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.

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.Résumé. Dans cette note, nous présentons un estimateur à noyau du quantile conditionnel d'un processus spatial non-stationnaire, pour un but de prédiction du processus considéré en un site non-observé. L'originalité vient du fait que l'estimateur permet de prendre en compte une éventuelle dépendance locale des données. Une étude asymptotique basée sur les convergences presque complète et en moyenne d'ordre q de l'estimateur est proposée.

The purpose of this work is to nonparametrically estimate the conditional quantile for a locally stationary multivariate spatial process. The new kernel quantile estimate derived from the one of conditional distribution function (CDF). The originality in the paper is based on the ability to take into account some local spatial dependency in estimate CDF form. Consistency and asymptotic normality of the estimates are obtained under α$$ \alpha $$‐mixing condition. Numerical study and application to real data are given in order to illustrate the performance of our methodology.

This paper develops the theory of the Gegenbauer AutoRegressive Fractionally Integrated Seasonal Moving Average (GARFISMA) process with alpha-stable innovations.We establish its conditions for causality and invertibility. This is a finite parameter process which exhibits high variability, long memory, cyclical, and seasonality in financial, hydrological data studies, and more. We perform some simulations to illustrate the behavior of our process.