Article
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
Keywords:
quantile regression; multivariate quantile; regression quantile; directional quantile; halfspace depth; regression depth; depth contour; Octave; MATLAB
quantile regression; multivariate quantile; regression quantile; directional quantile; halfspace depth; regression depth; depth contour; Octave; MATLAB
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.
References:
[1] Barber, C. B., Huhdanpaa, H.: The quickhull algorithm for convex hulls. ACM Trans. Math. Software 22 (1996), 469-483. DOI 10.1145/235815.235821 | MR 1428265 | Zbl 0884.65145
[2] Boček, P., Šiman, M.: Directional quantile regression in R. Submitted, 2016.
[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. DOI 10.1016/j.jspi.2003.06.017 | MR 2057917 | Zbl 1040.62038
[4] Cheng, Y., Gooijer, J. G. De: On the $u$th geometric conditional quantile. J. Statist. Planning Inference 137 (2007), 1914-1930. DOI 10.1016/j.jspi.2006.02.014 | MR 2323873 | Zbl 1118.62051
[5] Došlá, Š.: Conditions for bimodality and multimodality of a mixture of two unimodal densities. Kybernetika 45 (2009), 279-292. MR 2518152 | Zbl 1165.62304
[6] Dutta, S., Ghosh, A. K., Chaudhuri, P.: Some intriguing properties of Tukey's half-space depth. Bernoulli 17 (2011), 1420-1434. DOI 10.3150/10-bej322 | MR 2854779 | Zbl 1229.62063
[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.
[8] Hallin, M., Lu, Z., Paindaveine, D., Šiman, M.: Local bilinear multiple-output quantile/depth regression. Bernoulli 21 (2015), 1435-1466. DOI 10.3150/14-bej610 | MR 3352050
[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. DOI 10.1214/09-aos723 | MR 2604670 | Zbl 1183.62088
[10] Hallin, M., Paindaveine, D., Šiman, M.: Rejoinder. The Ann. Statist. 38 (2010), 694-703. DOI 10.1214/09-aos723rej | MR 2604674
[11] Koenker, R.: Quantile Regression. Cambridge University Press, New York 2005. DOI 10.1017/cbo9780511754098 | MR 2268657 | Zbl 1236.62031
[12] Koenker, R., Bassett, G. J.: Regression quantiles. Econometrica 46 (1978), 33-50. DOI 10.2307/1913643 | MR 0474644 | Zbl 0482.62023
[13] Koltchinskii, V.: $M$-estimation, convexity and quantiles. The Ann. Statist. 25 (1997), 435-477. DOI 10.1214/aos/1031833659 | MR 1439309 | Zbl 0878.62037
[14] Kong, L., Mizera, I.: Quantile tomography: Using quantiles with multivariate data. Statist. Sinica 22 (2012), 1589-1610. DOI 10.5705/ss.2010.224 | MR 3027100
[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. DOI 10.1017/s2040174411000572
[16] Paindaveine, D., Šiman, M.: On directional multiple-output quantile regression. J. Multivariate Anal. 102 (2011), 193-212. DOI 10.1016/j.jmva.2010.08.004 | MR 2739109 | Zbl 1328.62311
[17] Paindaveine, D., Šiman, M.: Computing multiple-output regression quantile regions. Comput. Statist. Data Anal. 56 (2012), 840-853. DOI 10.1016/j.csda.2010.11.014 | MR 2888729 | Zbl 1304.65060
[18] Paindaveine, D., Šiman, M.: Computing multiple-output regression quantile regions from projection quantiles. Computat. Statist. 27 (2012), 29-49. DOI 10.1007/s00180-011-0231-y | MR 2877809 | Zbl 1304.65060
[19] Team, R Development Core: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna 2008.
[20] Rousseeuw, P. J., Ruts, I.: The depth function of a population distribution. Metrika 49 (1999), 213-244. MR 1731769 | Zbl 1093.62540
[21] MathWorks, The, Inc.: MATLAB. Natick, Massachusetts 2013.
[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. DOI | MR 1778433 | Zbl 0973.90526
[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. DOI 10.1080/03610918.2011.560730 | MR 2792475 | Zbl 1219.62109
[24] Šiman, M.: Precision index in the multivariate context. Comm. Statist. - Theory and Methods 43 (2014), 377-387. DOI 10.1080/03610926.2012.661509 | MR 3171043
Search
Partner of
