Open Access Open Access  Restricted Access Subscription or Fee Access

Rate of uniform consistency for nonparametric of the conditional quantile estimate with functional variables in the single functional index model

Nadia Kadiri, Souad Mekkaoui, Abbes Rabhi


The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced.
Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis. For that, the whole observed time series has to be split into a set of functional data, and the functional conditional quantile approach can be employed both in foreseeing and building confidence prediction bands.


Conditional quantile, conditional cumulative distribution, derivatives of conditional cumulative distribution, functional random variable, kernel estimator, nonparametric estimation, strong mixing processes.

Full Text:


Regarding indexing issue:

We have provided the online access of all issues & papers to the all  indexing agencies (as given on our journal home web site). It’s depend on indexing agencies when, how and what manner they can index or not. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.