Reducing the sample size when estimating conditional quantiles

P. 769–781.

Shatskikh S. Y., Мелкумова Л. Э.

In this paper we propose an idea to use a certain property of multivariate probability distributions, that we call the conditional quan- tile reproducibility, to decrease the amount of observations required to construct a statistical estimate of a n-dimensional conditional quantile of the distribution. For the class of probability distributions, satisfying to this property, we present several results, proving that in many cases the reproducibility property allows us to restore the n-dimensional con- ditional quantile by solving a certain type of Pfaffian differential equa- tion. The equation is constructed from functions, derived only from the 2-dimensional marginal distributions of the initial distribution.

Keywords: conditional quantile reproducibility, quantile differential equation, Pfaffian equation, multivariate conditional quantiles, conditional quantile estimation

In book

CEUR Workshop Proceedings

Vol. 1638: ITNT 2016, Information Technology and Nanotechnology. , CEUR-WS.org, 2016.