Previous |  Up |  Next

Article

Title: Directional quantile regression in Octave (and MATLAB) (English)
Author: Boček, Pavel
Author: Šiman, Miroslav
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 52
Issue: 1
Year: 2016
Pages: 28-51
Summary lang: English
.
Category: math
.
Summary: Although many words have been written about two recent directional (regression) quantile concepts, their applications, and the algorithms for computing associated (regression) quantile regions, their software implementation is still not widely available, which, of course, severely hinders the dissemination of both methods. Wanting to partly fill in the gap here, we provide all the codes needed for computing and plotting the multivariate (regression) quantile regions in Octave and MATLAB, describe their use in detail, and explain their output with a few carefully designed examples. (English)
Keyword: quantile regression
Keyword: multivariate quantile
Keyword: regression quantile
Keyword: directional quantile
Keyword: halfspace depth
Keyword: regression depth
Keyword: depth contour
Keyword: Octave
Keyword: MATLAB
MSC: 62-04
MSC: 62H05
MSC: 62J99
MSC: 65C60
idZBL: Zbl 1374.62002
idMR: MR3482609
DOI: 10.14736/kyb-2016-1-0028
.
Date available: 2016-03-21T17:48:57Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/144861
.
Reference: [1] Barber, C. B., Huhdanpaa, H.: The quickhull algorithm for convex hulls..ACM Trans. Math. Software 22 (1996), 469-483. Zbl 0884.65145, MR 1428265, 10.1145/235815.235821
Reference: [2] Boček, P., Šiman, M.: Directional quantile regression in R..Submitted, 2016.
Reference: [3] Chen, Z., Tyler, D. E.: On the behavior of Tukey's depth and median under symmetric stable distributions..J. Statist. Planning Inference 122 (2004), 111-124. Zbl 1040.62038, MR 2057917, 10.1016/j.jspi.2003.06.017
Reference: [4] Cheng, Y., Gooijer, J. G. De: On the $u$th geometric conditional quantile..J. Statist. Planning Inference 137 (2007), 1914-1930. Zbl 1118.62051, MR 2323873, 10.1016/j.jspi.2006.02.014
Reference: [5] Došlá, Š.: Conditions for bimodality and multimodality of a mixture of two unimodal densities..Kybernetika 45 (2009), 279-292. Zbl 1165.62304, MR 2518152
Reference: [6] Dutta, S., Ghosh, A. K., Chaudhuri, P.: Some intriguing properties of Tukey's half-space depth..Bernoulli 17 (2011), 1420-1434. Zbl 1229.62063, MR 2854779, 10.3150/10-bej322
Reference: [7] Eaton, J. W., Bateman, D., Hauberg, S.: GNU Octave Version 3.0.1 Manual: A High-Level Interactive Language for Numerical Computations..CreateSpace Independent Publishing Platform, 2009.
Reference: [8] Hallin, M., Lu, Z., Paindaveine, D., Šiman, M.: Local bilinear multiple-output quantile/depth regression..Bernoulli 21 (2015), 1435-1466. MR 3352050, 10.3150/14-bej610
Reference: [9] Hallin, M., Paindaveine, D., Šiman, M.: Multivariate quantiles and multiple-output regression quantiles: From $L_1$ optimization to halfspace depth..The Ann. Statist. 38 (2010), 635-669. Zbl 1183.62088, MR 2604670, 10.1214/09-aos723
Reference: [10] Hallin, M., Paindaveine, D., Šiman, M.: Rejoinder..The Ann. Statist. 38 (2010), 694-703. MR 2604674, 10.1214/09-aos723rej
Reference: [11] Koenker, R.: Quantile Regression..Cambridge University Press, New York 2005. Zbl 1236.62031, MR 2268657, 10.1017/cbo9780511754098
Reference: [12] Koenker, R., Bassett, G. J.: Regression quantiles..Econometrica 46 (1978), 33-50. Zbl 0482.62023, MR 0474644, 10.2307/1913643
Reference: [13] Koltchinskii, V.: $M$-estimation, convexity and quantiles..The Ann. Statist. 25 (1997), 435-477. Zbl 0878.62037, MR 1439309, 10.1214/aos/1031833659
Reference: [14] Kong, L., Mizera, I.: Quantile tomography: Using quantiles with multivariate data..Statist. Sinica 22 (2012), 1589-1610. MR 3027100, 10.5705/ss.2010.224
Reference: [15] McKeague, I. W., López-Pintado, S., Hallin, M., Šiman, M.: Analyzing growth trajectories..J. Developmental Origins of Health and Disease 2 (2011), 322-329. 10.1017/s2040174411000572
Reference: [16] Paindaveine, D., Šiman, M.: On directional multiple-output quantile regression..J. Multivariate Anal. 102 (2011), 193-212. Zbl 1328.62311, MR 2739109, 10.1016/j.jmva.2010.08.004
Reference: [17] Paindaveine, D., Šiman, M.: Computing multiple-output regression quantile regions..Comput. Statist. Data Anal. 56 (2012), 840-853. Zbl 1304.65060, MR 2888729, 10.1016/j.csda.2010.11.014
Reference: [18] Paindaveine, D., Šiman, M.: Computing multiple-output regression quantile regions from projection quantiles..Computat. Statist. 27 (2012), 29-49. Zbl 1304.65060, MR 2877809, 10.1007/s00180-011-0231-y
Reference: [19] Team, R Development Core: R: A Language and Environment for Statistical Computing..R Foundation for Statistical Computing, Vienna 2008.
Reference: [20] Rousseeuw, P. J., Ruts, I.: The depth function of a population distribution..Metrika 49 (1999), 213-244. Zbl 1093.62540, MR 1731769
Reference: [21] MathWorks, The, Inc.: MATLAB..Natick, Massachusetts 2013.
Reference: [22] Sturm, J. F.: Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over Symmetric Cones.Optimization Methods and Software 11-12 (1999), 625-653. Zbl 0973.90526, MR 1778433,
Reference: [23] Šiman, M.: On exact computation of some statistics based on projection pursuit in a general regression context..Comm. Statist. - Simul. Comput. 40 (2011), 948-956. Zbl 1219.62109, MR 2792475, 10.1080/03610918.2011.560730
Reference: [24] Šiman, M.: Precision index in the multivariate context..Comm. Statist. - Theory and Methods 43 (2014), 377-387. MR 3171043, 10.1080/03610926.2012.661509
.

Files

Files Size Format View
Kybernetika_52-2016-1_3.pdf 1.612Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo