On Nonparametric Conditional Quantile Estimation for Non-stationary Random

Abstract

A kernel conditional quantile estimate of a real-valued non-stationary spatial process is proposed for a prediction goal at a non-observed location of the underlying process. The originality is based on the ability to take into account some local spatial dependency. Large sample properties based on almost complete and \(L^q\)-consistencies of the estimator are established. A numerical study is given in order to illustrate the performance of our methodology.

Asymptotic properties of nonparametric quantile estimation with spatial dependency

“…Li, Qin and Li (2020) used the empirical likelihood method to construct a confidence region for nonparametric regression model with autoregressive errors. Kanga, Hili and Dabo‐Niang (2021) established almost complete consistency and the weak consistency for quantile estimate. In the functional analysis context, Almanjahie, Chikr Elmezouar, Bachir and Kaid (2020) proposed a local linear quantile estimate for functional spatial data.…”