Abstract
The article deals with certain quantile regression methods for vector responses. In particular, it describes weighted and locally polynomial extensions to the projectional quantile regression, discusses their properties, addresses their computational side, compares their outcome with recent analogous generalizations of the competing multiple-output directional quantile regression, demonstrates a link between the two competing methodologies, complements the results already available in the literature, illustrates the concepts with a few simulated and insightful examples illustrating some of their features, and shows their application to a real financial data set, namely to Forex 1M exchange rates. The real-data example strongly indicates that the presented methods might have a huge impact on the analysis of multivariate time series consisting of two to four dimensional observations.
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Acknowledgements
This research was supported by the Czech Science Foundation Project GA14-07234S. Miroslav Šiman would like to thank Davy Paindaveine, Marc Hallin, Claude Adan, Nancy de Munck, and Romy Genin for their insight and encouragement, and also for all the good they did for him (and for all the good he could learn from them) during his stay at Université Libre de Bruxelles.
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Boček, P., Šiman, M. On weighted and locally polynomial directional quantile regression. Comput Stat 32, 929–946 (2017). https://doi.org/10.1007/s00180-016-0708-9
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DOI: https://doi.org/10.1007/s00180-016-0708-9