On monotonicity of regression quantile functions

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Nonparametric estimation and inference on conditional quantile processes (2015, methodology): “We use similar arguments as in Neocleous and Portnoy (2008). Consider”
Stepwise multiple quantile regression estimation using non-crossing constraints (2009, background): “However, as noted by Neocleousa and Portnoy (2007), even for linear regression quantiles, corresponding models can be much more general.”
Expectile and quantile regression—David and Goliath? (2015, background): “They also gave a good overview about earlier proposals including Koenker (1984), He (1997), Wu and Liu (2009) or Neocleous and Portnoy (2008).”