Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach

By Surya T. Tokdar, Joseph B. Kadane. 2012

96 citations recorded by the source corpus.

We introduce a semi-parametric Bayesian framework for a simultaneous analysis of linear quantile regression models. A simultaneous analysis is essential to attain the true potential of the quantile regression framework, but is computa- tionally challenging due to the associated monotonicity constraint on the quantile curves. For a univariate covariate, we present a simpler equivalent characterization of the monotonicity constraint through an interpolation of two monotone curves. The resulting formulation leads to a tractable likelihood function and is embedded within a Bayesian framework where the two monotone curves are modeled via lo- gistic transformations of a smooth Gaussian process. A multivariate extension is suggested by combining the full support univariate model with a linear projection of the predictors. The resulting single-index model remains easy to flt and provides substantial and measurable improvement over the flrst order linear heteroscedastic model. Two illustrative applications of the proposed method are provided.

Subfields: Analytical Chemistry, Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d46e7a891867e5f8c90fd99f90a1b6188de56341

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. S. Bentzien
2. Mauro Bernardi
3. Petra Friederichs
4. Ghislaine Gayraud
5. Lea Petrella

In Artificial Intelligence

1. S. Bentzien
2. Mauro Bernardi
3. Petra Friederichs
4. Ghislaine Gayraud
5. Lea Petrella

In Statistics and Probability

1. S. Bentzien
2. Mauro Bernardi
3. Petra Friederichs
4. Ghislaine Gayraud
5. Lea Petrella
6. Alex J. Cannon

Citations in the corpus

• Generating and Calibrating Probabilistic Quantitative Precipitation Forecasts from the High-Resolution NWP Model COSMO-DE (2012, methodology): “Extended logistic regression (Wilks 2009) and simultaneous quantile regression (Tokdar and Kadane 2012) aim to reduce the number of parameters and to avoid crossing quantile and probability curves, but come along with some restrictions on the regression coefficients.”
• Bayesian Tail Risk Interdependence Using Quantile Regression (2015, background): “See also Chao et al. (2012) and Taylor (2008) for recent developments.”