likelihood function based on the asymmetric Laplace distribution. It is shown that this is equivalent to the maximization problem as encountered in the classical approach. The advantage is that the Bayesian approach delivers exact and full inference. Moreover, this approach is very convenient when more complex quantile regression problems are faced, e.g. when dealing with qualitative dependent variables. This dissertation contains three studies. The first study is an application of quantile regression to a ‘customer lifetime value’ problem. It is shown that the methodology proposed delivers better predictions and more detailed insights compared to competing methods. Also a segmentation scheme based on the prediction intervals generated by quantile regression is described. The second study proposes a Bayesian estimation procedure for quantile regression with a binary dependent variable. The classical approach suffers from non-trivial optimization of the objective function and inference is not straightforward. The Bayesian approach avoids these difficulties by placing additional restrictions on the errors term and using the usual Bayesian machinery. Finally, the third study contains a method for quantile regression with multinomial distributed dependent variables. A Gibbs sampler is developed and the results show that the parameters of the data generating process indeed can be retrieved using the proposed methodology.
Please use this url to cite or link to this publication:
author
promoter
UGent
organization
year
type
dissertation (monograph)
subject
in
PhD Series. Ghent University
pages
112 pages
publisher
Ghent University. Faculty of Economics and Business Administration
place of publication
Ghent, Belgium
defense location
Gent : Het Pand (zaal rector Vermeylen)
defense date
2011-06-01 17:00
language
English
UGent publication?
yes
classification
D1
additional info
dissertation consists of copyrighted materials
copyright statement
I have transferred the copyright for this publication to the publisher
id
1256407
handle
http://hdl.handle.net/1854/LU-1256407
date created
2011-06-07 14:29:48
date last changed
2011-06-08 11:12:24
@phdthesis{1256407,
  abstract     = {The classical theory of linear models focuses on the conditional mean function, i.e. the function that describes how the mean of y changes with the vector of covariates x. Quantile regression extends the mean regression model to conditional quantiles of the response variable, such as the median. This approach provides a more nuanced view of the relationship of the dependent variable and the covariates, since it allows the user to examine the relationship between a set of covariates and the different parts of the distribution of the response variable. An additional advantage is that quantile regression parameter estimates are not biased by heteroskedasticity. The classical approach is to optimize an objective function and conduct inference using the bootstrap, as the sampling distribution is difficult to deduct analytically. The most popular Bayesian approach starts from a different point of view. The Bayesian approach is to employ a likelihood function based on the asymmetric Laplace distribution. It is shown that this is equivalent to the maximization problem as encountered in the classical approach. The advantage is that the Bayesian approach delivers exact and full inference. Moreover, this approach is very convenient when more complex quantile regression problems are faced, e.g. when dealing with qualitative dependent variables. This dissertation contains three studies. The first study is an application of quantile regression to a {\textquoteleft}customer lifetime value{\textquoteright} problem. It is shown that the methodology proposed delivers better predictions and more detailed insights compared to competing methods. Also a segmentation scheme based on the prediction intervals generated by quantile regression is described. The second study proposes a Bayesian estimation procedure for quantile regression with a binary dependent variable. The classical approach suffers from non-trivial optimization of the objective function and inference is not straightforward. The Bayesian approach avoids these difficulties by placing additional restrictions on the errors term and using the usual Bayesian machinery. Finally, the third study contains a method for quantile regression with multinomial distributed dependent variables. A Gibbs sampler is developed and the results show that the parameters of the data generating process indeed can be retrieved using the proposed methodology.},
  author       = {Benoit, Dries},
  language     = {eng},
  pages        = {112},
  publisher    = {Ghent University. Faculty of Economics and Business Administration},
  school       = {Ghent University},
  series       = {PhD Series. Ghent University},
  title        = {Essays on Bayesian quantile regression using Laplace-like distributions with applications in economics},
  year         = {2011},
}

Chicago
Benoit, Dries. 2011. “Essays on Bayesian Quantile Regression Using Laplace-like Distributions with Applications in Economics.” PhD Series. Ghent University. Ghent, Belgium: Ghent University. Faculty of Economics and Business Administration.
APA
Benoit, Dries. (2011). Essays on Bayesian quantile regression using Laplace-like distributions with applications in economics. PhD Series. Ghent University. Ghent University. Faculty of Economics and Business Administration, Ghent, Belgium.
Vancouver
1.
Benoit D. Essays on Bayesian quantile regression using Laplace-like distributions with applications in economics. PhD Series. Ghent University. [Ghent, Belgium]: Ghent University. Faculty of Economics and Business Administration; 2011.
MLA
Benoit, Dries. “Essays on Bayesian Quantile Regression Using Laplace-like Distributions with Applications in Economics.” PhD Series. Ghent University 2011 : n. pag. Print.