Geodesic
Pfaffian differential equations for conditional quantiles of multidimentional probability distributions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 32-47

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Our work is devoted to the study of Pfaff differential equations, which are constructed on the basis of two-dimensional conditional quantiles. However for some multidimentional probability distributions (distributions having the property of conditional quantiles reproducibility) solutions of these equations are the conditional quantiles of significantly higher dimensions. This fact allows us (for distributions of the pointed class) to reduce significantly the number of observations needed to build statistical estimations for multidimentional conditional medians and conditional quantiles.
Keywords: multidimentional probability distributions, reproducibility of conditional quantiles, completely integrable Pfaff`s differential equations. 
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     author = {I. S. Orlova and S. Ya. Shatskikh},
     title = {Pfaffian differential equations for conditional quantiles of multidimentional probability distributions},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {32--47},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2010_2_a3/}
}
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I. S. Orlova; S. Ya. Shatskikh. Pfaffian differential equations for conditional quantiles of multidimentional probability distributions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2010), pp. 32-47. http://geodesic.mathdoc.fr/item/VSGU_2010_2_a3/