Quantile Regression for Vector Responses
Directional Approaches Based on Parametric Linear Programming
Description
The software (described in [10] and [11]) may be used to obtain directional regression quantiles for all directions,
to compute related overall statistics and to analyze the resulted polyhedral
regression quantile regions (that are virtually the same for both implemented methods).
See all the references below
for further details and possible applications.
References
[01] Hallin, M., Paindaveine, D. and Šiman, M. (2010)
Multivariate quantiles and multiple-output regression quantiles:
from L1 optimization to halfspace depth.
Annals of Statistics 38, 635--669.
[02] Hallin, M., Paindaveine, D. and Šiman, M. (2010)
Rejoinder (to [01]).
Annals of Statistics 38, 694--703.
[03] Paindaveine, D. and Šiman, M. (2011)
On directional multiple-output quantile regression.
Journal of Multivariate Analysis 102, 193--212.
[04] Šiman, M. (2011)
On exact computation of some statistics based on projection
pursuit in a general regression context.
Communications in Statistics - Simulation and Computation 40, 948--956.
[05] McKeague, I. W., López-Pintado, S., Hallin, M. and Šiman, M. (2011)
Analyzing growth trajectories.
Journal of Developmental Origins of Health and Disease 2, 322--329.
[06] Paindaveine, D. and Šiman, M. (2012)
Computing multiple-output regression quantile regions.
Computational Statistics & Data Analysis 56, 840--853.
[07] Paindaveine, D. and Šiman, M. (2012)
Computing multiple-output regression quantile regions
from projection quantiles.
Computational Statistics 27, 29--49.
[08] Šiman, M. (2014)
Precision index in the multivariate context.
Communications in Statistics - Theory and Methods 43, 377--387.
[09] Hallin, M., Lu, Z., Paindaveine, D. and Šiman, M. (2015)
Local bilinear multiple-output quantile/depth regression.
Bernoulli 21, 1435--1466.
[10] Boček P., Šiman M. (2016)
Directional quantile regression in Octave (and MATLAB).
Kybernetika 52, 28--51.
[11] Boček P., Šiman M. (2017)
Directional quantile regression in R.
Kybernetika 53, 480--492.
[12] Boček P., Šiman M. (2017)
On weighted and locally polynomial directional quantile regression.
Computational Statistics 32, 929--946.
[13] Hallin M., Šiman M. (2017)
Multiple-output quantile regression.
In: Koenker Roger, Chernozhukov Victor, He Xuming and Peng Limin: Handbook of Quantile Regression, 185--208.
Matlab and Octave Source Codes (moQuantile toolbox [10])
moQuantile_0.1.zip 43kB
R Package modQR [11] in the CRAN Depository
modQR
Acknowledgements
The creation and maintenance of the software tools were supported by the research
grants GA14-07234S and GA17-07384S from the Czech Science Foundation.